TPTP Problem File: SCT170+2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT170+2 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 204, 500 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_500_fofmg_l204 [Bla11]
% Status : Theorem
% Rating : 0.89 v8.1.0, 0.83 v7.5.0, 0.91 v7.4.0, 0.87 v7.3.0, 0.90 v7.1.0, 0.91 v7.0.0, 0.97 v6.4.0, 0.96 v6.3.0, 0.92 v6.2.0, 0.84 v6.1.0, 0.97 v6.0.0, 0.91 v5.5.0, 0.93 v5.4.0, 0.96 v5.3.0
% Syntax : Number of formulae : 1012 ( 267 unt; 0 def)
% Number of atoms : 2625 ( 555 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1898 ( 285 ~; 69 |; 195 &)
% ( 120 <=>;1229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of predicates : 16 ( 15 usr; 0 prp; 1-2 aty)
% Number of functors : 792 ( 792 usr; 251 con; 0-3 aty)
% Number of variables : 2664 (2611 !; 53 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:14:14
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (204)
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OIIA,axiom,
is_fun292781289l_bool(arrow_885770895le_IIA) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin,axiom,
is_fun1420103068l_bool(arrow_912654623le_Lin) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OProf,axiom,
is_fun701126715l_bool(arrow_583275979e_Prof) ).
fof(gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Ounanimity,axiom,
is_fun292781289l_bool(arrow_1550141362nimity) ).
fof(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000,axiom,
! [B_1_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun866579754t_bool(in_rel1361124802le_alt(B_1_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_1_1)
=> is_fun701126715l_bool(pi_Arr1801471756t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_1_1)
=> is_fun292781289l_bool(pi_fun1555365306t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun1420103068l_bool(pi_Pro1873779901t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
is_Arr723427730le_alt(undefi1471133025le_alt(arrow_1486210539le_alt)) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
is_Arr859726945e_indi(undefi1052853330e_indi(arrow_132732488e_indi)) ).
fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
is_fun1264457267t_bool(undefi426827556t_bool(fun(arrow_132732488e_indi,fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool)))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
is_fun48324065t_bool(undefi396693458t_bool(fun(fun(arrow_132732488e_indi,fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool)),fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool)))) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
is_fun20916972t_bool(undefi541132219t_bool(fun(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt),bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
is_Pro1004667236le_alt(undefi1522782549le_alt(product_prod(arrow_1486210539le_alt,arrow_1486210539le_alt))) ).
fof(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] : is_Arr723427730le_alt(hd_Arr1814706386le_alt(B_1_1)) ).
fof(gsy_c_List_Ohd_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
! [B_1_1] : is_Arr859726945e_indi(hd_Arr1280875809e_indi(B_1_1)) ).
fof(gsy_c_List_Ohd_000tc__HOL__Obool,axiom,
! [B_1_1] : is_bool(hd_bool(B_1_1)) ).
fof(gsy_c_List_Ohd_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_,axiom,
! [B_1_1] : is_fun1264457267t_bool(hd_fun780865267t_bool(B_1_1)) ).
fof(gsy_c_List_Ohd_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmt,axiom,
! [B_1_1] : is_fun48324065t_bool(hd_fun1289819809t_bool(B_1_1)) ).
fof(gsy_c_List_Ohd_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
! [B_1_1] : is_fun20916972t_bool(hd_fun1937506860t_bool(B_1_1)) ).
fof(gsy_c_List_Ohd_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_,axiom,
! [B_1_1] : is_Pro1004667236le_alt(hd_Pro804272676le_alt(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] : is_Arr723427730le_alt(last_A1066338328le_alt(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
! [B_1_1] : is_Arr859726945e_indi(last_A560832347e_indi(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__HOL__Obool,axiom,
! [B_1_1] : is_bool(last_bool(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oind,axiom,
! [B_1_1] : is_fun1264457267t_bool(last_f1921219373t_bool(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunq,axiom,
! [B_1_1] : is_fun48324065t_bool(last_f584510683t_bool(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsun,axiom,
! [B_1_1] : is_fun20916972t_bool(last_f1172522866t_bool(B_1_1)) ).
fof(gsy_c_List_Olast_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oal,axiom,
! [B_1_1] : is_Pro1004667236le_alt(last_P15572062le_alt(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] : is_fun1651000642t_bool(set_Ar426477344le_alt(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
! [B_1_1] : is_fun2015243113i_bool(set_Ar1035526739e_indi(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__HOL__Obool,axiom,
! [B_1_1] : is_fun_bool_bool(set_bool(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
! [B_1_1] : is_fun701126715l_bool(set_fu222164517t_bool(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqm,axiom,
! [B_1_1] : is_fun292781289l_bool(set_fu1433968595t_bool(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunq,axiom,
! [B_1_1] : is_fun1420103068l_bool(set_fu444796538t_bool(B_1_1)) ).
fof(gsy_c_List_Oset_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] : is_fun20916972t_bool(set_Pr2031705942le_alt(B_1_1)) ).
fof(gsy_c_Order__Relation_Ostrict__linear__order__on_000tc__Arrow____Order____Mirabe,axiom,
! [B_1_1] :
( is_fun1651000642t_bool(B_1_1)
=> is_fun1420103068l_bool(order_1844940151le_alt(B_1_1)) ) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,axiom,
is_bool(top_top_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____,axiom,
is_fun1651000642t_bool(top_to186242507t_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____001,axiom,
is_fun2015243113i_bool(top_to207207712i_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
is_fun_bool_bool(top_to1647826457l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira,axiom,
is_fun701126715l_bool(top_to935749874l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,axiom,
is_fun292781289l_bool(top_to1849101472l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,axiom,
is_fun1420103068l_bool(top_to846262053l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,axiom,
is_fun20916972t_bool(top_to1773227171t_bool) ).
fof(gsy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oal,axiom,
! [B_1_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun866579754t_bool(produc616221118t_bool(B_1_1)) ) ).
fof(gsy_c_Product__Type_Oprod_Oprod__case_000tc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1] :
( is_fun866579754t_bool(B_1_1)
=> is_fun20916972t_bool(produc278404511t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
! [B_1_1] :
( is_fun1651000642t_bool(B_1_1)
=> is_fun1651000642t_bool(collec591097828le_alt(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi,axiom,
! [B_1_1] :
( is_fun2015243113i_bool(B_1_1)
=> is_fun2015243113i_bool(collec279390863e_indi(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi,axiom,
! [B_1_1] :
( is_fun701126715l_bool(B_1_1)
=> is_fun701126715l_bool(collec1567922785t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu,axiom,
! [B_1_1] :
( is_fun292781289l_bool(B_1_1)
=> is_fun292781289l_bool(collec1517527055t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1] :
( is_fun1420103068l_bool(B_1_1)
=> is_fun1420103068l_bool(collec612883262t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
! [B_1_1] :
( is_fun20916972t_bool(B_1_1)
=> is_fun20916972t_bool(collec1376511890le_alt(B_1_1)) ) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fNot,axiom,
is_fun_bool_bool(fNot) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt,axiom,
is_fun866579754t_bool(fequal21574094le_alt) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob,axiom,
! [B_1_1,B_2_1] :
( ( is_fun1651000642t_bool(B_1_1)
& is_Arr723427730le_alt(B_2_1) )
=> is_bool(hAPP_A1120018583t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc,axiom,
! [B_1_1,B_2_1] :
( ( is_fun866579754t_bool(B_1_1)
& is_Arr723427730le_alt(B_2_1) )
=> is_fun1651000642t_bool(hAPP_A1781286015t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_002,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun1264457267t_bool(hAPP_A630236912t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_003,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun701126715l_bool(hAPP_A1745457982l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_004,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun48324065t_bool(hAPP_A88621982t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_005,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun292781289l_bool(hAPP_A990651116l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_006,axiom,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun1420103068l_bool(hAPP_A433435097l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_007,hypothesis,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_fun20916972t_bool(hAPP_A1014090479t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__prod_It,hypothesis,
! [B_1_1,B_2_1] :
( is_Arr723427730le_alt(B_2_1)
=> is_Pro1004667236le_alt(hAPP_A1561816353le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O,axiom,
! [B_1_1,B_2_1] :
( ( is_fun2015243113i_bool(B_1_1)
& is_Arr859726945e_indi(B_2_1) )
=> is_bool(hAPP_A416869060i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun2015243113i_bool(hAPP_A1609075839i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_008,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun1264457267t_bool(hAPP_A739031709t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_009,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun701126715l_bool(hAPP_A701636433l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_010,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun48324065t_bool(hAPP_A1433148491t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_011,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun292781289l_bool(hAPP_A955165183l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_012,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_fun1420103068l_bool(hAPP_A659996934l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_013,hypothesis,
! [B_1_1,B_2_1] :
( ( is_fun1264457267t_bool(B_1_1)
& is_Arr859726945e_indi(B_2_1) )
=> is_fun20916972t_bool(hAPP_A340536322t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__prod_I,axiom,
! [B_1_1,B_2_1] :
( is_Arr859726945e_indi(B_2_1)
=> is_Pro1004667236le_alt(hAPP_A503573454le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( ( is_fun_bool_bool(B_1_1)
& is_bool(B_2_1) )
=> is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun1651000642t_bool(hAPP_b287951269t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls_014,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_b2116075462i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls_015,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun1264457267t_bool(hAPP_b821377302t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun_bool_bool(hAPP_b589554111l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun701126715l_bool(hAPP_b1461182872l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_016,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun48324065t_bool(hAPP_b327863236t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun292781289l_bool(hAPP_b651754310l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun1420103068l_bool(hAPP_b805997823l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun20916972t_bool(hAPP_b763490121t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_Pro1004667236le_alt(hAPP_b1482008903le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l300482276t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l479254477i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_list_bool_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__List__Olist_Itc__Arrow____Order____Mirabelle_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l784127213t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l4338847l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l1936415565l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l1684828478l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l548550096t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l1642116416t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__,axiom,
! [B_1_1,B_2_1] :
( is_fun1651000642t_bool(B_2_1)
=> is_bool(hAPP_f87553445l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc___017,axiom,
! [B_1_1,B_2_1] :
( is_fun1651000642t_bool(B_2_1)
=> is_fun1651000642t_bool(hAPP_f246757773t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc___018,axiom,
! [B_1_1,B_2_1] :
( is_fun866579754t_bool(B_2_1)
=> is_fun866579754t_bool(hAPP_f271508829t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_2_1)
=> is_bool(hAPP_f160177134l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__019,axiom,
! [B_1_1,B_2_1] :
( is_fun2015243113i_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_f1282033109i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__020,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_Arr723427730le_alt(hAPP_f1287961430le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__021,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_Arr859726945e_indi(hAPP_f350403485e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__022,axiom,
! [B_1_1,B_2_1] :
( ( is_fun701126715l_bool(B_1_1)
& is_fun1264457267t_bool(B_2_1) )
=> is_bool(hAPP_f1378099862l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__023,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_fun1651000642t_bool(hAPP_f3167870t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__024,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_f1570138413i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__025,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_fun_bool_bool(hAPP_f591334822l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__026,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_fun701126715l_bool(hAPP_f1901083135l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__027,axiom,
! [B_1_1,B_2_1] :
( is_fun1264457267t_bool(B_2_1)
=> is_fun1420103068l_bool(hAPP_f1895971544l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__028,axiom,
! [B_1_1,B_2_1] :
( ( is_fun48324065t_bool(B_1_1)
& is_fun1264457267t_bool(B_2_1) )
=> is_fun20916972t_bool(hAPP_f1817389232t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] :
( is_fun_bool_bool(B_2_1)
=> is_bool(hAPP_f387058535l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc__HOL__Obo,axiom,
! [B_1_1,B_2_1] :
( is_fun_bool_bool(B_2_1)
=> is_fun_bool_bool(hAPP_f961197973l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wylsu,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1472889102l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2140553640l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_029,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1134444118l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_030,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f640821677l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_031,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2129568089l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_032,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1898839893l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_033,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2016919811l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_034,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_2_1)
=> is_bool(hAPP_f147218624l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_035,axiom,
! [B_1_1,B_2_1] :
( is_fun701126715l_bool(B_2_1)
=> is_fun701126715l_bool(hAPP_f189058133l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_036,axiom,
! [B_1_1,B_2_1] :
( is_fun48324065t_bool(B_2_1)
=> is_Arr723427730le_alt(hAPP_f1273877800le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_037,axiom,
! [B_1_1,B_2_1] :
( is_fun48324065t_bool(B_2_1)
=> is_Arr859726945e_indi(hAPP_f2043811403e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_038,axiom,
! [B_1_1,B_2_1] :
( ( is_fun292781289l_bool(B_1_1)
& is_fun48324065t_bool(B_2_1) )
=> is_bool(hAPP_f446648900l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_039,axiom,
! [B_1_1,B_2_1] :
( is_fun48324065t_bool(B_2_1)
=> is_fun1651000642t_bool(hAPP_f1741989420t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_040,axiom,
! [B_1_1,B_2_1] :
( is_fun48324065t_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_f783549695i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_041,axiom,
! [B_1_1,B_2_1] :
( is_fun48324065t_bool(B_2_1)
=> is_fun_bool_bool(hAPP_f721327224l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_042,axiom,
! [B_1_1,B_2_1] :
( is_fun48324065t_bool(B_2_1)
=> is_fun292781289l_bool(hAPP_f656614015l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_043,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1291635206l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f620747982l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f740740988l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f937100551l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2053170815l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f412569108l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_044,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f882250837l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_045,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1138659662l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_046,axiom,
! [B_1_1,B_2_1] :
( is_fun292781289l_bool(B_2_1)
=> is_bool(hAPP_f322109294l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_047,axiom,
! [B_1_1,B_2_1] :
( is_fun292781289l_bool(B_2_1)
=> is_fun292781289l_bool(hAPP_f1028172757l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_048,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f505027144l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1094272486l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_049,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f742658307l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_050,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f750478076l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_051,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1484382710l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1518247545l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_052,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1021828400l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_053,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f560261801l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_054,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f270557859l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f784749731l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_055,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f817344902l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_056,axiom,
! [B_1_1,B_2_1] :
( is_fun1420103068l_bool(B_2_1)
=> is_bool(hAPP_f560517119l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_057,axiom,
! [B_1_1,B_2_1] :
( is_fun1420103068l_bool(B_2_1)
=> is_fun1420103068l_bool(hAPP_f574392641l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_058,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f437011961l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f404365000l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____059,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2139503478l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____060,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1488127117l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____061,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2031902329l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_Arr723427730le_alt(hAPP_f459545019le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___062,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_Arr859726945e_indi(hAPP_f1283454584e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___063,hypothesis,
! [B_1_1,B_2_1] :
( ( is_fun1420103068l_bool(B_1_1)
& is_fun20916972t_bool(B_2_1) )
=> is_bool(hAPP_f1733357041l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___064,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun1651000642t_bool(hAPP_f1068593625t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___065,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun866579754t_bool(hAPP_f1840820673t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___066,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun2015243113i_bool(hAPP_f431432850i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___067,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun1264457267t_bool(hAPP_f590186314t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___068,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun_bool_bool(hAPP_f812095627l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___069,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun1420103068l_bool(hAPP_f1344932147l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___070,axiom,
! [B_1_1,B_2_1] :
( is_fun20916972t_bool(B_2_1)
=> is_fun20916972t_bool(hAPP_f137597973t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___071,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f511649569l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__HOL__Obool_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1098788115l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f890578273l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabell_072,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1140617841l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__HOL__Obool_J_Mtc__List__Ol,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f263022001l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__List__Olist_Itc__Arrow____,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2099712241l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__Arrow____Order___,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f288803825l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__fun_Itc__Arrow___,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1456773233l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__fun_Itc__prod_Itc__Arrow__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1422872597l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__Arrow____Order__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1342253361l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f2078996785l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1508705733l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f140107297l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f891725169l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1720639399l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f704486919l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_,axiom,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_Arr723427730le_alt(hAPP_P870295781le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__073,axiom,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_Arr859726945e_indi(hAPP_P1645359566e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__074,axiom,
! [B_1_1,B_2_1] :
( ( is_fun20916972t_bool(B_1_1)
& is_Pro1004667236le_alt(B_2_1) )
=> is_bool(hAPP_P1813625415t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__075,axiom,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_fun1651000642t_bool(hAPP_P1116266031t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__076,axiom,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_fun2015243113i_bool(hAPP_P957402556i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__077,axiom,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_fun_bool_bool(hAPP_P1122857141l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__078,hypothesis,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_fun1420103068l_bool(hAPP_P1151433609l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__079,axiom,
! [B_1_1,B_2_1] :
( is_Pro1004667236le_alt(B_2_1)
=> is_fun20916972t_bool(hAPP_P1999019327t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_P1373277879t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_080,axiom,
! [B_1_1,B_2_1] : is_fun1264457267t_bool(hAPP_P1689126160t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_081,axiom,
! [B_1_1,B_2_1] : is_fun701126715l_bool(hAPP_P2049543454l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_082,axiom,
! [B_1_1,B_2_1] : is_fun48324065t_bool(hAPP_P482525630t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_083,axiom,
! [B_1_1,B_2_1] : is_fun292781289l_bool(hAPP_P1533476044l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_084,axiom,
! [B_1_1,B_2_1] : is_fun1420103068l_bool(hAPP_P467353593l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_085,axiom,
! [B_1_1,B_2_1] : is_fun20916972t_bool(hAPP_P651748559t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_086,axiom,
! [B_1_1,B_2_1] : is_Pro1004667236le_alt(hAPP_P802532161le_alt(B_1_1,B_2_1)) ).
fof(gsy_v_F,axiom,
is_fun48324065t_bool(f) ).
fof(gsy_v_P_H____,axiom,
is_fun1264457267t_bool(p_1) ).
fof(gsy_v_P____,hypothesis,
is_fun1264457267t_bool(p) ).
fof(gsy_v_a____,hypothesis,
is_Arr723427730le_alt(a) ).
fof(gsy_v_b____,hypothesis,
is_Arr723427730le_alt(b) ).
fof(gsy_v_c____,hypothesis,
is_Arr723427730le_alt(c) ).
%----Relevant facts (700)
fof(fact_0__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,p),arrow_583275979e_Prof)) ).
fof(fact_1_assms_I3_J,axiom,
hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,f)) ).
fof(fact_2_u,axiom,
hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,f)) ).
fof(fact_3__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_4_dist,axiom,
hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,a),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,b),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,c),nil_Ar1135217151le_alt))))) ).
fof(fact_5_iff,axiom,
! [I] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_A340536322t_bool(p,I)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,b),a)),hAPP_A340536322t_bool(p_1,I))) ) ).
fof(fact_6__096_B_Bthesis_O_A_I_B_Bc_O_Adistinct_A_091a_M_Ab_M_Ac_093_A_061_061_062_,axiom,
~ ! [C] :
( is_Arr723427730le_alt(C)
=> ~ hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,a),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,b),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,C),nil_Ar1135217151le_alt))))) ) ).
fof(fact_7__096_I_Fp_O_Abelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_A_058_AProf_096,axiom,
hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,arrow_207701375_below),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,arrow_207701375_below),p)),c)),b))),b)),a)),arrow_583275979e_Prof)) ).
fof(fact_8__096_I_Fp_O_Abelow_A_Ibelow_A_Ibelow_A_IP_Ap_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_J_A_,axiom,
hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,arrow_207701375_below),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,arrow_207701375_below),hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,arrow_207701375_below),p)),c)),b))),b)),a))),a)),c)),arrow_583275979e_Prof)) ).
fof(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,arrow_207701375_below),p)),c)),b)),arrow_583275979e_Prof)) ).
fof(fact_10_in__mkbot,axiom,
! [X_1,Y_2,L_1,Z_1] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Z_1) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(arrow_163947511_mkbot(L_1),Z_1)))
<=> ( Y_2 != Z_1
& ( X_1 = Z_1
=> X_1 != Y_2 )
& ( X_1 != Z_1
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)) ) ) ) ) ).
fof(fact_11_in__mktop,axiom,
! [X_1,Y_2,L_1,Z_1] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Z_1) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(arrow_312654597_mktop(L_1),Z_1)))
<=> ( X_1 != Z_1
& ( Y_2 = Z_1
=> X_1 != Y_2 )
& ( Y_2 != Z_1
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)) ) ) ) ) ).
fof(fact_12_in__below,axiom,
! [X_1,Y_2,L_1,Aa,Ba] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_207701375_below,L_1),Aa),Ba)))
<=> ( X_1 != Y_2
& ( Y_2 = Aa
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Ba)),L_1)) )
& ( Y_2 != Aa
=> ( ( X_1 = Aa
=> ( Y_2 = Ba
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Y_2)),L_1)) ) )
& ( X_1 != Aa
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)) ) ) ) ) ) ) ) ) ).
fof(fact_13_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P1373277879t_bool(Pa,X1))
<=> ! [A,B] : hBOOL(hAPP_P1373277879t_bool(Pa,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B))) ) ).
fof(fact_14_split__paired__All,axiom,
! [Pa] :
( ! [X1] :
( is_Pro1004667236le_alt(X1)
=> hBOOL(hAPP_P1813625415t_bool(Pa,X1)) )
<=> ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B))) ) ) ).
fof(fact_15_Pair__eq,axiom,
! [Aa,Ba,A_2,B_3] :
( hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba) = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A_2),B_3)
<=> ( Aa = A_2
& Ba = B_3 ) ) ).
fof(fact_16_Pair__eq,axiom,
! [Aa,Ba,A_2,B_3] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba)
& is_Arr723427730le_alt(A_2)
& is_Arr723427730le_alt(B_3) )
=> ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)
<=> ( Aa = A_2
& Ba = B_3 ) ) ) ).
fof(fact_17_Pair__inject,axiom,
! [A_7,B_5,A_6,B_4] :
( hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A_7),B_5) = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A_6),B_4)
=> ~ ( A_7 = A_6
=> B_5 != B_4 ) ) ).
fof(fact_18_Pair__inject,axiom,
! [A_7,B_5,A_6,B_4] :
( ( is_Arr723427730le_alt(A_7)
& is_Arr723427730le_alt(B_5)
& is_Arr723427730le_alt(A_6)
& is_Arr723427730le_alt(B_4) )
=> ( hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_7),B_5) = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_6),B_4)
=> ~ ( A_7 = A_6
=> B_5 != B_4 ) ) ) ).
fof(fact_19_in__rel__def,axiom,
! [R_2,X_1,Y_2] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(in_rel264468792le_alt(R_2),X_1),Y_2))
<=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_2)) ) ).
fof(fact_20_in__rel__def,axiom,
! [R_2,X_1,Y_2] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(in_rel1361124802le_alt(R_2),X_1),Y_2))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_2)) ) ).
fof(fact_21_below__Lin,axiom,
! [L_1,X_1,Y_2] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( X_1 != Y_2
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_207701375_below,L_1),X_1),Y_2)),arrow_912654623le_Lin)) ) ) ) ).
fof(fact_22__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,p_1),arrow_583275979e_Prof)) ).
fof(fact_23__C1_C,axiom,
! [P_a,Pa,A_2,B_3,Aa,Ba] :
( ( is_Arr723427730le_alt(A_2)
& is_Arr723427730le_alt(B_3)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( A_2 != B_3
=> ( Aa != B_3
=> ( Ba != A_2
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_a),arrow_583275979e_Prof))
=> ( ! [I] :
( is_Arr859726945e_indi(I)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_A340536322t_bool(P_a,I))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_f1817389232t_bool(f,P_a))) ) ) ) ) ) ) ) ) ) ).
fof(fact_24__C2_C,axiom,
! [P_a,Pa,A_2,B_3,Aa,Ba] :
( ( is_Arr723427730le_alt(A_2)
& is_Arr723427730le_alt(B_3)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( A_2 != B_3
=> ( Aa != B_3
=> ( Ba != A_2
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Pa),arrow_583275979e_Prof))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,P_a),arrow_583275979e_Prof))
=> ( ! [I] :
( is_Arr859726945e_indi(I)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_A340536322t_bool(Pa,I)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_A340536322t_bool(P_a,I))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),hAPP_f1817389232t_bool(f,Pa)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A_2),B_3)),hAPP_f1817389232t_bool(f,P_a))) ) ) ) ) ) ) ) ) ) ).
fof(fact_25_assms_I1_J,axiom,
hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,f),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin)))) ).
fof(fact_26_const__Lin__Prof,axiom,
! [L_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_f590186314t_bool(cOMBK_776703103e_indi,L_1)),arrow_583275979e_Prof)) ) ).
fof(fact_27_mkbot__Lin,axiom,
! [X_1,L_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(arrow_163947511_mkbot(L_1),X_1)),arrow_912654623le_Lin)) ) ).
fof(fact_28_mktop__Lin,axiom,
! [X_1,L_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(arrow_312654597_mktop(L_1),X_1)),arrow_912654623le_Lin)) ) ).
fof(fact_29_Lin__irrefl,axiom,
! [Aa,Ba,L_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),L_1))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Ba),Aa)),L_1)) ) ) ).
fof(fact_30_notin__Lin__iff,axiom,
! [X_1,Y_2,L_1] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> ( X_1 != Y_2
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),X_1)),L_1)) ) ) ) ) ).
fof(fact_31_third__alt,axiom,
! [A_5,B_2] :
( ( is_Arr723427730le_alt(A_5)
& is_Arr723427730le_alt(B_2) )
=> ( A_5 != B_2
=> ? [C] :
( is_Arr723427730le_alt(C)
& hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_5),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,B_2),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,C),nil_Ar1135217151le_alt))))) ) ) ) ).
fof(fact_32_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP_f446648900l_bool(arrow_885770895le_IIA,Fa))
<=> ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof))
=> ! [Xa] :
( is_fun1264457267t_bool(Xa)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Xa),arrow_583275979e_Prof))
=> ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> ( ! [I] :
( is_Arr859726945e_indi(I)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(X_2,I)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(Xa,I))) ) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,X_2)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,Xa))) ) ) ) ) ) ) ) ) ).
fof(fact_33_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP_f446648900l_bool(arrow_1550141362nimity,Fa))
<=> ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof))
=> ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> ( ! [I] :
( is_Arr859726945e_indi(I)
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(X_2,I))) )
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,X_2))) ) ) ) ) ) ).
fof(fact_34_complete__Lin,axiom,
! [Aa,Ba] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ? [X_2] :
( is_fun20916972t_bool(X_2)
& hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),arrow_912654623le_Lin))
& hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),X_2)) ) ) ) ).
fof(fact_35_in__above,axiom,
! [X_1,Y_2,L_1,Aa,Ba] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),hAPP_A1014090479t_bool(arrow_1046586475_above(L_1,Aa),Ba)))
<=> ( X_1 != Y_2
& ( X_1 = Ba
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Y_2)),L_1)) )
& ( X_1 != Ba
=> ( ( Y_2 = Ba
=> ( X_1 = Aa
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Aa)),L_1)) ) )
& ( Y_2 != Ba
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),L_1)) ) ) ) ) ) ) ) ) ).
fof(fact_36_distinct_Osimps_I1_J,axiom,
hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,nil_Ar1135217151le_alt)) ).
fof(fact_37_list_Osimps_I2_J,axiom,
! [A_4,List_4] : nil_Ar1135217151le_alt != hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_4),List_4) ).
fof(fact_38_list_Osimps_I3_J,axiom,
! [A_3,List_3] : hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_3),List_3) != nil_Ar1135217151le_alt ).
fof(fact_39_alt3,axiom,
? [A,B,C] :
( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B)
& is_Arr723427730le_alt(C)
& hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,B),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,C),nil_Ar1135217151le_alt))))) ) ).
fof(fact_40_linear__alt,axiom,
? [L_2] :
( is_fun20916972t_bool(L_2)
& hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_2),arrow_912654623le_Lin)) ) ).
fof(fact_41_list_Oinject,axiom,
! [Aa,List_2,A_2,List_1] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(A_2) )
=> ( hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Aa),List_2) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A_2),List_1)
<=> ( Aa = A_2
& List_2 = List_1 ) ) ) ).
fof(fact_42_not__Cons__self2,axiom,
! [X_23,Xs_41] : hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_23),Xs_41) != Xs_41 ).
fof(fact_43_not__Cons__self,axiom,
! [Xs_40,X_22] : Xs_40 != hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_22),Xs_40) ).
fof(fact_44_above__Lin,axiom,
! [L_1,X_1,Y_2] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( X_1 != Y_2
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,L_1),arrow_912654623le_Lin))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(arrow_1046586475_above(L_1,X_1),Y_2)),arrow_912654623le_Lin)) ) ) ) ).
fof(fact_45_dictatorI,axiom,
! [I_4,Fa] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Fa),pi_fun1555365306t_bool(arrow_583275979e_Prof,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,arrow_912654623le_Lin))))
=> ( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof))
=> ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> ( A != B
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_A340536322t_bool(X_2,I_4)))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),hAPP_f1817389232t_bool(Fa,X_2))) ) ) ) ) )
=> hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_4)) ) ) ).
fof(fact_46_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) ) ) ).
fof(fact_47_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_1)),hAPP_A1014090479t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) ) ) ).
fof(fact_48_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_1)),hAPP_A340536322t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) ) ) ).
fof(fact_49_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_1)),hAPP_P651748559t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) ) ) ).
fof(fact_50_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_1)),hAPP_b763490121t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).
fof(fact_51_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_1)),hAPP_A1745457982l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) ) ) ).
fof(fact_52_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_1)),hAPP_A701636433l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) ) ) ).
fof(fact_53_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_1)),hAPP_P2049543454l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) ) ) ).
fof(fact_54_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_1)),hAPP_b1461182872l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).
fof(fact_55_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_1)),hAPP_A433435097l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) ) ) ).
fof(fact_56_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_1)),hAPP_P467353593l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) ) ) ).
fof(fact_57_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_1)),hAPP_b805997823l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).
fof(fact_58_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_1)),hAPP_A990651116l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1)) ) ) ).
fof(fact_59_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_1)),hAPP_A955165183l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) ) ) ).
fof(fact_60_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_1)),hAPP_P1533476044l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1)) ) ) ).
fof(fact_61_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_1)),hAPP_b651754310l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1)) ) ) ).
fof(fact_62_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_1)),hAPP_P1116266031t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) ) ) ).
fof(fact_63_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_1)),hAPP_P957402556i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) ) ) ).
fof(fact_64_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_1)),hAPP_P1436281263t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1)) ) ) ).
fof(fact_65_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_1)),hAPP_f3167870t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) ) ) ).
fof(fact_66_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_1)),hAPP_f1570138413i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) ) ) ).
fof(fact_67_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_1)),hAPP_f1329247136t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) ) ) ).
fof(fact_68_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_1)),hAPP_f591334822l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) ) ) ).
fof(fact_69_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_1)),hAPP_f1068593625t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) ) ) ).
fof(fact_70_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_1)),hAPP_f431432850i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) ) ) ).
fof(fact_71_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_1)),hAPP_f1681297285t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) ) ) ).
fof(fact_72_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_1)),hAPP_f812095627l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1)) ) ) ).
fof(fact_73_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_1)),hAPP_f1741989420t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) ) ) ).
fof(fact_74_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_1)),hAPP_f783549695i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) ) ) ).
fof(fact_75_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_1)),hAPP_f1114489970t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) ) ) ).
fof(fact_76_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_1)),hAPP_f721327224l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1)) ) ) ).
fof(fact_77_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1)) ) ) ).
fof(fact_78_PiE,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1)))
=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1)) ) ) ).
fof(fact_79_list_Oexhaust,axiom,
! [Y_5] :
( Y_5 != nil_Ar1135217151le_alt
=> ~ ! [A,List] :
( is_Arr723427730le_alt(A)
=> Y_5 != hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A),List) ) ) ).
fof(fact_80_neq__Nil__conv,axiom,
! [Xs] :
( Xs != nil_Ar1135217151le_alt
<=> ? [Y_1,Ys] :
( is_Arr723427730le_alt(Y_1)
& Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys) ) ) ).
fof(fact_81_dictator__def,axiom,
! [Fa,I_4] :
( hBOOL(hAPP_A416869060i_bool(hAPP_f783549695i_bool(arrow_1549387998ctator,Fa),I_4))
<=> ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),arrow_583275979e_Prof))
=> hAPP_f1817389232t_bool(Fa,X_2) = hAPP_A340536322t_bool(X_2,I_4) ) ) ) ).
fof(fact_82_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B_1))))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_83_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,hAPP_f342341961t_bool(cOMBK_980874600le_alt,B_1))))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_84_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,hAPP_f3439105i_bool(cOMBK_520250367le_alt,B_1))))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_85_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,hAPP_f2022891751t_bool(cOMBK_1634281074le_alt,B_1))))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_86_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,hAPP_f1698272152t_bool(cOMBK_242036279t_bool,B_1))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_87_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,hAPP_f1274922098i_bool(cOMBK_948333518t_bool,B_1))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_88_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,hAPP_f303195352t_bool(cOMBK_1264040257t_bool,B_1))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_89_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,hAPP_f498119908l_bool(cOMBK_874213703t_bool,B_1))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_1)),B_1)) ) ) ).
fof(fact_90_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,hAPP_f391873743t_bool(cOMBK_339579368t_bool,B_1))))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_91_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B_1))))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_92_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,hAPP_f684471657t_bool(cOMBK_509674590t_bool,B_1))))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_93_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,hAPP_f2062029545l_bool(cOMBK_753699544t_bool,B_1))))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_1)),B_1)) ) ) ).
fof(fact_94_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,hAPP_f1300833606t_bool(cOMBK_1961253349t_bool,B_1))))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_95_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,hAPP_f1377869636i_bool(cOMBK_1847391868t_bool,B_1))))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_96_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,hAPP_f1228246954t_bool(cOMBK_906927855t_bool,B_1))))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_97_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,hAPP_f1459432374l_bool(cOMBK_1068969205t_bool,B_1))))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_1)),B_1)) ) ) ).
fof(fact_98_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,hAPP_f102394819t_bool(cOMBK_78615028le_alt,B_1))))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_99_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,hAPP_f590186314t_bool(cOMBK_776703103e_indi,B_1))))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_100_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,hAPP_f1737373975t_bool(cOMBK_1925322610le_alt,B_1))))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_101_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_102_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,hAPP_f1973254019l_bool(cOMBK_1744976613le_alt,B_1))))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_103_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,hAPP_f1932802664l_bool(cOMBK_1217667022e_indi,B_1))))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_104_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,hAPP_f978113205l_bool(cOMBK_1549622337le_alt,B_1))))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_105_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,hAPP_f1768325679l_bool(cOMBK_391161927l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_106_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,hAPP_f1954218281l_bool(cOMBK_549130676le_alt,B_1))))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_107_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,hAPP_f905851705l_bool(cOMBK_740566962le_alt,B_1))))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_108_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,hAPP_f118515775l_bool(cOMBK_1028572856l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_109_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,hAPP_f1136405251l_bool(cOMBK_1435997879le_alt,B_1))))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_110_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,hAPP_f206814660l_bool(cOMBK_472365180e_indi,B_1))))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_111_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,hAPP_f1197671953l_bool(cOMBK_165199855le_alt,B_1))))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_112_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,hAPP_f1756719499l_bool(cOMBK_1377637877l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_113_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B_1))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_114_funcset__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B_1))))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_115_splice_Osimps_I2_J,axiom,
! [V_1,Va] : splice1369921490le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,V_1),Va),nil_Ar1135217151le_alt) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,V_1),Va) ).
fof(fact_116_splice_Osimps_I3_J,axiom,
! [X_21,Xs_39,Y_4,Ys_18] : splice1369921490le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_21),Xs_39),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_4),Ys_18)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_21),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_4),splice1369921490le_alt(Xs_39,Ys_18))) ).
fof(fact_117_splice_Osimps_I1_J,axiom,
! [Ys_17] : splice1369921490le_alt(nil_Ar1135217151le_alt,Ys_17) = Ys_17 ).
fof(fact_118_splice__Nil2,axiom,
! [Xs_38] : splice1369921490le_alt(Xs_38,nil_Ar1135217151le_alt) = Xs_38 ).
fof(fact_119_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_1)),hAPP_P1122857141l_bool(B_1,X_1))) ) ) ).
fof(fact_120_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_1)),hAPP_P1116266031t_bool(B_1,X_1))) ) ) ).
fof(fact_121_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1)))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_1)),hAPP_P957402556i_bool(B_1,X_1))) ) ) ).
fof(fact_122_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_1)),hAPP_P1436281263t_bool(B_1,X_1))) ) ) ).
fof(fact_123_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_1)),hAPP_f3167870t_bool(B_1,X_1))) ) ) ).
fof(fact_124_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1)))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_1)),hAPP_f1570138413i_bool(B_1,X_1))) ) ) ).
fof(fact_125_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_1)),hAPP_f1329247136t_bool(B_1,X_1))) ) ) ).
fof(fact_126_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_1)),hAPP_f591334822l_bool(B_1,X_1))) ) ) ).
fof(fact_127_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_1)),hAPP_f1068593625t_bool(B_1,X_1))) ) ) ).
fof(fact_128_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1)))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_1)),hAPP_f431432850i_bool(B_1,X_1))) ) ) ).
fof(fact_129_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_1)),hAPP_f1681297285t_bool(B_1,X_1))) ) ) ).
fof(fact_130_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_1)),hAPP_f812095627l_bool(B_1,X_1))) ) ) ).
fof(fact_131_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_1)),hAPP_f1741989420t_bool(B_1,X_1))) ) ) ).
fof(fact_132_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1)))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_1)),hAPP_f783549695i_bool(B_1,X_1))) ) ) ).
fof(fact_133_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_1)),hAPP_f1114489970t_bool(B_1,X_1))) ) ) ).
fof(fact_134_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_1)),hAPP_f721327224l_bool(B_1,X_1))) ) ) ).
fof(fact_135_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_1)),hAPP_A1014090479t_bool(B_1,X_1))) ) ) ).
fof(fact_136_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_1)),hAPP_A340536322t_bool(B_1,X_1))) ) ) ).
fof(fact_137_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_1)),hAPP_P651748559t_bool(B_1,X_1))) ) ) ).
fof(fact_138_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_1)),hAPP_b763490121t_bool(B_1,X_1))) ) ) ).
fof(fact_139_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_1)),hAPP_A1745457982l_bool(B_1,X_1))) ) ) ).
fof(fact_140_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_1)),hAPP_A701636433l_bool(B_1,X_1))) ) ) ).
fof(fact_141_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_1)),hAPP_P2049543454l_bool(B_1,X_1))) ) ) ).
fof(fact_142_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_1)),hAPP_b1461182872l_bool(B_1,X_1))) ) ) ).
fof(fact_143_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_1)),hAPP_A433435097l_bool(B_1,X_1))) ) ) ).
fof(fact_144_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_1)),hAPP_P467353593l_bool(B_1,X_1))) ) ) ).
fof(fact_145_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_1)),hAPP_b805997823l_bool(B_1,X_1))) ) ) ).
fof(fact_146_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_1)),hAPP_A990651116l_bool(B_1,X_1))) ) ) ).
fof(fact_147_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_1)),hAPP_A955165183l_bool(B_1,X_1))) ) ) ).
fof(fact_148_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_1)),hAPP_P1533476044l_bool(B_1,X_1))) ) ) ).
fof(fact_149_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_1)),hAPP_b651754310l_bool(B_1,X_1))) ) ) ).
fof(fact_150_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_1)),hAPP_f1895971544l_bool(B_1,X_1))) ) ) ).
fof(fact_151_Pi__mem,axiom,
! [X_1,F,A_1,B_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1)))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_1)),hAPP_A659996934l_bool(B_1,X_1))) ) ) ).
fof(fact_152_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_2)),hAPP_P1116266031t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1))) ) ).
fof(fact_153_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1))) ) ).
fof(fact_154_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_2)),hAPP_P1436281263t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1))) ) ).
fof(fact_155_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_2)),hAPP_f3167870t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1))) ) ).
fof(fact_156_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1))) ) ).
fof(fact_157_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_2)),hAPP_f1329247136t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1))) ) ).
fof(fact_158_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1))) ) ).
fof(fact_159_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_2)),hAPP_f1068593625t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1))) ) ).
fof(fact_160_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1))) ) ).
fof(fact_161_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_2)),hAPP_f1681297285t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1))) ) ).
fof(fact_162_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1))) ) ).
fof(fact_163_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_2)),hAPP_f1741989420t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1))) ) ).
fof(fact_164_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1))) ) ).
fof(fact_165_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_2)),hAPP_f1114489970t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1))) ) ).
fof(fact_166_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1))) ) ).
fof(fact_167_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_2)),hAPP_A1014090479t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1))) ) ).
fof(fact_168_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1))) ) ).
fof(fact_169_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_2)),hAPP_P651748559t_bool(B_1,X_2))) )
=> hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1))) ) ).
fof(fact_170_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1))) ) ).
fof(fact_171_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_2)),hAPP_A1745457982l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1))) ) ).
fof(fact_172_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1))) ) ).
fof(fact_173_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_2)),hAPP_P2049543454l_bool(B_1,X_2))) )
=> hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1))) ) ).
fof(fact_174_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1))) ) ).
fof(fact_175_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_2)),hAPP_A433435097l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1))) ) ).
fof(fact_176_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_2)),hAPP_P467353593l_bool(B_1,X_2))) )
=> hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1))) ) ).
fof(fact_177_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1))) ) ).
fof(fact_178_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_2)),hAPP_A990651116l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1))) ) ).
fof(fact_179_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1))) ) ).
fof(fact_180_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_2)),hAPP_P1533476044l_bool(B_1,X_2))) )
=> hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1))) ) ).
fof(fact_181_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1))) ) ).
fof(fact_182_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))) ) ).
fof(fact_183_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))) ) ).
fof(fact_184_Pi__I,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1))) ) ).
fof(fact_185_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,hAPP_f342341961t_bool(cOMBK_980874600le_alt,B_1)))) ) ).
fof(fact_186_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,hAPP_f3439105i_bool(cOMBK_520250367le_alt,B_1)))) ) ).
fof(fact_187_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,hAPP_f2022891751t_bool(cOMBK_1634281074le_alt,B_1)))) ) ).
fof(fact_188_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,hAPP_f1698272152t_bool(cOMBK_242036279t_bool,B_1)))) ) ).
fof(fact_189_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,hAPP_f1274922098i_bool(cOMBK_948333518t_bool,B_1)))) ) ).
fof(fact_190_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,hAPP_f303195352t_bool(cOMBK_1264040257t_bool,B_1)))) ) ).
fof(fact_191_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,hAPP_f498119908l_bool(cOMBK_874213703t_bool,B_1)))) ) ).
fof(fact_192_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,hAPP_f391873743t_bool(cOMBK_339579368t_bool,B_1)))) ) ).
fof(fact_193_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,B_1)))) ) ).
fof(fact_194_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,hAPP_f684471657t_bool(cOMBK_509674590t_bool,B_1)))) ) ).
fof(fact_195_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,hAPP_f2062029545l_bool(cOMBK_753699544t_bool,B_1)))) ) ).
fof(fact_196_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,hAPP_f1300833606t_bool(cOMBK_1961253349t_bool,B_1)))) ) ).
fof(fact_197_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,hAPP_f1377869636i_bool(cOMBK_1847391868t_bool,B_1)))) ) ).
fof(fact_198_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,hAPP_f1228246954t_bool(cOMBK_906927855t_bool,B_1)))) ) ).
fof(fact_199_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,hAPP_f1459432374l_bool(cOMBK_1068969205t_bool,B_1)))) ) ).
fof(fact_200_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,hAPP_f102394819t_bool(cOMBK_78615028le_alt,B_1)))) ) ).
fof(fact_201_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,hAPP_f590186314t_bool(cOMBK_776703103e_indi,B_1)))) ) ).
fof(fact_202_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_2)),B_1)) )
=> hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,hAPP_f1737373975t_bool(cOMBK_1925322610le_alt,B_1)))) ) ).
fof(fact_203_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,hAPP_f581841297t_bool(cOMBK_1685845624l_bool,B_1)))) ) ).
fof(fact_204_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,hAPP_f1973254019l_bool(cOMBK_1744976613le_alt,B_1)))) ) ).
fof(fact_205_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,hAPP_f1932802664l_bool(cOMBK_1217667022e_indi,B_1)))) ) ).
fof(fact_206_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_2)),B_1)) )
=> hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,hAPP_f978113205l_bool(cOMBK_1549622337le_alt,B_1)))) ) ).
fof(fact_207_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,hAPP_f1768325679l_bool(cOMBK_391161927l_bool,B_1)))) ) ).
fof(fact_208_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,hAPP_f1954218281l_bool(cOMBK_549130676le_alt,B_1)))) ) ).
fof(fact_209_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_2)),B_1)) )
=> hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,hAPP_f905851705l_bool(cOMBK_740566962le_alt,B_1)))) ) ).
fof(fact_210_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,hAPP_f118515775l_bool(cOMBK_1028572856l_bool,B_1)))) ) ).
fof(fact_211_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,hAPP_f1136405251l_bool(cOMBK_1435997879le_alt,B_1)))) ) ).
fof(fact_212_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,hAPP_f206814660l_bool(cOMBK_472365180e_indi,B_1)))) ) ).
fof(fact_213_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_2)),B_1)) )
=> hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,hAPP_f1197671953l_bool(cOMBK_165199855le_alt,B_1)))) ) ).
fof(fact_214_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,hAPP_f1756719499l_bool(cOMBK_1377637877l_bool,B_1)))) ) ).
fof(fact_215_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,B_1)))) ) ).
fof(fact_216_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,B_1)))) ) ).
fof(fact_217_funcsetI,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),B_1)) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,B_1)))) ) ).
fof(fact_218_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_P870295781le_alt(F,X_2)),hAPP_P1116266031t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f784749731l_bool(hAPP_f731818989l_bool(member385159430le_alt,F),pi_Pro222743023le_alt(A_1,B_1))) ) ).
fof(fact_219_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_P1645359566e_indi(F,X_2)),hAPP_P957402556i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f817344902l_bool(hAPP_f1387788301l_bool(member220564739e_indi,F),pi_Pro58544964e_indi(A_1,B_1))) ) ).
fof(fact_220_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_P1576037953le_alt(F,X_2)),hAPP_P1436281263t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f437011961l_bool(hAPP_f1325762381l_bool(member2074697974le_alt,F),pi_Pro368504503le_alt(A_1,B_1))) ) ).
fof(fact_221_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1287961430le_alt(F,X_2)),hAPP_f3167870t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f412569108l_bool(hAPP_f1136111951l_bool(member1464733303le_alt,F),pi_fun1083455072le_alt(A_1,B_1))) ) ).
fof(fact_222_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f350403485e_indi(F,X_2)),hAPP_f1570138413i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f882250837l_bool(hAPP_f1140532045l_bool(member1618799570e_indi,F),pi_fun268174099e_indi(A_1,B_1))) ) ).
fof(fact_223_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f597551504le_alt(F,X_2)),hAPP_f1329247136t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f505027144l_bool(hAPP_f1140553229l_bool(member39203141le_alt,F),pi_fun1110020102le_alt(A_1,B_1))) ) ).
fof(fact_224_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1378099862l_bool(F,X_2)),hAPP_f591334822l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1138659662l_bool(hAPP_f1338606733l_bool(member1402889547l_bool,F),pi_fun1236347660l_bool(A_1,B_1))) ) ).
fof(fact_225_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f459545019le_alt(F,X_2)),hAPP_f1068593625t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1518247545l_bool(hAPP_f599048525l_bool(member2142449782le_alt,F),pi_fun1197906993le_alt(A_1,B_1))) ) ).
fof(fact_226_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f1283454584e_indi(F,X_2)),hAPP_f431432850i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1021828400l_bool(hAPP_f2022872455l_bool(member1935624595e_indi,F),pi_fun596906370e_indi(A_1,B_1))) ) ).
fof(fact_227_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f1643422699le_alt(F,X_2)),hAPP_f1681297285t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f270557859l_bool(hAPP_f635489773l_bool(member1687274886le_alt,F),pi_fun404660213le_alt(A_1,B_1))) ) ).
fof(fact_228_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f1733357041l_bool(F,X_2)),hAPP_f812095627l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f560261801l_bool(hAPP_f1171266041l_bool(member2021375116l_bool,F),pi_fun568395771l_bool(A_1,B_1))) ) ).
fof(fact_229_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hAPP_f1273877800le_alt(F,X_2)),hAPP_f1741989420t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1094272486l_bool(hAPP_f1880077555l_bool(member567993161le_alt,F),pi_fun158009906le_alt(A_1,B_1))) ) ).
fof(fact_230_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hAPP_f2043811403e_indi(F,X_2)),hAPP_f783549695i_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f742658307l_bool(hAPP_f749156301l_bool(member234310528e_indi,F),pi_fun1353458625e_indi(A_1,B_1))) ) ).
fof(fact_231_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_f444731198le_alt(F,X_2)),hAPP_f1114489970t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1484382710l_bool(hAPP_f1894818957l_bool(member1953881075le_alt,F),pi_fun481655732le_alt(A_1,B_1))) ) ).
fof(fact_232_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_f446648900l_bool(F,X_2)),hAPP_f721327224l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f750478076l_bool(hAPP_f2087408397l_bool(member48503289l_bool,F),pi_fun187048122l_bool(A_1,B_1))) ) ).
fof(fact_233_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(F,X_2)),hAPP_A1014090479t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2129568089l_bool(hAPP_f884817497l_bool(member442467260le_alt,F),pi_Arr914263595le_alt(A_1,B_1))) ) ).
fof(fact_234_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A503573454le_alt(F,X_2)),hAPP_A340536322t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1291635206l_bool(hAPP_f1234917389l_bool(member219620739le_alt,F),pi_Arr1064242500le_alt(A_1,B_1))) ) ).
fof(fact_235_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_P802532161le_alt(F,X_2)),hAPP_P651748559t_bool(B_1,X_2))) )
=> hBOOL(hAPP_f2031902329l_bool(hAPP_f772908877l_bool(member1097202038le_alt,F),pi_Pro1742482359le_alt(A_1,B_1))) ) ).
fof(fact_236_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_b1482008903le_alt(F,X_2)),hAPP_b763490121t_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2053170815l_bool(hAPP_f452450509l_bool(member300433020le_alt,F),pi_boo1542163389le_alt(A_1,B_1))) ) ).
fof(fact_237_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A630236912t_bool(F,X_2)),hAPP_A1745457982l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2140553640l_bool(hAPP_f1101355639l_bool(member1423816203t_bool,F),pi_Arr425730554t_bool(A_1,B_1))) ) ).
fof(fact_238_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_A739031709t_bool(F,X_2)),hAPP_A701636433l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1898839893l_bool(hAPP_f1836999501l_bool(member104322770t_bool,F),pi_Arr656802323t_bool(A_1,B_1))) ) ).
fof(fact_239_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_P1689126160t_bool(F,X_2)),hAPP_P2049543454l_bool(B_1,X_2))) )
=> hBOOL(hAPP_f404365000l_bool(hAPP_f4855309l_bool(member30324165t_bool,F),pi_Pro54111110t_bool(A_1,B_1))) ) ).
fof(fact_240_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hAPP_b821377302t_bool(F,X_2)),hAPP_b1461182872l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f620747982l_bool(hAPP_f1518101645l_bool(member1024929995t_bool,F),pi_boo679625100t_bool(A_1,B_1))) ) ).
fof(fact_241_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A1014090479t_bool(F,X_2)),hAPP_A433435097l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f640821677l_bool(hAPP_f1475191373l_bool(member1194332074t_bool,F),pi_Arr1752452453t_bool(A_1,B_1))) ) ).
fof(fact_242_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_P651748559t_bool(F,X_2)),hAPP_P467353593l_bool(B_1,X_2))) )
=> hBOOL(hAPP_f1488127117l_bool(hAPP_f1070625729l_bool(member1770643824t_bool,F),pi_Pro1560469721t_bool(A_1,B_1))) ) ).
fof(fact_243_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_b763490121t_bool(F,X_2)),hAPP_b805997823l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f937100551l_bool(hAPP_f840347317l_bool(member1258284266t_bool,F),pi_boo1746012499t_bool(A_1,B_1))) ) ).
fof(fact_244_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A88621982t_bool(F,X_2)),hAPP_A990651116l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f1134444118l_bool(hAPP_f850619859l_bool(member821152697t_bool,F),pi_Arr1120237736t_bool(A_1,B_1))) ) ).
fof(fact_245_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_A1433148491t_bool(F,X_2)),hAPP_A955165183l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f2016919811l_bool(hAPP_f1063991245l_bool(member689634176t_bool,F),pi_Arr742795713t_bool(A_1,B_1))) ) ).
fof(fact_246_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_P482525630t_bool(F,X_2)),hAPP_P1533476044l_bool(B_1,X_2))) )
=> hBOOL(hAPP_f2139503478l_bool(hAPP_f115737741l_bool(member1712829811t_bool,F),pi_Pro519450164t_bool(A_1,B_1))) ) ).
fof(fact_247_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hAPP_b327863236t_bool(F,X_2)),hAPP_b651754310l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f740740988l_bool(hAPP_f2134766349l_bool(member930088569t_bool,F),pi_boo68262458t_bool(A_1,B_1))) ) ).
fof(fact_248_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hAPP_P1813625415t_bool(F,X_2)),hAPP_P1122857141l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1))) ) ).
fof(fact_249_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_f1817389232t_bool(F,X_2)),hAPP_f1895971544l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1))) ) ).
fof(fact_250_Pi__I_H,axiom,
! [F,B_1,A_1] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hAPP_A340536322t_bool(F,X_2)),hAPP_A659996934l_bool(B_1,X_2))) ) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1))) ) ).
fof(fact_251_Pi__cong,axiom,
! [B_1,G,F,A_1] :
( ! [W] :
( is_Pro1004667236le_alt(W)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,W),A_1))
=> ( hBOOL(hAPP_P1813625415t_bool(F,W))
<=> hBOOL(hAPP_P1813625415t_bool(G,W)) ) ) )
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,F),pi_Pro1873779901t_bool(A_1,B_1)))
<=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,G),pi_Pro1873779901t_bool(A_1,B_1))) ) ) ).
fof(fact_252_Pi__cong,axiom,
! [B_1,F,G,A_1] :
( ! [W] :
( is_fun1264457267t_bool(W)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,W),A_1))
=> hAPP_f1817389232t_bool(F,W) = hAPP_f1817389232t_bool(G,W) ) )
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,F),pi_fun1555365306t_bool(A_1,B_1)))
<=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,G),pi_fun1555365306t_bool(A_1,B_1))) ) ) ).
fof(fact_253_Pi__cong,axiom,
! [B_1,F,G,A_1] :
( ! [W] :
( is_Arr859726945e_indi(W)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,W),A_1))
=> hAPP_A340536322t_bool(F,W) = hAPP_A340536322t_bool(G,W) ) )
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,F),pi_Arr1801471756t_bool(A_1,B_1)))
<=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,G),pi_Arr1801471756t_bool(A_1,B_1))) ) ) ).
fof(fact_254_pred__equals__eq2,axiom,
! [S_1,R_2] :
( ! [X_2,Xa] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Xa)),R_2))
<=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Xa)),S_1)) )
<=> R_2 = S_1 ) ).
fof(fact_255_pred__equals__eq2,axiom,
! [S_1,R_2] :
( ( is_fun20916972t_bool(S_1)
& is_fun20916972t_bool(R_2) )
=> ( ! [X_2,Xa] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Xa) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Xa)),R_2))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Xa)),S_1)) ) )
<=> R_2 = S_1 ) ) ).
fof(fact_256_prod_Oexhaust,axiom,
! [Y_3] :
~ ! [A,B] : Y_3 != hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B) ).
fof(fact_257_prod_Oexhaust,axiom,
! [Y_3] :
( is_Pro1004667236le_alt(Y_3)
=> ~ ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> Y_3 != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B) ) ) ).
fof(fact_258_PairE,axiom,
! [P_2] :
~ ! [X_2,Y_1] : P_2 != hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1) ).
fof(fact_259_PairE,axiom,
! [P_2] :
( is_Pro1004667236le_alt(P_2)
=> ~ ! [X_2,Y_1] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_1) )
=> P_2 != hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1) ) ) ).
fof(fact_260_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] : hBOOL(hAPP_P1373277879t_bool(Pa,X1))
<=> ? [A,B] : hBOOL(hAPP_P1373277879t_bool(Pa,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B))) ) ).
fof(fact_261_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] :
( is_Pro1004667236le_alt(X1)
& hBOOL(hAPP_P1813625415t_bool(Pa,X1)) )
<=> ? [A,B] :
( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B)
& hBOOL(hAPP_P1813625415t_bool(Pa,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B))) ) ) ).
fof(fact_262_insert__Nil,axiom,
! [X_20] : insert1969589781le_alt(X_20,nil_Ar1135217151le_alt) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_20),nil_Ar1135217151le_alt) ).
fof(fact_263_distinct__insert,axiom,
! [X_19,Xs_37] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_37))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,insert1969589781le_alt(X_19,Xs_37))) ) ).
fof(fact_264_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),A_1))
<=> hBOOL(hAPP_A1120018583t_bool(A_1,X_1)) ) ).
fof(fact_265_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),A_1))
<=> hBOOL(hAPP_A416869060i_bool(A_1,X_1)) ) ).
fof(fact_266_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),A_1))
<=> hBOOL(hAPP_P1373277879t_bool(A_1,X_1)) ) ).
fof(fact_267_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),A_1))
<=> hBOOL(hAPP_bool_bool(A_1,X_1)) ) ).
fof(fact_268_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),A_1))
<=> hBOOL(hAPP_P1813625415t_bool(A_1,X_1)) ) ).
fof(fact_269_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),A_1))
<=> hBOOL(hAPP_f1378099862l_bool(A_1,X_1)) ) ).
fof(fact_270_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),A_1))
<=> hBOOL(hAPP_f1733357041l_bool(A_1,X_1)) ) ).
fof(fact_271_mem__def,axiom,
! [X_1,A_1] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),A_1))
<=> hBOOL(hAPP_f446648900l_bool(A_1,X_1)) ) ).
fof(fact_272_Collect__def,axiom,
! [Pa] :
( is_fun1651000642t_bool(Pa)
=> collec591097828le_alt(Pa) = Pa ) ).
fof(fact_273_Collect__def,axiom,
! [Pa] :
( is_fun2015243113i_bool(Pa)
=> collec279390863e_indi(Pa) = Pa ) ).
fof(fact_274_Collect__def,axiom,
! [Pa] :
( is_fun1420103068l_bool(Pa)
=> collec612883262t_bool(Pa) = Pa ) ).
fof(fact_275_list__nonempty__induct,axiom,
! [Pa,Xs] :
( Xs != nil_Ar1135217151le_alt
=> ( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> hBOOL(hAPP_l300482276t_bool(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),nil_Ar1135217151le_alt))) )
=> ( ! [X_2,Xs_9] :
( is_Arr723427730le_alt(X_2)
=> ( Xs_9 != nil_Ar1135217151le_alt
=> ( hBOOL(hAPP_l300482276t_bool(Pa,Xs_9))
=> hBOOL(hAPP_l300482276t_bool(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9))) ) ) )
=> hBOOL(hAPP_l300482276t_bool(Pa,Xs)) ) ) ) ).
fof(fact_276_curry__def,axiom,
! [X_2,Xa,Xb] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(X_2),Xa),Xb))
<=> hBOOL(hAPP_P1813625415t_bool(X_2,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Xa),Xb))) ) ).
fof(fact_277_curryI,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_P1373277879t_bool(F,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba)))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(produc930723380t_bool(F),Aa),Ba)) ) ).
fof(fact_278_curryI,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)))
=> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba)) ) ).
fof(fact_279_null__rec_I2_J,axiom,
hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,nil_Ar1135217151le_alt)) ).
fof(fact_280_List_Onull__def,axiom,
! [Xs] :
( hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs))
<=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_281_eq__Nil__null,axiom,
! [Xs] :
( Xs = nil_Ar1135217151le_alt
<=> hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs)) ) ).
fof(fact_282_null__rec_I1_J,axiom,
! [X_18,Xs_36] : ~ hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_18),Xs_36))) ).
fof(fact_283_curryD,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(produc930723380t_bool(F),Aa),Ba))
=> hBOOL(hAPP_P1373277879t_bool(F,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))) ) ).
fof(fact_284_curryD,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba))
=> hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) ) ).
fof(fact_285_curryE,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(produc930723380t_bool(F),Aa),Ba))
=> hBOOL(hAPP_P1373277879t_bool(F,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))) ) ).
fof(fact_286_curryE,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba))
=> hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) ) ).
fof(fact_287_curry__conv,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(produc616221118t_bool(F),Aa),Ba))
<=> hBOOL(hAPP_P1813625415t_bool(F,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) ) ).
fof(fact_288_equal__Nil__null,axiom,
! [Xs] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,Xs),nil_Ar1135217151le_alt))
<=> hBOOL(hAPP_l300482276t_bool(null_A1369988103le_alt,Xs)) ) ).
fof(fact_289_Prof__def,axiom,
arrow_583275979e_Prof = pi_Arr1801471756t_bool(top_to207207712i_bool,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,arrow_912654623le_Lin)) ).
fof(fact_290_lexord__cons__cons,axiom,
! [Aa,X_1,Ba,Y_2,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Aa),X_1)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Ba),Y_2))),hAPP_f664322981t_bool(lexord717456039le_alt,R_1)))
<=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba)),R_1))
| ( Aa = Ba
& hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,X_1),Y_2)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) ) ) ) ).
fof(fact_291_lexord__cons__cons,axiom,
! [Aa,X_1,Ba,Y_2,R_1] :
( ( is_Arr723427730le_alt(Aa)
& is_Arr723427730le_alt(Ba) )
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Aa),X_1)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Ba),Y_2))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
<=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),R_1))
| ( Aa = Ba
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ) ) ) ).
fof(fact_292_distinct__butlast,axiom,
! [Xs_35] :
( Xs_35 != nil_Ar1135217151le_alt
=> ( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_35))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,butlas123970891le_alt(Xs_35))) ) ) ).
fof(fact_293_last__ConsL,axiom,
! [X_17,Xs_34] :
( is_Arr723427730le_alt(X_17)
=> ( Xs_34 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_17),Xs_34)) = X_17 ) ) ).
fof(fact_294_last__ConsR,axiom,
! [X_16,Xs_33] :
( Xs_33 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_16),Xs_33)) = last_A1066338328le_alt(Xs_33) ) ).
fof(fact_295_top1I,axiom,
! [X_1] : hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_1)) ).
fof(fact_296_top1I,axiom,
! [X_1] : hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_1)) ).
fof(fact_297_top1I,axiom,
! [X_1] : hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_1)) ).
fof(fact_298_top1I,axiom,
! [X_1] : hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_1)) ).
fof(fact_299_top1I,axiom,
! [X_1] : hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_1)) ).
fof(fact_300_top1I,axiom,
! [X_1] : hBOOL(hAPP_A1120018583t_bool(top_to186242507t_bool,X_1)) ).
fof(fact_301_equal__list__def,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_1),Y_2))
<=> X_1 = Y_2 ) ).
fof(fact_302_Pi__UNIV,axiom,
! [A_1] : pi_Pro1873779901t_bool(A_1,hAPP_f719005683l_bool(cOMBK_1673635960le_alt,top_to1647826457l_bool)) = top_to846262053l_bool ).
fof(fact_303_Pi__UNIV,axiom,
! [A_1] : pi_fun1555365306t_bool(A_1,hAPP_f633903640l_bool(cOMBK_1918246033t_bool,top_to846262053l_bool)) = top_to1849101472l_bool ).
fof(fact_304_Pi__UNIV,axiom,
! [A_1] : pi_Arr1801471756t_bool(A_1,hAPP_f1639180358l_bool(cOMBK_350223551e_indi,top_to846262053l_bool)) = top_to935749874l_bool ).
fof(fact_305_butlast_Osimps_I1_J,axiom,
butlas123970891le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_306_lexord__Nil__right,axiom,
! [X_1,R_1] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ).
fof(fact_307_butlast_Osimps_I2_J,axiom,
! [X_15,Xs_32] :
( ( Xs_32 = nil_Ar1135217151le_alt
=> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_15),Xs_32)) = nil_Ar1135217151le_alt )
& ( Xs_32 != nil_Ar1135217151le_alt
=> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_15),Xs_32)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_15),butlas123970891le_alt(Xs_32)) ) ) ).
fof(fact_308_last_Osimps,axiom,
! [X_14,Xs_31] :
( is_Arr723427730le_alt(X_14)
=> ( ( Xs_31 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_14),Xs_31)) = X_14 )
& ( Xs_31 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_14),Xs_31)) = last_A1066338328le_alt(Xs_31) ) ) ) ).
fof(fact_309_lexord__Nil__left,axiom,
! [Y_2,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
<=> ? [A,X_2] :
( is_Arr723427730le_alt(A)
& Y_2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,A),X_2) ) ) ).
fof(fact_310_lexord__irreflexive,axiom,
! [Xs,R_1] :
( ! [X_2] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),X_2)),R_1))
=> ~ hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Xs)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) ) ).
fof(fact_311_lexord__irreflexive,axiom,
! [Xs,R_1] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),X_2)),R_1)) )
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Xs)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ).
fof(fact_312_lexord__linear,axiom,
! [X_1,Y_2,R_1] :
( ! [A,B] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B)),R_1))
| A = B
| hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,B),A)),R_1)) )
=> ( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,X_1),Y_2)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1)))
| X_1 = Y_2
| hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Y_2),X_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) ) ) ).
fof(fact_313_lexord__linear,axiom,
! [X_1,Y_2,R_1] :
( ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)),R_1))
| A = B
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,B),A)),R_1)) ) )
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
| X_1 = Y_2
| hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Y_2),X_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ) ).
fof(fact_314_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),top_to818291475t_bool)) ).
fof(fact_315_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool)) ).
fof(fact_316_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),top_to207207712i_bool)) ).
fof(fact_317_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),top_to186242507t_bool)) ).
fof(fact_318_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),top_to1773227171t_bool)) ).
fof(fact_319_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),top_to935749874l_bool)) ).
fof(fact_320_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),top_to846262053l_bool)) ).
fof(fact_321_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),top_to1849101472l_bool)) ).
fof(fact_322_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),top_to818291475t_bool)) ).
fof(fact_323_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),top_to1647826457l_bool)) ).
fof(fact_324_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),top_to207207712i_bool)) ).
fof(fact_325_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),top_to186242507t_bool)) ).
fof(fact_326_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),top_to1773227171t_bool)) ).
fof(fact_327_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),top_to935749874l_bool)) ).
fof(fact_328_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),top_to846262053l_bool)) ).
fof(fact_329_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),top_to1849101472l_bool)) ).
fof(fact_330_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_f446648900l_bool(top_to1849101472l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_331_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_f1733357041l_bool(top_to846262053l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_332_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_f1378099862l_bool(top_to935749874l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_333_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_P1813625415t_bool(top_to1773227171t_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_334_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_A416869060i_bool(top_to207207712i_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_335_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_A1120018583t_bool(top_to186242507t_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_336_takeWhile__not__last,axiom,
! [Xs] :
( Xs != nil_Ar1135217151le_alt
=> ( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs))
=> takeWh1545314552le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),last_A1066338328le_alt(Xs))),Xs) = butlas123970891le_alt(Xs) ) ) ).
fof(fact_337_partition_Osimps_I1_J,axiom,
! [Pa] : partit1336600824le_alt(Pa,nil_Ar1135217151le_alt) = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),nil_Ar1135217151le_alt) ).
fof(fact_338_takeWhile_Osimps_I1_J,axiom,
! [Pa] : takeWh1545314552le_alt(Pa,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_339_distinct__takeWhile,axiom,
! [Pa,Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,takeWh1545314552le_alt(Pa,Xs))) ) ).
fof(fact_340_takeWhile_Osimps_I2_J,axiom,
! [Xs,Pa,X_1] :
( ( hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),takeWh1545314552le_alt(Pa,Xs)) )
& ( ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = nil_Ar1135217151le_alt ) ) ).
fof(fact_341_UNIV__def,axiom,
top_to1849101472l_bool = collec1517527055t_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,fTrue)) ).
fof(fact_342_UNIV__def,axiom,
top_to935749874l_bool = collec1567922785t_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,fTrue)) ).
fof(fact_343_UNIV__def,axiom,
top_to1773227171t_bool = collec1376511890le_alt(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,fTrue)) ).
fof(fact_344_UNIV__def,axiom,
top_to207207712i_bool = collec279390863e_indi(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,fTrue)) ).
fof(fact_345_UNIV__def,axiom,
top_to186242507t_bool = collec591097828le_alt(hAPP_b287951269t_bool(cOMBK_507931254le_alt,fTrue)) ).
fof(fact_346_UNIV__def,axiom,
top_to846262053l_bool = collec612883262t_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,fTrue)) ).
fof(fact_347_UNIV__eq__I,axiom,
! [A_1] :
( ! [X_2] : hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),A_1))
=> top_to818291475t_bool = A_1 ) ).
fof(fact_348_UNIV__eq__I,axiom,
! [A_1] :
( is_fun_bool_bool(A_1)
=> ( ! [X_2] :
( is_bool(X_2)
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),A_1)) )
=> top_to1647826457l_bool = A_1 ) ) ).
fof(fact_349_UNIV__eq__I,axiom,
! [A_1] :
( is_fun2015243113i_bool(A_1)
=> ( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),A_1)) )
=> top_to207207712i_bool = A_1 ) ) ).
fof(fact_350_UNIV__eq__I,axiom,
! [A_1] :
( is_fun1651000642t_bool(A_1)
=> ( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),A_1)) )
=> top_to186242507t_bool = A_1 ) ) ).
fof(fact_351_UNIV__eq__I,axiom,
! [A_1] :
( is_fun20916972t_bool(A_1)
=> ( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),A_1)) )
=> top_to1773227171t_bool = A_1 ) ) ).
fof(fact_352_UNIV__eq__I,axiom,
! [A_1] :
( is_fun701126715l_bool(A_1)
=> ( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),A_1)) )
=> top_to935749874l_bool = A_1 ) ) ).
fof(fact_353_UNIV__eq__I,axiom,
! [A_1] :
( is_fun1420103068l_bool(A_1)
=> ( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),A_1)) )
=> top_to846262053l_bool = A_1 ) ) ).
fof(fact_354_UNIV__eq__I,axiom,
! [A_1] :
( is_fun292781289l_bool(A_1)
=> ( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),A_1)) )
=> top_to1849101472l_bool = A_1 ) ) ).
fof(fact_355_UNIV__witness,axiom,
? [X_2] : hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),top_to818291475t_bool)) ).
fof(fact_356_UNIV__witness,axiom,
? [X_2] :
( is_bool(X_2)
& hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),top_to1647826457l_bool)) ) ).
fof(fact_357_UNIV__witness,axiom,
? [X_2] :
( is_Arr859726945e_indi(X_2)
& hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),top_to207207712i_bool)) ) ).
fof(fact_358_UNIV__witness,axiom,
? [X_2] :
( is_Arr723427730le_alt(X_2)
& hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),top_to186242507t_bool)) ) ).
fof(fact_359_UNIV__witness,axiom,
? [X_2] :
( is_Pro1004667236le_alt(X_2)
& hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),top_to1773227171t_bool)) ) ).
fof(fact_360_UNIV__witness,axiom,
? [X_2] :
( is_fun1264457267t_bool(X_2)
& hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),top_to935749874l_bool)) ) ).
fof(fact_361_UNIV__witness,axiom,
? [X_2] :
( is_fun20916972t_bool(X_2)
& hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),top_to846262053l_bool)) ) ).
fof(fact_362_UNIV__witness,axiom,
? [X_2] :
( is_fun48324065t_bool(X_2)
& hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),top_to1849101472l_bool)) ) ).
fof(fact_363_Lin__def,axiom,
arrow_912654623le_Lin = collec612883262t_bool(order_1844940151le_alt(top_to186242507t_bool)) ).
fof(fact_364_append__butlast__last__id,axiom,
! [Xs_30] :
( Xs_30 != nil_Ar1135217151le_alt
=> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,butlas123970891le_alt(Xs_30)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,last_A1066338328le_alt(Xs_30)),nil_Ar1135217151le_alt)) = Xs_30 ) ).
fof(fact_365_snoc__eq__iff__butlast,axiom,
! [Xs,X_1,Ys_1] :
( is_Arr723427730le_alt(X_1)
=> ( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt)) = Ys_1
<=> ( Ys_1 != nil_Ar1135217151le_alt
& butlas123970891le_alt(Ys_1) = Xs
& last_A1066338328le_alt(Ys_1) = X_1 ) ) ) ).
fof(fact_366_Nil2__notin__lex,axiom,
! [Xs,R_1] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1))) ).
fof(fact_367_Nil__notin__lex,axiom,
! [Ys_1,R_1] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Ys_1)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1))) ).
fof(fact_368_append__eq__appendI,axiom,
! [Ys_16,Us_2,Xs_29,Xs1_1,Zs_4] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_29),Xs1_1) = Zs_4
=> ( Ys_16 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs1_1),Us_2)
=> hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_29),Ys_16) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_4),Us_2) ) ) ).
fof(fact_369_append__same__eq,axiom,
! [Ys_1,Xs,Zs_1] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Xs) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_1),Xs)
<=> Ys_1 = Zs_1 ) ).
fof(fact_370_same__append__eq,axiom,
! [Xs,Ys_1,Zs_1] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Zs_1)
<=> Ys_1 = Zs_1 ) ).
fof(fact_371_append__eq__append__conv2,axiom,
! [Xs,Ys_1,Zs_1,Ts] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_1),Ts)
<=> ? [Us] :
( ( Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Zs_1),Us)
& hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),Ys_1) = Ts )
| ( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Us) = Zs_1
& Ys_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),Ts) ) ) ) ).
fof(fact_372_append__assoc,axiom,
! [Xs_28,Ys_15,Zs_3] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_28),Ys_15)),Zs_3) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_28),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_15),Zs_3)) ).
fof(fact_373_append__Cons,axiom,
! [X_13,Xs_27,Ys_14] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_13),Xs_27)),Ys_14) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_13),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_27),Ys_14)) ).
fof(fact_374_Cons__eq__appendI,axiom,
! [Xs_26,Zs_2,X_12,Xs1,Ys_13] :
( hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_12),Xs1) = Ys_13
=> ( Xs_26 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs1),Zs_2)
=> hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_12),Xs_26) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_13),Zs_2) ) ) ).
fof(fact_375_append__Nil,axiom,
! [Ys_12] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,nil_Ar1135217151le_alt),Ys_12) = Ys_12 ).
fof(fact_376_Nil__is__append__conv,axiom,
! [Xs,Ys_1] :
( nil_Ar1135217151le_alt = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)
<=> ( Xs = nil_Ar1135217151le_alt
& Ys_1 = nil_Ar1135217151le_alt ) ) ).
fof(fact_377_append__Nil2,axiom,
! [Xs_25] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_25),nil_Ar1135217151le_alt) = Xs_25 ).
fof(fact_378_self__append__conv,axiom,
! [Xs,Ys_1] :
( Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)
<=> Ys_1 = nil_Ar1135217151le_alt ) ).
fof(fact_379_self__append__conv2,axiom,
! [Ys_1,Xs] :
( Ys_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)
<=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_380_append__is__Nil__conv,axiom,
! [Xs,Ys_1] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = nil_Ar1135217151le_alt
<=> ( Xs = nil_Ar1135217151le_alt
& Ys_1 = nil_Ar1135217151le_alt ) ) ).
fof(fact_381_append__self__conv,axiom,
! [Xs,Ys_1] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = Xs
<=> Ys_1 = nil_Ar1135217151le_alt ) ).
fof(fact_382_append__self__conv2,axiom,
! [Xs,Ys_1] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1) = Ys_1
<=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_383_eq__Nil__appendI,axiom,
! [Xs_24,Ys_11] :
( Xs_24 = Ys_11
=> Xs_24 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,nil_Ar1135217151le_alt),Ys_11) ) ).
fof(fact_384_append__eq__Cons__conv,axiom,
! [Ys_1,Zs_1,X_1,Xs] :
( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Zs_1) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)
<=> ( ( Ys_1 = nil_Ar1135217151le_alt
& Zs_1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) )
| ? [Ys_10] :
( Ys_1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Ys_10)
& hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_10),Zs_1) = Xs ) ) ) ).
fof(fact_385_Cons__eq__append__conv,axiom,
! [X_1,Xs,Ys_1,Zs_1] :
( hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Zs_1)
<=> ( ( Ys_1 = nil_Ar1135217151le_alt
& hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) = Zs_1 )
| ? [Ys_10] :
( hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Ys_10) = Ys_1
& Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_10),Zs_1) ) ) ) ).
fof(fact_386_append1__eq__conv,axiom,
! [Xs,X_1,Ys_1,Y_2] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),nil_Ar1135217151le_alt))
<=> ( Xs = Ys_1
& X_1 = Y_2 ) ) ) ).
fof(fact_387_takeWhile__tail,axiom,
! [Xs,L,Pa,X_1] :
( ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),L))) = takeWh1545314552le_alt(Pa,Xs) ) ).
fof(fact_388_butlast__append,axiom,
! [Xs_23,Ys_9] :
( ( Ys_9 = nil_Ar1135217151le_alt
=> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_23),Ys_9)) = butlas123970891le_alt(Xs_23) )
& ( Ys_9 != nil_Ar1135217151le_alt
=> butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_23),Ys_9)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_23),butlas123970891le_alt(Ys_9)) ) ) ).
fof(fact_389_last__append,axiom,
! [Xs_22,Ys_8] :
( ( Ys_8 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_22),Ys_8)) = last_A1066338328le_alt(Xs_22) )
& ( Ys_8 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_22),Ys_8)) = last_A1066338328le_alt(Ys_8) ) ) ).
fof(fact_390_last__appendR,axiom,
! [Xs_21,Ys_7] :
( Ys_7 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_21),Ys_7)) = last_A1066338328le_alt(Ys_7) ) ).
fof(fact_391_last__appendL,axiom,
! [Xs_20,Ys_6] :
( Ys_6 = nil_Ar1135217151le_alt
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_20),Ys_6)) = last_A1066338328le_alt(Xs_20) ) ).
fof(fact_392_lexord__append__leftI,axiom,
! [X_1,U,V,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,U),V)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),U)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),V))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ).
fof(fact_393_butlast__snoc,axiom,
! [Xs_19,X_11] : butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_19),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_11),nil_Ar1135217151le_alt))) = Xs_19 ).
fof(fact_394_last__snoc,axiom,
! [Xs_18,X_10] :
( is_Arr723427730le_alt(X_10)
=> last_A1066338328le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_18),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_10),nil_Ar1135217151le_alt))) = X_10 ) ).
fof(fact_395_lexord__append__left__rightI,axiom,
! [U,X_1,Y_2,Aa,Ba,R_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)),R_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,U),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Aa),X_1))),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,U),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Ba),Y_2)))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ).
fof(fact_396_lexord__append__left__rightI,axiom,
! [U,X_1,Y_2,Aa,Ba,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba)),R_1))
=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,U),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Aa),X_1))),hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,U),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Ba),Y_2)))),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) ) ).
fof(fact_397_lexord__append__rightI,axiom,
! [X_1,R_1,Y_2] :
( ? [B,Z] : Y_2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,B),Z)
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),Y_2))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ).
fof(fact_398_lexord__append__leftD,axiom,
! [X_1,U,V,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,X_1),U)),hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,X_1),V))),hAPP_f664322981t_bool(lexord717456039le_alt,R_1)))
=> ( ! [A] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),A)),R_1))
=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,U),V)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) ) ) ).
fof(fact_399_lexord__append__leftD,axiom,
! [X_1,U,V,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),U)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,X_1),V))),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
=> ( ! [A] :
( is_Arr723427730le_alt(A)
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),A)),R_1)) )
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,U),V)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ) ).
fof(fact_400_rev__induct,axiom,
! [Xs,Pa] :
( hBOOL(hAPP_l300482276t_bool(Pa,nil_Ar1135217151le_alt))
=> ( ! [X_2,Xs_9] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_l300482276t_bool(Pa,Xs_9))
=> hBOOL(hAPP_l300482276t_bool(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_9),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),nil_Ar1135217151le_alt)))) ) )
=> hBOOL(hAPP_l300482276t_bool(Pa,Xs)) ) ) ).
fof(fact_401_rev__cases,axiom,
! [Xs_17] :
( Xs_17 != nil_Ar1135217151le_alt
=> ~ ! [Ys,Y_1] :
( is_Arr723427730le_alt(Y_1)
=> Xs_17 != hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),nil_Ar1135217151le_alt)) ) ) ).
fof(fact_402_snoc__listrel1__snoc__iff,axiom,
! [Xs,X_1,Ys_1,Y_2,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Xs),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),nil_li7342420le_alt))),hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Ys_1),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),nil_li7342420le_alt)))),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))
<=> ( ( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))
& X_1 = Y_2 )
| ( Xs = Ys_1
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1)) ) ) ) ).
fof(fact_403_snoc__listrel1__snoc__iff,axiom,
! [Xs,X_1,Ys_1,Y_2,R_1] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt))),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),nil_Ar1135217151le_alt)))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
<=> ( ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
& X_1 = Y_2 )
| ( Xs = Ys_1
& hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1)) ) ) ) ) ).
fof(fact_404_rotate1__def,axiom,
! [Xs] : rotate184372300le_alt(Xs) = list_c1434691767le_alt(nil_Ar1135217151le_alt,hAPP_f904937452le_alt(hAPP_f239458941le_alt(cOMBB_521986850le_alt,hAPP_f268020663le_alt(cOMBC_168079159le_alt,append28105492le_alt)),hAPP_l1693669363le_alt(hAPP_f18365135le_alt(cOMBC_1169281096le_alt,cons_A77766063le_alt),nil_Ar1135217151le_alt)),Xs) ).
fof(fact_405_rotate1__is__Nil__conv,axiom,
! [Xs] :
( rotate184372300le_alt(Xs) = nil_Ar1135217151le_alt
<=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_406_distinct1__rotate,axiom,
! [Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,rotate184372300le_alt(Xs)))
<=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) ) ).
fof(fact_407_listrel1I2,axiom,
! [X_1,Xs,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Ys_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ).
fof(fact_408_not__listrel1__Nil,axiom,
! [Xs,R_1] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ).
fof(fact_409_not__Nil__listrel1,axiom,
! [Xs,R_1] : ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Xs)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ).
fof(fact_410_append__listrel1I,axiom,
! [Us_1,Vs_1,Xs,Ys_1,R_1] :
( ( ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
& Us_1 = Vs_1 )
| ( Xs = Ys_1
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Us_1),Vs_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) )
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Us_1)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys_1),Vs_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ).
fof(fact_411_Cons__listrel1__Cons,axiom,
! [X_1,Xs,Y_2,Ys_1,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))
<=> ( ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1))
& Xs = Ys_1 )
| ( X_1 = Y_2
& hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) ) ) ) ).
fof(fact_412_Cons__listrel1__Cons,axiom,
! [X_1,Xs,Y_2,Ys_1,R_1] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
<=> ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1))
& Xs = Ys_1 )
| ( X_1 = Y_2
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ) ) ) ).
fof(fact_413_listrel1I1,axiom,
! [Xs,X_1,Y_2,R_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Xs))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ).
fof(fact_414_listrel1I1,axiom,
! [Xs,X_1,Y_2,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1))
=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Xs))),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) ) ).
fof(fact_415_listrel1I,axiom,
! [Ys_1,Xs,Us_1,Vs_1,X_1,Y_2,R_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1))
=> ( Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Vs_1))
=> ( Ys_1 = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Vs_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ) ) ).
fof(fact_416_listrel1I,axiom,
! [Ys_1,Xs,Us_1,Vs_1,X_1,Y_2,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1))
=> ( Xs = hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us_1),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Vs_1))
=> ( Ys_1 = hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us_1),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Vs_1))
=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) ) ) ) ).
fof(fact_417_listrel1E,axiom,
! [Xs,Ys_1,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))
=> ~ ! [X_2,Y_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)),R_1))
=> ! [Us,Vs] :
( Xs = hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Vs))
=> Ys_1 != hAPP_l1425181461le_alt(hAPP_l1626273389le_alt(append1413540863le_alt,Us),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Vs)) ) ) ) ).
fof(fact_418_listrel1E,axiom,
! [Xs,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
=> ~ ! [X_2,Y_1] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_1) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)),R_1))
=> ! [Us,Vs] :
( Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Vs))
=> Ys_1 != hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Us),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Vs)) ) ) ) ) ).
fof(fact_419_Cons__listrel1E1,axiom,
! [X_1,Xs,Ys_1,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))
=> ( ! [Y_1] :
( Ys_1 = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Xs)
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_1)),R_1)) )
=> ~ ! [Zs] :
( Ys_1 = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Zs)
=> ~ hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Zs)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) ) ) ) ).
fof(fact_420_Cons__listrel1E1,axiom,
! [X_1,Xs,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
=> ( ! [Y_1] :
( is_Arr723427730le_alt(Y_1)
=> ( Ys_1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Xs)
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_1)),R_1)) ) )
=> ~ ! [Zs] :
( Ys_1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Zs)
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Zs)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ) ) ).
fof(fact_421_Cons__listrel1E2,axiom,
! [Xs,Y_2,Ys_1,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre868094907le_alt,R_1)))
=> ( ! [X_2] :
( Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Ys_1)
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_2)),R_1)) )
=> ~ ! [Zs] :
( Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Zs)
=> ~ hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Zs),Ys_1)),hAPP_f664322981t_bool(listre868094907le_alt,R_1))) ) ) ) ).
fof(fact_422_Cons__listrel1E2,axiom,
! [Xs,Y_2,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
=> ( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Ys_1)
=> ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1)) ) )
=> ~ ! [Zs] :
( Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Zs)
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Zs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1))) ) ) ) ).
fof(fact_423_Cons__in__lex,axiom,
! [X_1,Xs,Y_2,Ys_1,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(lex_li910676976le_alt,R_1)))
<=> ( ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1))
& size_s101148091le_alt(Xs) = size_s101148091le_alt(Ys_1) )
| ( X_1 = Y_2
& hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(lex_li910676976le_alt,R_1))) ) ) ) ).
fof(fact_424_Cons__in__lex,axiom,
! [X_1,Xs,Y_2,Ys_1,R_1] :
( ( is_Arr723427730le_alt(X_1)
& is_Arr723427730le_alt(Y_2) )
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1)))
<=> ( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1))
& size_s2106320494le_alt(Xs) = size_s2106320494le_alt(Ys_1) )
| ( X_1 = Y_2
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1))) ) ) ) ) ).
fof(fact_425_dropWhile__eq__Cons__conv,axiom,
! [Pa,Xs,Y_2,Ys_1] :
( dropWh1165804960le_alt(Pa,Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1)
<=> ( Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,takeWh1545314552le_alt(Pa,Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))
& ~ hBOOL(hAPP_A1120018583t_bool(Pa,Y_2)) ) ) ).
fof(fact_426_partition_Osimps_I2_J,axiom,
! [Pa,X_1,Xs] : partit1336600824le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = hAPP_P2096362161le_alt(produc1250814607le_alt(hAPP_f794134621le_alt(hAPP_f2122335314le_alt(cOMBS_1569784209le_alt,hAPP_f310101886le_alt(hAPP_f1558754397le_alt(cOMBB_1988247237le_alt,cOMBS_1626428525le_alt),hAPP_f1504748473le_alt(hAPP_f1949171529le_alt(cOMBB_215060470le_alt,hAPP_f1654251593le_alt(cOMBB_1675847172le_alt,if_Pro1659200999le_alt(hAPP_A1120018583t_bool(Pa,X_1)))),hAPP_f670565125le_alt(hAPP_f1124725731le_alt(cOMBB_1236261828le_alt,produc2031778509le_alt),hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1))))),hAPP_f670565125le_alt(hAPP_f351228915le_alt(cOMBC_72147604le_alt,hAPP_f593033837le_alt(hAPP_f332249751le_alt(cOMBB_96247696le_alt,cOMBB_1303549321le_alt),produc2031778509le_alt)),hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1)))),partit1336600824le_alt(Pa,Xs)) ).
fof(fact_427_dropWhile_Osimps_I2_J,axiom,
! [Xs,Pa,X_1] :
( ( hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = dropWh1165804960le_alt(Pa,Xs) )
& ( ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) ) ) ).
fof(fact_428_dropWhile_Osimps_I1_J,axiom,
! [Pa] : dropWh1165804960le_alt(Pa,nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_429_distinct__dropWhile,axiom,
! [Pa,Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,dropWh1165804960le_alt(Pa,Xs))) ) ).
fof(fact_430_split__curry,axiom,
! [F] :
( is_fun20916972t_bool(F)
=> produc278404511t_bool(produc616221118t_bool(F)) = F ) ).
fof(fact_431_curry__split,axiom,
! [F] :
( is_fun866579754t_bool(F)
=> produc616221118t_bool(produc278404511t_bool(F)) = F ) ).
fof(fact_432_listrel1__eq__len,axiom,
! [Xs,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1913026136le_alt,R_1)))
=> size_s2106320494le_alt(Xs) = size_s2106320494le_alt(Ys_1) ) ).
fof(fact_433_takeWhile__dropWhile__id,axiom,
! [Pa,Xs] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,takeWh1545314552le_alt(Pa,Xs)),dropWh1165804960le_alt(Pa,Xs)) = Xs ).
fof(fact_434_lexord__lex,axiom,
! [X_1,Y_2,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lex_Ar1264540259le_alt,R_1)))
<=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
& size_s2106320494le_alt(X_1) = size_s2106320494le_alt(Y_2) ) ) ).
fof(fact_435_lexn__length,axiom,
! [Xs,Ys_1,R_1,N] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),lexn_A19384479le_alt(R_1,N)))
=> ( size_s2106320494le_alt(Xs) = N
& size_s2106320494le_alt(Ys_1) = N ) ) ).
fof(fact_436_splitI,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(F,Aa),Ba))
=> hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(F),hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))) ) ).
fof(fact_437_splitI,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(F,Aa),Ba))
=> hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(F),hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) ) ).
fof(fact_438_prod__caseI,axiom,
! [F1,Aa,Ba] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(F1,Aa),Ba))
=> hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(F1),hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba))) ) ).
fof(fact_439_prod__caseI,axiom,
! [F1,Aa,Ba] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(F1,Aa),Ba))
=> hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(F1),hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba))) ) ).
fof(fact_440_splitD,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(F),hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Aa),Ba)))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(F,Aa),Ba)) ) ).
fof(fact_441_splitD,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(F),hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Aa),Ba)))
=> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(F,Aa),Ba)) ) ).
fof(fact_442_splitI2,axiom,
! [Ca,P_1] :
( ! [A,B] :
( P_1 = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A),B)
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(Ca,A),B)) )
=> hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(Ca),P_1)) ) ).
fof(fact_443_splitI2,axiom,
! [Ca,P_1] :
( is_Pro1004667236le_alt(P_1)
=> ( ! [A,B] :
( ( is_Arr723427730le_alt(A)
& is_Arr723427730le_alt(B) )
=> ( P_1 = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,A),B)
=> hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(Ca,A),B)) ) )
=> hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(Ca),P_1)) ) ) ).
fof(fact_444_splitE,axiom,
! [Ca,P_1] :
( hBOOL(hAPP_P1373277879t_bool(produc1802641557t_bool(Ca),P_1))
=> ~ ! [X_2,Y_1] :
( P_1 = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)
=> ~ hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(Ca,X_2),Y_1)) ) ) ).
fof(fact_445_splitE,axiom,
! [Ca,P_1] :
( is_Pro1004667236le_alt(P_1)
=> ( hBOOL(hAPP_P1813625415t_bool(produc278404511t_bool(Ca),P_1))
=> ~ ! [X_2,Y_1] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_1) )
=> ( P_1 = hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)
=> ~ hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(Ca,X_2),Y_1)) ) ) ) ) ).
fof(fact_446_not__distinct__decomp,axiom,
! [Ws] :
( ~ hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Ws))
=> ? [Xs_9,Ys,Zs,Y_1] :
( is_Arr723427730le_alt(Y_1)
& Ws = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_9),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),nil_Ar1135217151le_alt)),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),nil_Ar1135217151le_alt)),Zs)))) ) ) ).
fof(fact_447_listrel_OCons,axiom,
! [Xs,Ys_1,X_1,Y_2,R_1] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_1),Y_2)),R_1))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) ) ) ).
fof(fact_448_listrel_OCons,axiom,
! [Xs,Ys_1,X_1,Y_2,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_1),Y_2)),R_1))
=> ( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))
=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_1),Xs)),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) ) ) ).
fof(fact_449_tl__append,axiom,
! [Xs,Ys_1] : tl_Arr314474198le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = list_c1434691767le_alt(tl_Arr314474198le_alt(Ys_1),hAPP_f921948995le_alt(cOMBK_1825575856le_alt,hAPP_l1390889510le_alt(hAPP_f268020663le_alt(cOMBC_168079159le_alt,append28105492le_alt),Ys_1)),Xs) ).
fof(fact_450_listrel__Nil2,axiom,
! [Xs,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_451_listrel__Nil1,axiom,
! [Xs,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),Xs)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_452_tl_Osimps_I2_J,axiom,
! [X_9,Xs_16] : tl_Arr314474198le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_9),Xs_16)) = Xs_16 ).
fof(fact_453_tl_Osimps_I1_J,axiom,
tl_Arr314474198le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_454_distinct__tl,axiom,
! [Xs_15] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_15))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,tl_Arr314474198le_alt(Xs_15))) ) ).
fof(fact_455_listrel_ONil,axiom,
! [R_1] : hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,nil_Ar1135217151le_alt),nil_Ar1135217151le_alt)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) ).
fof(fact_456_listrel__eq__len,axiom,
! [Xs,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
=> size_s2106320494le_alt(Xs) = size_s2106320494le_alt(Ys_1) ) ).
fof(fact_457_tl__append2,axiom,
! [Ys_5,Xs_14] :
( Xs_14 != nil_Ar1135217151le_alt
=> tl_Arr314474198le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_14),Ys_5)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,tl_Arr314474198le_alt(Xs_14)),Ys_5) ) ).
fof(fact_458_listrel__Cons2,axiom,
! [Xs,Y_2,Ys_1,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1))),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))
=> ~ ! [X_2,Xs_9] :
( Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Xs_9)
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_2)),R_1))
=> ~ hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs_9),Ys_1)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) ) ) ) ).
fof(fact_459_listrel__Cons2,axiom,
! [Xs,Y_2,Ys_1,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
=> ~ ! [X_2,Xs_9] :
( is_Arr723427730le_alt(X_2)
=> ( Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_2)),R_1))
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs_9),Ys_1)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) ) ) ) ) ).
fof(fact_460_listrel__Cons1,axiom,
! [Y_2,Ys_1,Xs,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_2),Ys_1)),Xs)),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))
=> ~ ! [Y_1,Ys] :
( Xs = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Ys)
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Y_2),Y_1)),R_1))
=> ~ hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Ys_1),Ys)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) ) ) ) ).
fof(fact_461_listrel__Cons1,axiom,
! [Y_2,Ys_1,Xs,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1)),Xs)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
=> ~ ! [Y_1,Ys] :
( is_Arr723427730le_alt(Y_1)
=> ( Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_2),Y_1)),R_1))
=> ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Ys_1),Ys)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) ) ) ) ) ).
fof(fact_462_listrelp__listrel__eq,axiom,
! [R_1,X_2,Xa] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,hAPP_f1092358369t_bool(hAPP_f1682340965t_bool(cOMBB_333235735le_alt,cOMBC_943734388l_bool),hAPP_f1747206697l_bool(hAPP_f274832101l_bool(cOMBB_885534287le_alt,hAPP_f1585690341l_bool(cOMBB_711698847le_alt,member720722004le_alt)),produc1456060119le_alt))),R_1)),X_2),Xa))
<=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Xa)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) ) ).
fof(fact_463_listrelp__listrel__eq,axiom,
! [R_1,X_2,Xa] :
( hBOOL(hAPP_l784127213t_bool(hAPP_l508185643t_bool(listre1064220282le_alt(hAPP_f1895633847t_bool(hAPP_f1997384703t_bool(cOMBC_1696964078t_bool,hAPP_f1837837439t_bool(hAPP_f1503353479t_bool(cOMBB_1326560562le_alt,cOMBC_1827582133l_bool),hAPP_f1893731349l_bool(hAPP_f1418100887l_bool(cOMBB_1150645560le_alt,hAPP_f1224738111l_bool(cOMBB_1407335828le_alt,member1373125444le_alt)),produc2031778509le_alt))),R_1)),X_2),Xa))
<=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,X_2),Xa)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) ) ).
fof(fact_464_rotate1__hd__tl,axiom,
! [Xs_13] :
( Xs_13 != nil_Ar1135217151le_alt
=> rotate184372300le_alt(Xs_13) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,tl_Arr314474198le_alt(Xs_13)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,hd_Arr1814706386le_alt(Xs_13)),nil_Ar1135217151le_alt)) ) ).
fof(fact_465_listrel_Osimps,axiom,
! [A1,A2,R_1] :
( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,A1),A2)),hAPP_f664322981t_bool(listre870705708le_alt,R_1)))
<=> ( ( A1 = nil_li7342420le_alt
& A2 = nil_li7342420le_alt )
| ? [X_2,Y_1,Xs_9,Ys] :
( A1 = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,X_2),Xs_9)
& A2 = hAPP_l1425181461le_alt(hAPP_l1663319606le_alt(cons_l882637220le_alt,Y_1),Ys)
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)),R_1))
& hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs_9),Ys)),hAPP_f664322981t_bool(listre870705708le_alt,R_1))) ) ) ) ).
fof(fact_466_listrel_Osimps,axiom,
! [A1,A2,R_1] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,A1),A2)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1)))
<=> ( ( A1 = nil_Ar1135217151le_alt
& A2 = nil_Ar1135217151le_alt )
| ? [X_2,Y_1,Xs_9,Ys] :
( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_1)
& A1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9)
& A2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys)
& hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)),R_1))
& hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs_9),Ys)),hAPP_f1681297285t_bool(listre1769678631le_alt,R_1))) ) ) ) ).
fof(fact_467_hd_Osimps,axiom,
! [X_8,Xs_12] :
( is_Arr723427730le_alt(X_8)
=> hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_8),Xs_12)) = X_8 ) ).
fof(fact_468_listrelp_OCons,axiom,
! [Xs,Ys_1,R_1,X_1,Y_2] :
( hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(R_1,X_1),Y_2))
=> ( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),Xs),Ys_1))
=> hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1))) ) ) ).
fof(fact_469_listrelp_ONil,axiom,
! [R_1] : hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),nil_Ar1135217151le_alt),nil_Ar1135217151le_alt)) ).
fof(fact_470_hd__append,axiom,
! [Ys_4,Xs_11] :
( ( Xs_11 = nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_11),Ys_4)) = hd_Arr1814706386le_alt(Ys_4) )
& ( Xs_11 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_11),Ys_4)) = hd_Arr1814706386le_alt(Xs_11) ) ) ).
fof(fact_471_hd__append2,axiom,
! [Ys_3,Xs_10] :
( Xs_10 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_10),Ys_3)) = hd_Arr1814706386le_alt(Xs_10) ) ).
fof(fact_472_hd__dropWhile,axiom,
! [Pa,Xs] :
( dropWh1165804960le_alt(Pa,Xs) != nil_Ar1135217151le_alt
=> ~ hBOOL(hAPP_A1120018583t_bool(Pa,hd_Arr1814706386le_alt(dropWh1165804960le_alt(Pa,Xs)))) ) ).
fof(fact_473_listrelp_Osimps,axiom,
! [R_1,A1,A2] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),A1),A2))
<=> ( ( A1 = nil_Ar1135217151le_alt
& A2 = nil_Ar1135217151le_alt )
| ? [X_2,Y_1,Xs_9,Ys] :
( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_1)
& A1 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Xs_9)
& A2 = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_1),Ys)
& hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(R_1,X_2),Y_1))
& hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(listre1062185049le_alt(R_1),Xs_9),Ys)) ) ) ) ).
fof(fact_474_equal,axiom,
equal_732151074le_alt = fequal1028827333le_alt ).
fof(fact_475_equal__refl,axiom,
! [X_7] : hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_7),X_7)) ).
fof(fact_476_equal__eq,axiom,
! [X_1,Y_2] :
( hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(equal_732151074le_alt,X_1),Y_2))
<=> X_1 = Y_2 ) ).
fof(fact_477_eq__equal,axiom,
fequal1028827333le_alt = equal_732151074le_alt ).
fof(fact_478_last__rev,axiom,
! [Xs_8] :
( Xs_8 != nil_Ar1135217151le_alt
=> last_A1066338328le_alt(rev_Ar955429983le_alt(Xs_8)) = hd_Arr1814706386le_alt(Xs_8) ) ).
fof(fact_479_hd__rev,axiom,
! [Xs_7] :
( Xs_7 != nil_Ar1135217151le_alt
=> hd_Arr1814706386le_alt(rev_Ar955429983le_alt(Xs_7)) = last_A1066338328le_alt(Xs_7) ) ).
fof(fact_480_replicate__append__same,axiom,
! [I_3,X_6] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(I_3,X_6)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_6),nil_Ar1135217151le_alt)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_6),replic1360561849le_alt(I_3,X_6)) ).
fof(fact_481_dropWhile__eq__drop,axiom,
! [Pa,Xs] : dropWh1165804960le_alt(Pa,Xs) = hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,size_s2106320494le_alt(takeWh1545314552le_alt(Pa,Xs))),Xs) ).
fof(fact_482_butlast__drop,axiom,
! [N_6,Xs_6] : butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_6),Xs_6)) = hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_6),butlas123970891le_alt(Xs_6)) ).
fof(fact_483_drop__butlast,axiom,
! [N_5,Xs_5] : hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_5),butlas123970891le_alt(Xs_5)) = butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_5),Xs_5)) ).
fof(fact_484_drop__Nil,axiom,
! [N_4] : hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N_4),nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_485_distinct__drop,axiom,
! [I_2,Xs_4] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs_4))
=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,I_2),Xs_4))) ) ).
fof(fact_486_rev__append,axiom,
! [Xs_3,Ys_2] : rev_Ar955429983le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs_3),Ys_2)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,rev_Ar955429983le_alt(Ys_2)),rev_Ar955429983le_alt(Xs_3)) ).
fof(fact_487_rev__is__Nil__conv,axiom,
! [Xs] :
( rev_Ar955429983le_alt(Xs) = nil_Ar1135217151le_alt
<=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_488_Nil__is__rev__conv,axiom,
! [Xs] :
( nil_Ar1135217151le_alt = rev_Ar955429983le_alt(Xs)
<=> Xs = nil_Ar1135217151le_alt ) ).
fof(fact_489_rev_Osimps_I1_J,axiom,
rev_Ar955429983le_alt(nil_Ar1135217151le_alt) = nil_Ar1135217151le_alt ).
fof(fact_490_append__replicate__commute,axiom,
! [N_3,X_5,K_1] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(N_3,X_5)),replic1360561849le_alt(K_1,X_5)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(K_1,X_5)),replic1360561849le_alt(N_3,X_5)) ).
fof(fact_491_distinct__rev,axiom,
! [Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,rev_Ar955429983le_alt(Xs)))
<=> hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) ) ).
fof(fact_492_rev__singleton__conv,axiom,
! [Xs,X_1] :
( rev_Ar955429983le_alt(Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt)
<=> Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt) ) ).
fof(fact_493_singleton__rev__conv,axiom,
! [X_1,Xs] :
( hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt) = rev_Ar955429983le_alt(Xs)
<=> Xs = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),nil_Ar1135217151le_alt) ) ).
fof(fact_494_replicate__app__Cons__same,axiom,
! [N_2,X_4,Xs_2] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(N_2,X_4)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_4),Xs_2)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_4),hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,replic1360561849le_alt(N_2,X_4)),Xs_2)) ).
fof(fact_495_rev_Osimps_I2_J,axiom,
! [X_3,Xs_1] : rev_Ar955429983le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_3),Xs_1)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,rev_Ar955429983le_alt(Xs_1)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_3),nil_Ar1135217151le_alt)) ).
fof(fact_496_rev__eq__Cons__iff,axiom,
! [Xs,Y_2,Ys_1] :
( rev_Ar955429983le_alt(Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),Ys_1)
<=> Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,rev_Ar955429983le_alt(Ys_1)),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,Y_2),nil_Ar1135217151le_alt)) ) ).
fof(fact_497_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> takeWh1545314552le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),rev_Ar955429983le_alt(Xs)) = rev_Ar955429983le_alt(tl_Arr314474198le_alt(dropWh1165804960le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),Xs))) ) ) ).
fof(fact_498_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,Xs))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> takeWh768831342le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),rev_Pr816629831le_alt(Xs)) = rev_Pr816629831le_alt(tl_Pro645285392le_alt(dropWh1957015750le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),Xs))) ) ) ).
fof(fact_499_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,Xs))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> takeWh1088896635e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),rev_Ar758908116e_indi(Xs)) = rev_Ar758908116e_indi(tl_Arr282712093e_indi(dropWh1417102291e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),Xs))) ) ) ).
fof(fact_500_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_list_bool_bool(distinct_bool,Xs))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),rev_bool(Xs)) = rev_bool(tl_bool(dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),Xs))) ) ) ).
fof(fact_501_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,Xs))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> takeWh1268567035t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),rev_fu580432980t_bool(Xs)) = rev_fu580432980t_bool(tl_fun1512606109t_bool(dropWh1122107731t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),Xs))) ) ) ).
fof(fact_502_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,Xs))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> takeWh572506194t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),rev_fu101184185t_bool(Xs)) = rev_fu101184185t_bool(tl_fun1131179056t_bool(dropWh193383674t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),Xs))) ) ) ).
fof(fact_503_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,Xs))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> takeWh1813199437t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),rev_fu313987494t_bool(Xs)) = rev_fu313987494t_bool(tl_fun542205423t_bool(dropWh2056378277t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),Xs))) ) ) ).
fof(fact_504_takeWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,Xs))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> takeWh808795006le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),rev_Pr1722970583le_alt(Xs)) = rev_Pr1722970583le_alt(tl_Pro1439282464le_alt(dropWh1186971862le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),Xs))) ) ) ).
fof(fact_505_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> dropWh1165804960le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),rev_Ar955429983le_alt(Xs)) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),rev_Ar955429983le_alt(takeWh1545314552le_alt(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,fNot),hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,fequal21574094le_alt),X_1)),Xs))) ) ) ).
fof(fact_506_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,Xs))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> dropWh1957015750le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),rev_Pr816629831le_alt(Xs)) = hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),rev_Pr816629831le_alt(takeWh768831342le_alt(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,fNot),hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,fequal1025934616le_alt),X_1)),Xs))) ) ) ).
fof(fact_507_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,Xs))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> dropWh1417102291e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),rev_Ar758908116e_indi(Xs)) = hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),rev_Ar758908116e_indi(takeWh1088896635e_indi(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,fNot),hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,fequal2012472101e_indi),X_1)),Xs))) ) ) ).
fof(fact_508_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_list_bool_bool(distinct_bool,Xs))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> dropWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),rev_bool(Xs)) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),rev_bool(takeWhile_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,fNot),hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,fequal_bool),X_1)),Xs))) ) ) ).
fof(fact_509_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,Xs))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> dropWh1122107731t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),rev_fu580432980t_bool(Xs)) = hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),rev_fu580432980t_bool(takeWh1268567035t_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,fNot),hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,fequal547890341t_bool),X_1)),Xs))) ) ) ).
fof(fact_510_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,Xs))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> dropWh193383674t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),rev_fu101184185t_bool(Xs)) = hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),rev_fu101184185t_bool(takeWh572506194t_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,fNot),hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,fequal318101288t_bool),X_1)),Xs))) ) ) ).
fof(fact_511_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,Xs))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> dropWh2056378277t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),rev_fu313987494t_bool(Xs)) = hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),rev_fu313987494t_bool(takeWh1813199437t_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,fNot),hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,fequal1289369847t_bool),X_1)),Xs))) ) ) ).
fof(fact_512_dropWhile__neq__rev,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,Xs))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> dropWh1186971862le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),rev_Pr1722970583le_alt(Xs)) = hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),rev_Pr1722970583le_alt(takeWh808795006le_alt(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,fNot),hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,fequal1881358376le_alt),X_1)),Xs))) ) ) ).
fof(fact_513_drop__Cons,axiom,
! [N,X_1,Xs] : hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)) = nat_ca247420624le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs),hAPP_l1244209582le_alt(hAPP_f1660378693le_alt(cOMBC_1158490499le_alt,drop_A1195732799le_alt),Xs),N) ).
fof(fact_514_rev__foldl__cons,axiom,
! [Xs] : rev_Ar955429983le_alt(Xs) = foldl_107212092le_alt(hAPP_f18365135le_alt(cOMBC_1169281096le_alt,cons_A77766063le_alt),nil_Ar1135217151le_alt,Xs) ).
fof(fact_515_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(hAPP_l372964747le_alt(hAPP_n344665784le_alt(drop_A1195732799le_alt,N),Xs))))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) ) ).
fof(fact_516_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(hAPP_l182884309le_alt(hAPP_n323901960le_alt(drop_P635442535le_alt,N),Xs))))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) ) ).
fof(fact_517_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(hAPP_l1557274901e_indi(hAPP_n568645704e_indi(drop_A1853358580e_indi,N),Xs))))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) ) ).
fof(fact_518_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(hAPP_l1189022293t_bool(hAPP_n479129736t_bool(drop_bool,N),Xs))))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) ) ).
fof(fact_519_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(hAPP_l1149974805t_bool(hAPP_n587545160t_bool(drop_f1274868084t_bool,N),Xs))))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) ) ).
fof(fact_520_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(hAPP_l342779967t_bool(hAPP_n2058955628t_bool(drop_f1849462169t_bool,N),Xs))))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) ) ).
fof(fact_521_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(hAPP_l1130749077t_bool(hAPP_n2099236808t_bool(drop_f1584869062t_bool,N),Xs))))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) ) ).
fof(fact_522_in__set__dropD,axiom,
! [X_1,N,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(hAPP_l850073941le_alt(hAPP_n2100915976le_alt(drop_P1440509687le_alt,N),Xs))))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) ) ).
fof(fact_523_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(takeWh1545314552le_alt(Pa,Xs))))
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
& hBOOL(hAPP_A1120018583t_bool(Pa,X_1)) ) ) ).
fof(fact_524_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(takeWh768831342le_alt(Pa,Xs))))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
& hBOOL(hAPP_P1373277879t_bool(Pa,X_1)) ) ) ).
fof(fact_525_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(takeWh1088896635e_indi(Pa,Xs))))
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
& hBOOL(hAPP_A416869060i_bool(Pa,X_1)) ) ) ).
fof(fact_526_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(takeWhile_bool(Pa,Xs))))
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
& hBOOL(hAPP_bool_bool(Pa,X_1)) ) ) ).
fof(fact_527_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(takeWh1268567035t_bool(Pa,Xs))))
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
& hBOOL(hAPP_f446648900l_bool(Pa,X_1)) ) ) ).
fof(fact_528_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(takeWh572506194t_bool(Pa,Xs))))
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
& hBOOL(hAPP_f1733357041l_bool(Pa,X_1)) ) ) ).
fof(fact_529_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(takeWh1813199437t_bool(Pa,Xs))))
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
& hBOOL(hAPP_f1378099862l_bool(Pa,X_1)) ) ) ).
fof(fact_530_set__takeWhileD,axiom,
! [X_1,Pa,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(takeWh808795006le_alt(Pa,Xs))))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
& hBOOL(hAPP_P1813625415t_bool(Pa,X_1)) ) ) ).
fof(fact_531_takeWhile__eq__all__conv,axiom,
! [Pa,Xs] :
( takeWh1545314552le_alt(Pa,Xs) = Xs
<=> ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs)))
=> hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) ) ) ) ).
fof(fact_532_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(Xs))))
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs))) ) ).
fof(fact_533_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(Xs))))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs))) ) ).
fof(fact_534_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(Xs))))
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs))) ) ).
fof(fact_535_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Xs))))
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs))) ) ).
fof(fact_536_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(Xs))))
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs))) ) ).
fof(fact_537_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(Xs))))
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs))) ) ).
fof(fact_538_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(Xs))))
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs))) ) ).
fof(fact_539_in__set__butlastD,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(Xs))))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs))) ) ).
fof(fact_540_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( ( is_Arr723427730le_alt(Y_2)
& is_Arr723427730le_alt(X_1) )
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,Y_2),set_Ar426477344le_alt(hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,Y_2),set_Ar426477344le_alt(Xs))) ) ) ) ).
fof(fact_541_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,Y_2),set_Pr1756729158le_alt(hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,Y_2),set_Pr1756729158le_alt(Xs))) ) ) ).
fof(fact_542_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( ( is_Arr859726945e_indi(Y_2)
& is_Arr859726945e_indi(X_1) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),set_Ar1035526739e_indi(hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,Y_2),set_Ar1035526739e_indi(Xs))) ) ) ) ).
fof(fact_543_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs))))
=> ( ( hBOOL(Y_2)
<=> hBOOL(X_1) )
| hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,Y_2),set_bool(Xs))) ) ) ).
fof(fact_544_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( ( is_fun48324065t_bool(Y_2)
& is_fun48324065t_bool(X_1) )
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Y_2),set_fu1433968595t_bool(hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,Y_2),set_fu1433968595t_bool(Xs))) ) ) ) ).
fof(fact_545_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( ( is_fun20916972t_bool(Y_2)
& is_fun20916972t_bool(X_1) )
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Y_2),set_fu444796538t_bool(hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,Y_2),set_fu444796538t_bool(Xs))) ) ) ) ).
fof(fact_546_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( ( is_fun1264457267t_bool(Y_2)
& is_fun1264457267t_bool(X_1) )
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Y_2),set_fu222164517t_bool(hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,Y_2),set_fu222164517t_bool(Xs))) ) ) ) ).
fof(fact_547_set__ConsD,axiom,
! [Y_2,X_1,Xs] :
( ( is_Pro1004667236le_alt(Y_2)
& is_Pro1004667236le_alt(X_1) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Y_2),set_Pr2031705942le_alt(hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs))))
=> ( Y_2 = X_1
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,Y_2),set_Pr2031705942le_alt(Xs))) ) ) ) ).
fof(fact_548_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> insert1969589781le_alt(X_1,Xs) = Xs ) ).
fof(fact_549_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> insert531176721le_alt(X_1,Xs) = Xs ) ).
fof(fact_550_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> insert1731565726e_indi(X_1,Xs) = Xs ) ).
fof(fact_551_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> insert_bool(X_1,Xs) = Xs ) ).
fof(fact_552_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> insert897399838t_bool(X_1,Xs) = Xs ) ).
fof(fact_553_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> insert1409495663t_bool(X_1,Xs) = Xs ) ).
fof(fact_554_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> insert22093680t_bool(X_1,Xs) = Xs ) ).
fof(fact_555_in__set__insert,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> insert1683711393le_alt(X_1,Xs) = Xs ) ).
fof(fact_556_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
& hBOOL(hAPP_l300482276t_bool(distin85347314le_alt,Xs)) ) ) ).
fof(fact_557_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
& hBOOL(hAPP_l1642116416t_bool(distin1906002420le_alt,Xs)) ) ) ).
fof(fact_558_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
& hBOOL(hAPP_l479254477i_bool(distin26300929e_indi,Xs)) ) ) ).
fof(fact_559_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_list_bool_bool(distinct_bool,hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
& hBOOL(hAPP_list_bool_bool(distinct_bool,Xs)) ) ) ).
fof(fact_560_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
& hBOOL(hAPP_l1936415565l_bool(distin943033217t_bool,Xs)) ) ) ).
fof(fact_561_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
& hBOOL(hAPP_l1684828478l_bool(distin751056204t_bool,Xs)) ) ) ).
fof(fact_562_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
& hBOOL(hAPP_l4338847l_bool(distin526492627t_bool,Xs)) ) ) ).
fof(fact_563_distinct_Osimps_I2_J,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs)))
<=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
& hBOOL(hAPP_l548550096t_bool(distin135982852le_alt,Xs)) ) ) ).
fof(fact_564_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> ( ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = takeWh1545314552le_alt(Pa,Xs) ) ) ).
fof(fact_565_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> ( ~ hBOOL(hAPP_P1373277879t_bool(Pa,X_1))
=> takeWh768831342le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)) = takeWh768831342le_alt(Pa,Xs) ) ) ).
fof(fact_566_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> ( ~ hBOOL(hAPP_A416869060i_bool(Pa,X_1))
=> takeWh1088896635e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = takeWh1088896635e_indi(Pa,Xs) ) ) ).
fof(fact_567_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> ( ~ hBOOL(hAPP_bool_bool(Pa,X_1))
=> takeWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = takeWhile_bool(Pa,Xs) ) ) ).
fof(fact_568_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> ( ~ hBOOL(hAPP_f446648900l_bool(Pa,X_1))
=> takeWh1268567035t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)) = takeWh1268567035t_bool(Pa,Xs) ) ) ).
fof(fact_569_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(Pa,X_1))
=> takeWh572506194t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1)) = takeWh572506194t_bool(Pa,Xs) ) ) ).
fof(fact_570_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> ( ~ hBOOL(hAPP_f1378099862l_bool(Pa,X_1))
=> takeWh1813199437t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)) = takeWh1813199437t_bool(Pa,Xs) ) ) ).
fof(fact_571_takeWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> ( ~ hBOOL(hAPP_P1813625415t_bool(Pa,X_1))
=> takeWh808795006le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1)) = takeWh808795006le_alt(Pa,Xs) ) ) ).
fof(fact_572_last__in__set,axiom,
! [As] :
( As != nil_Ar1135217151le_alt
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,last_A1066338328le_alt(As)),set_Ar426477344le_alt(As))) ) ).
fof(fact_573_last__in__set,axiom,
! [As] :
( As != nil_Pr1710246567le_alt
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,last_P1076199502le_alt(As)),set_Pr1756729158le_alt(As))) ) ).
fof(fact_574_last__in__set,axiom,
! [As] :
( As != nil_Ar637146932e_indi
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,last_A560832347e_indi(As)),set_Ar1035526739e_indi(As))) ) ).
fof(fact_575_last__in__set,axiom,
! [As] :
( As != nil_bool
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,last_bool(As)),set_bool(As))) ) ).
fof(fact_576_last__in__set,axiom,
! [As] :
( As != nil_fu1180010164t_bool
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,last_f584510683t_bool(As)),set_fu1433968595t_bool(As))) ) ).
fof(fact_577_last__in__set,axiom,
! [As] :
( As != nil_fu1714546777t_bool
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,last_f1172522866t_bool(As)),set_fu444796538t_bool(As))) ) ).
fof(fact_578_last__in__set,axiom,
! [As] :
( As != nil_fu247759878t_bool
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,last_f1921219373t_bool(As)),set_fu222164517t_bool(As))) ) ).
fof(fact_579_last__in__set,axiom,
! [As] :
( As != nil_Pr1368032311le_alt
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,last_P15572062le_alt(As)),set_Pr2031705942le_alt(As))) ) ).
fof(fact_580_dropWhile__eq__Nil__conv,axiom,
! [Pa,Xs] :
( dropWh1165804960le_alt(Pa,Xs) = nil_Ar1135217151le_alt
<=> ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs)))
=> hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) ) ) ) ).
fof(fact_581_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(Xs))))
| hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(Ys_1)))) )
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(butlas123970891le_alt(hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1))))) ) ).
fof(fact_582_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(Xs))))
| hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(Ys_1)))) )
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(butlas1808913499le_alt(hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1))))) ) ).
fof(fact_583_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(Xs))))
| hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(Ys_1)))) )
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(butlas1811107560e_indi(hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1))))) ) ).
fof(fact_584_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Xs))))
| hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(Ys_1)))) )
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(butlast_bool(hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1))))) ) ).
fof(fact_585_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(Xs))))
| hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(Ys_1)))) )
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(butlas423814760t_bool(hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1))))) ) ).
fof(fact_586_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(Xs))))
| hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(Ys_1)))) )
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(butlas217264037t_bool(hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1))))) ) ).
fof(fact_587_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(Xs))))
| hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(Ys_1)))) )
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(butlas813551546t_bool(hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1))))) ) ).
fof(fact_588_in__set__butlast__appendI,axiom,
! [Ys_1,X_1,Xs] :
( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(Xs))))
| hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(Ys_1)))) )
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(butlas1168145387le_alt(hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1))))) ) ).
fof(fact_589_hd__in__set,axiom,
! [Xs] :
( Xs != nil_Ar1135217151le_alt
=> hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,hd_Arr1814706386le_alt(Xs)),set_Ar426477344le_alt(Xs))) ) ).
fof(fact_590_hd__in__set,axiom,
! [Xs] :
( Xs != nil_Pr1710246567le_alt
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hd_Pro53798164le_alt(Xs)),set_Pr1756729158le_alt(Xs))) ) ).
fof(fact_591_hd__in__set,axiom,
! [Xs] :
( Xs != nil_Ar637146932e_indi
=> hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,hd_Arr1280875809e_indi(Xs)),set_Ar1035526739e_indi(Xs))) ) ).
fof(fact_592_hd__in__set,axiom,
! [Xs] :
( Xs != nil_bool
=> hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,hd_bool(Xs)),set_bool(Xs))) ) ).
fof(fact_593_hd__in__set,axiom,
! [Xs] :
( Xs != nil_fu1180010164t_bool
=> hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,hd_fun1289819809t_bool(Xs)),set_fu1433968595t_bool(Xs))) ) ).
fof(fact_594_hd__in__set,axiom,
! [Xs] :
( Xs != nil_fu1714546777t_bool
=> hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,hd_fun1937506860t_bool(Xs)),set_fu444796538t_bool(Xs))) ) ).
fof(fact_595_hd__in__set,axiom,
! [Xs] :
( Xs != nil_fu247759878t_bool
=> hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,hd_fun780865267t_bool(Xs)),set_fu222164517t_bool(Xs))) ) ).
fof(fact_596_hd__in__set,axiom,
! [Xs] :
( Xs != nil_Pr1368032311le_alt
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hd_Pro804272676le_alt(Xs)),set_Pr2031705942le_alt(Xs))) ) ).
fof(fact_597_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> ( ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_1))
=> dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,dropWh1165804960le_alt(Pa,Xs)),Ys_1) ) ) ).
fof(fact_598_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> ( ~ hBOOL(hAPP_P1373277879t_bool(Pa,X_1))
=> dropWh1957015750le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)) = hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,dropWh1957015750le_alt(Pa,Xs)),Ys_1) ) ) ).
fof(fact_599_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> ( ~ hBOOL(hAPP_A416869060i_bool(Pa,X_1))
=> dropWh1417102291e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,dropWh1417102291e_indi(Pa,Xs)),Ys_1) ) ) ).
fof(fact_600_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> ( ~ hBOOL(hAPP_bool_bool(Pa,X_1))
=> dropWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,dropWhile_bool(Pa,Xs)),Ys_1) ) ) ).
fof(fact_601_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> ( ~ hBOOL(hAPP_f446648900l_bool(Pa,X_1))
=> dropWh1122107731t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)) = hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,dropWh1122107731t_bool(Pa,Xs)),Ys_1) ) ) ).
fof(fact_602_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> ( ~ hBOOL(hAPP_f1733357041l_bool(Pa,X_1))
=> dropWh193383674t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1)) = hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,dropWh193383674t_bool(Pa,Xs)),Ys_1) ) ) ).
fof(fact_603_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> ( ~ hBOOL(hAPP_f1378099862l_bool(Pa,X_1))
=> dropWh2056378277t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)) = hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,dropWh2056378277t_bool(Pa,Xs)),Ys_1) ) ) ).
fof(fact_604_dropWhile__append1,axiom,
! [Ys_1,Pa,X_1,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> ( ~ hBOOL(hAPP_P1813625415t_bool(Pa,X_1))
=> dropWh1186971862le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1)) = hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,dropWh1186971862le_alt(Pa,Xs)),Ys_1) ) ) ).
fof(fact_605_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> insert1969589781le_alt(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> insert1969589781le_alt(X_1,Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) ) ) ).
fof(fact_606_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> insert531176721le_alt(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> insert531176721le_alt(X_1,Xs) = hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs) ) ) ).
fof(fact_607_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> insert1731565726e_indi(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> insert1731565726e_indi(X_1,Xs) = hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs) ) ) ).
fof(fact_608_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> insert_bool(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> insert_bool(X_1,Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) ) ) ).
fof(fact_609_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> insert897399838t_bool(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> insert897399838t_bool(X_1,Xs) = hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs) ) ) ).
fof(fact_610_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> insert1409495663t_bool(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> insert1409495663t_bool(X_1,Xs) = hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs) ) ) ).
fof(fact_611_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> insert22093680t_bool(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> insert22093680t_bool(X_1,Xs) = hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs) ) ) ).
fof(fact_612_List_Oinsert__def,axiom,
! [X_1,Xs] :
( ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> insert1683711393le_alt(X_1,Xs) = Xs )
& ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> insert1683711393le_alt(X_1,Xs) = hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs) ) ) ).
fof(fact_613_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_1),set_Ar426477344le_alt(Xs)))
=> insert1969589781le_alt(X_1,Xs) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_1),Xs) ) ).
fof(fact_614_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_1),set_Pr1756729158le_alt(Xs)))
=> insert531176721le_alt(X_1,Xs) = hAPP_l182884309le_alt(hAPP_P469465955le_alt(cons_P1245424375le_alt,X_1),Xs) ) ).
fof(fact_615_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_1),set_Ar1035526739e_indi(Xs)))
=> insert1731565726e_indi(X_1,Xs) = hAPP_l1557274901e_indi(hAPP_A273991894e_indi(cons_A920022916e_indi,X_1),Xs) ) ).
fof(fact_616_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_1),set_bool(Xs)))
=> insert_bool(X_1,Xs) = hAPP_l1189022293t_bool(hAPP_b994696797t_bool(cons_bool,X_1),Xs) ) ).
fof(fact_617_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_1),set_fu1433968595t_bool(Xs)))
=> insert897399838t_bool(X_1,Xs) = hAPP_l1149974805t_bool(hAPP_f597269334t_bool(cons_f1113423620t_bool,X_1),Xs) ) ).
fof(fact_618_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
=> insert1409495663t_bool(X_1,Xs) = hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Xs) ) ).
fof(fact_619_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
=> insert22093680t_bool(X_1,Xs) = hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Xs) ) ).
fof(fact_620_not__in__set__insert,axiom,
! [X_1,Xs] :
( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
=> insert1683711393le_alt(X_1,Xs) = hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Xs) ) ).
fof(fact_621_partition__P,axiom,
! [Pa,Xs,Yes,No] :
( partit1336600824le_alt(Pa,Xs) = hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Yes),No)
=> ( ! [X_2] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Yes)))
=> hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) )
& ! [X_2] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(No)))
=> ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) ) ) ) ).
fof(fact_622_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_Arr723427730le_alt(X_2)
& is_Arr723427730le_alt(Y_1)
& is_Arr723427730le_alt(Z) )
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs)))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,Y_1),Z)),R_1))
=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Ys_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Ys_1),Zs_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1)))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Xs),Zs_1)),hAPP_f1681297285t_bool(lexord807118444le_alt,R_1))) ) ) ) ).
fof(fact_623_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( hBOOL(hAPP_f1472889102l_bool(hAPP_l1197505987l_bool(member1245674225le_alt,X_2),set_li1879521523le_alt(Xs)))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,Y_1),Z)),R_1))
=> hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,hAPP_l591780830le_alt(hAPP_l1148780281le_alt(produc2031778509le_alt,X_2),Z)),R_1)) ) ) )
=> ( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Ys_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1)))
=> ( hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Ys_1),Zs_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1)))
=> hBOOL(hAPP_f2099712241l_bool(hAPP_P142941065l_bool(member694465108le_alt,hAPP_l2112442743le_alt(hAPP_l400262709le_alt(produc1707341143le_alt,Xs),Zs_1)),hAPP_f664322981t_bool(lexord717456039le_alt,R_1))) ) ) ) ).
fof(fact_624_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),set_Pr1756729158le_alt(Xs)))
=> ( hBOOL(hAPP_f704486919l_bool(hAPP_P1992806581l_bool(member985525226le_alt,hAPP_P937918807le_alt(hAPP_P1109943007le_alt(produc218110963le_alt,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f704486919l_bool(hAPP_P1992806581l_bool(member985525226le_alt,hAPP_P937918807le_alt(hAPP_P1109943007le_alt(produc218110963le_alt,Y_1),Z)),R_1))
=> hBOOL(hAPP_f704486919l_bool(hAPP_P1992806581l_bool(member985525226le_alt,hAPP_P937918807le_alt(hAPP_P1109943007le_alt(produc218110963le_alt,X_2),Z)),R_1)) ) ) )
=> ( hBOOL(hAPP_f2078996785l_bool(hAPP_P1085061129l_bool(member1805745300le_alt,hAPP_l1556767370le_alt(hAPP_l1615793307le_alt(produc499297815le_alt,Xs),Ys_1)),hAPP_f304790207t_bool(lexord170366202le_alt,R_1)))
=> ( hBOOL(hAPP_f2078996785l_bool(hAPP_P1085061129l_bool(member1805745300le_alt,hAPP_l1556767370le_alt(hAPP_l1615793307le_alt(produc499297815le_alt,Ys_1),Zs_1)),hAPP_f304790207t_bool(lexord170366202le_alt,R_1)))
=> hBOOL(hAPP_f2078996785l_bool(hAPP_P1085061129l_bool(member1805745300le_alt,hAPP_l1556767370le_alt(hAPP_l1615793307le_alt(produc499297815le_alt,Xs),Zs_1)),hAPP_f304790207t_bool(lexord170366202le_alt,R_1))) ) ) ) ).
fof(fact_625_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_Arr859726945e_indi(X_2)
& is_Arr859726945e_indi(Y_1)
& is_Arr859726945e_indi(Z) )
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),set_Ar1035526739e_indi(Xs)))
=> ( hBOOL(hAPP_f511649569l_bool(hAPP_P1435933929l_bool(member258426884e_indi,hAPP_A2054143614e_indi(hAPP_A785351481e_indi(produc2070216205e_indi,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f511649569l_bool(hAPP_P1435933929l_bool(member258426884e_indi,hAPP_A2054143614e_indi(hAPP_A785351481e_indi(produc2070216205e_indi,Y_1),Z)),R_1))
=> hBOOL(hAPP_f511649569l_bool(hAPP_P1435933929l_bool(member258426884e_indi,hAPP_A2054143614e_indi(hAPP_A785351481e_indi(produc2070216205e_indi,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f1140617841l_bool(hAPP_P173682825l_bool(member912023252e_indi,hAPP_l2129529815e_indi(hAPP_l1484722549e_indi(produc1849892183e_indi,Xs),Ys_1)),hAPP_f695049061i_bool(lexord1918670343e_indi,R_1)))
=> ( hBOOL(hAPP_f1140617841l_bool(hAPP_P173682825l_bool(member912023252e_indi,hAPP_l2129529815e_indi(hAPP_l1484722549e_indi(produc1849892183e_indi,Ys_1),Zs_1)),hAPP_f695049061i_bool(lexord1918670343e_indi,R_1)))
=> hBOOL(hAPP_f1140617841l_bool(hAPP_P173682825l_bool(member912023252e_indi,hAPP_l2129529815e_indi(hAPP_l1484722549e_indi(produc1849892183e_indi,Xs),Zs_1)),hAPP_f695049061i_bool(lexord1918670343e_indi,R_1))) ) ) ) ).
fof(fact_626_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_bool(X_2)
& is_bool(Y_1)
& is_bool(Z) )
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs)))
=> ( hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,Y_1),Z)),R_1))
=> hBOOL(hAPP_f1098788115l_bool(hAPP_P738148045l_bool(member624253174l_bool,hAPP_b2048821609l_bool(hAPP_b1115999851l_bool(produc1246214911l_bool,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs),Ys_1)),hAPP_f1114274611l_bool(lexord_bool,R_1)))
=> ( hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Ys_1),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_1)))
=> hBOOL(hAPP_f263022001l_bool(hAPP_P1870454025l_bool(member1058364180t_bool,hAPP_l1349316624t_bool(hAPP_l218095399t_bool(produc1067887767t_bool,Xs),Zs_1)),hAPP_f1114274611l_bool(lexord_bool,R_1))) ) ) ) ).
fof(fact_627_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_fun48324065t_bool(X_2)
& is_fun48324065t_bool(Y_1)
& is_fun48324065t_bool(Z) )
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),set_fu1433968595t_bool(Xs)))
=> ( hBOOL(hAPP_f140107297l_bool(hAPP_P1099469545l_bool(member205384452t_bool,hAPP_f38433022t_bool(hAPP_f1596466233t_bool(produc882973453t_bool,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f140107297l_bool(hAPP_P1099469545l_bool(member205384452t_bool,hAPP_f38433022t_bool(hAPP_f1596466233t_bool(produc882973453t_bool,Y_1),Z)),R_1))
=> hBOOL(hAPP_f140107297l_bool(hAPP_P1099469545l_bool(member205384452t_bool,hAPP_f38433022t_bool(hAPP_f1596466233t_bool(produc882973453t_bool,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f1456773233l_bool(hAPP_P776750217l_bool(member200634580t_bool,hAPP_l1242238295t_bool(hAPP_l1784712821t_bool(produc49085783t_bool,Xs),Ys_1)),hAPP_f357296741l_bool(lexord1145600903t_bool,R_1)))
=> ( hBOOL(hAPP_f1456773233l_bool(hAPP_P776750217l_bool(member200634580t_bool,hAPP_l1242238295t_bool(hAPP_l1784712821t_bool(produc49085783t_bool,Ys_1),Zs_1)),hAPP_f357296741l_bool(lexord1145600903t_bool,R_1)))
=> hBOOL(hAPP_f1456773233l_bool(hAPP_P776750217l_bool(member200634580t_bool,hAPP_l1242238295t_bool(hAPP_l1784712821t_bool(produc49085783t_bool,Xs),Zs_1)),hAPP_f357296741l_bool(lexord1145600903t_bool,R_1))) ) ) ) ).
fof(fact_628_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_fun20916972t_bool(X_2)
& is_fun20916972t_bool(Y_1)
& is_fun20916972t_bool(Z) )
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),set_fu444796538t_bool(Xs)))
=> ( hBOOL(hAPP_f891725169l_bool(hAPP_P1919864457l_bool(member2100323796t_bool,hAPP_f1265889019t_bool(hAPP_f1999636669t_bool(produc1802651735t_bool,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f891725169l_bool(hAPP_P1919864457l_bool(member2100323796t_bool,hAPP_f1265889019t_bool(hAPP_f1999636669t_bool(produc1802651735t_bool,Y_1),Z)),R_1))
=> hBOOL(hAPP_f891725169l_bool(hAPP_P1919864457l_bool(member2100323796t_bool,hAPP_f1265889019t_bool(hAPP_f1999636669t_bool(produc1802651735t_bool,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f1422872597l_bool(hAPP_P328558801l_bool(member1477971960t_bool,hAPP_l839073004t_bool(hAPP_l131013165t_bool(produc1134856577t_bool,Xs),Ys_1)),hAPP_f2031254713l_bool(lexord1692326342t_bool,R_1)))
=> ( hBOOL(hAPP_f1422872597l_bool(hAPP_P328558801l_bool(member1477971960t_bool,hAPP_l839073004t_bool(hAPP_l131013165t_bool(produc1134856577t_bool,Ys_1),Zs_1)),hAPP_f2031254713l_bool(lexord1692326342t_bool,R_1)))
=> hBOOL(hAPP_f1422872597l_bool(hAPP_P328558801l_bool(member1477971960t_bool,hAPP_l839073004t_bool(hAPP_l131013165t_bool(produc1134856577t_bool,Xs),Zs_1)),hAPP_f2031254713l_bool(lexord1692326342t_bool,R_1))) ) ) ) ).
fof(fact_629_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_fun1264457267t_bool(X_2)
& is_fun1264457267t_bool(Y_1)
& is_fun1264457267t_bool(Z) )
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),set_fu222164517t_bool(Xs)))
=> ( hBOOL(hAPP_f1508705733l_bool(hAPP_P1374173745l_bool(member1765007528t_bool,hAPP_f1639289588t_bool(hAPP_f1785736029t_bool(produc999701681t_bool,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f1508705733l_bool(hAPP_P1374173745l_bool(member1765007528t_bool,hAPP_f1639289588t_bool(hAPP_f1785736029t_bool(produc999701681t_bool,Y_1),Z)),R_1))
=> hBOOL(hAPP_f1508705733l_bool(hAPP_P1374173745l_bool(member1765007528t_bool,hAPP_f1639289588t_bool(hAPP_f1785736029t_bool(produc999701681t_bool,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f288803825l_bool(hAPP_P981043081l_bool(member976989780t_bool,hAPP_l607015721t_bool(hAPP_l1064263321t_bool(produc436944087t_bool,Xs),Ys_1)),hAPP_f363884353l_bool(lexord373145049t_bool,R_1)))
=> ( hBOOL(hAPP_f288803825l_bool(hAPP_P981043081l_bool(member976989780t_bool,hAPP_l607015721t_bool(hAPP_l1064263321t_bool(produc436944087t_bool,Ys_1),Zs_1)),hAPP_f363884353l_bool(lexord373145049t_bool,R_1)))
=> hBOOL(hAPP_f288803825l_bool(hAPP_P981043081l_bool(member976989780t_bool,hAPP_l607015721t_bool(hAPP_l1064263321t_bool(produc436944087t_bool,Xs),Zs_1)),hAPP_f363884353l_bool(lexord373145049t_bool,R_1))) ) ) ) ).
fof(fact_630_lexord__partial__trans,axiom,
! [Zs_1,Ys_1,R_1,Xs] :
( ! [X_2,Y_1,Z] :
( ( is_Pro1004667236le_alt(X_2)
& is_Pro1004667236le_alt(Y_1)
& is_Pro1004667236le_alt(Z) )
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),set_Pr2031705942le_alt(Xs)))
=> ( hBOOL(hAPP_f1720639399l_bool(hAPP_P626359285l_bool(member852432522le_alt,hAPP_P29732487le_alt(hAPP_P1725284223le_alt(produc744410643le_alt,X_2),Y_1)),R_1))
=> ( hBOOL(hAPP_f1720639399l_bool(hAPP_P626359285l_bool(member852432522le_alt,hAPP_P29732487le_alt(hAPP_P1725284223le_alt(produc744410643le_alt,Y_1),Z)),R_1))
=> hBOOL(hAPP_f1720639399l_bool(hAPP_P626359285l_bool(member852432522le_alt,hAPP_P29732487le_alt(hAPP_P1725284223le_alt(produc744410643le_alt,X_2),Z)),R_1)) ) ) ) )
=> ( hBOOL(hAPP_f1342253361l_bool(hAPP_P585301513l_bool(member1353676180le_alt,hAPP_l309028378le_alt(hAPP_l794402875le_alt(produc1787549079le_alt,Xs),Ys_1)),hAPP_f846944031t_bool(lexord1008325386le_alt,R_1)))
=> ( hBOOL(hAPP_f1342253361l_bool(hAPP_P585301513l_bool(member1353676180le_alt,hAPP_l309028378le_alt(hAPP_l794402875le_alt(produc1787549079le_alt,Ys_1),Zs_1)),hAPP_f846944031t_bool(lexord1008325386le_alt,R_1)))
=> hBOOL(hAPP_f1342253361l_bool(hAPP_P585301513l_bool(member1353676180le_alt,hAPP_l309028378le_alt(hAPP_l794402875le_alt(produc1787549079le_alt,Xs),Zs_1)),hAPP_f846944031t_bool(lexord1008325386le_alt,R_1))) ) ) ) ).
fof(fact_631_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs)))
=> hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) ) )
=> dropWh1165804960le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = dropWh1165804960le_alt(Pa,Ys_1) ) ).
fof(fact_632_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),set_Pr1756729158le_alt(Xs)))
=> hBOOL(hAPP_P1373277879t_bool(Pa,X_2)) )
=> dropWh1957015750le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)) = dropWh1957015750le_alt(Pa,Ys_1) ) ).
fof(fact_633_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),set_Ar1035526739e_indi(Xs)))
=> hBOOL(hAPP_A416869060i_bool(Pa,X_2)) ) )
=> dropWh1417102291e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = dropWh1417102291e_indi(Pa,Ys_1) ) ).
fof(fact_634_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs)))
=> hBOOL(hAPP_bool_bool(Pa,X_2)) ) )
=> dropWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = dropWhile_bool(Pa,Ys_1) ) ).
fof(fact_635_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),set_fu1433968595t_bool(Xs)))
=> hBOOL(hAPP_f446648900l_bool(Pa,X_2)) ) )
=> dropWh1122107731t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)) = dropWh1122107731t_bool(Pa,Ys_1) ) ).
fof(fact_636_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),set_fu444796538t_bool(Xs)))
=> hBOOL(hAPP_f1733357041l_bool(Pa,X_2)) ) )
=> dropWh193383674t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1)) = dropWh193383674t_bool(Pa,Ys_1) ) ).
fof(fact_637_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),set_fu222164517t_bool(Xs)))
=> hBOOL(hAPP_f1378099862l_bool(Pa,X_2)) ) )
=> dropWh2056378277t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)) = dropWh2056378277t_bool(Pa,Ys_1) ) ).
fof(fact_638_dropWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),set_Pr2031705942le_alt(Xs)))
=> hBOOL(hAPP_P1813625415t_bool(Pa,X_2)) ) )
=> dropWh1186971862le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1)) = dropWh1186971862le_alt(Pa,Ys_1) ) ).
fof(fact_639_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_Arr723427730le_alt(X_2)
=> ( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs)))
=> hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) ) )
=> takeWh1545314552le_alt(Pa,hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),Ys_1)) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Xs),takeWh1545314552le_alt(Pa,Ys_1)) ) ).
fof(fact_640_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( hBOOL(hAPP_f890578273l_bool(hAPP_P2032392041l_bool(member1373125444le_alt,X_2),set_Pr1756729158le_alt(Xs)))
=> hBOOL(hAPP_P1373277879t_bool(Pa,X_2)) )
=> takeWh768831342le_alt(Pa,hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),Ys_1)) = hAPP_l182884309le_alt(hAPP_l2076130586le_alt(append1768277586le_alt,Xs),takeWh768831342le_alt(Pa,Ys_1)) ) ).
fof(fact_641_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_Arr859726945e_indi(X_2)
=> ( hBOOL(hAPP_f160177134l_bool(hAPP_A45661955l_bool(member161528657e_indi,X_2),set_Ar1035526739e_indi(Xs)))
=> hBOOL(hAPP_A416869060i_bool(Pa,X_2)) ) )
=> takeWh1088896635e_indi(Pa,hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),Ys_1)) = hAPP_l1557274901e_indi(hAPP_l203258125e_indi(append968919903e_indi,Xs),takeWh1088896635e_indi(Pa,Ys_1)) ) ).
fof(fact_642_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_bool(X_2)
=> ( hBOOL(hAPP_f387058535l_bool(hAPP_b1787118453l_bool(member_bool,X_2),set_bool(Xs)))
=> hBOOL(hAPP_bool_bool(Pa,X_2)) ) )
=> takeWhile_bool(Pa,hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),Ys_1)) = hAPP_l1189022293t_bool(hAPP_l1947611924t_bool(append_bool,Xs),takeWhile_bool(Pa,Ys_1)) ) ).
fof(fact_643_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_fun48324065t_bool(X_2)
=> ( hBOOL(hAPP_f322109294l_bool(hAPP_f881677315l_bool(member1619170513t_bool,X_2),set_fu1433968595t_bool(Xs)))
=> hBOOL(hAPP_f446648900l_bool(Pa,X_2)) ) )
=> takeWh1268567035t_bool(Pa,hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),Ys_1)) = hAPP_l1149974805t_bool(hAPP_l1032792973t_bool(append1480696031t_bool,Xs),takeWh1268567035t_bool(Pa,Ys_1)) ) ).
fof(fact_644_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_fun20916972t_bool(X_2)
=> ( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_2),set_fu444796538t_bool(Xs)))
=> hBOOL(hAPP_f1733357041l_bool(Pa,X_2)) ) )
=> takeWh572506194t_bool(Pa,hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),Ys_1)) = hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Xs),takeWh572506194t_bool(Pa,Ys_1)) ) ).
fof(fact_645_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_fun1264457267t_bool(X_2)
=> ( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_2),set_fu222164517t_bool(Xs)))
=> hBOOL(hAPP_f1378099862l_bool(Pa,X_2)) ) )
=> takeWh1813199437t_bool(Pa,hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),Ys_1)) = hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Xs),takeWh1813199437t_bool(Pa,Ys_1)) ) ).
fof(fact_646_takeWhile__append2,axiom,
! [Ys_1,Pa,Xs] :
( ! [X_2] :
( is_Pro1004667236le_alt(X_2)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_2),set_Pr2031705942le_alt(Xs)))
=> hBOOL(hAPP_P1813625415t_bool(Pa,X_2)) ) )
=> takeWh808795006le_alt(Pa,hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),Ys_1)) = hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Xs),takeWh808795006le_alt(Pa,Ys_1)) ) ).
fof(fact_647_split__list__propE,axiom,
! [Pa,Xs] :
( ? [X_2] :
( hBOOL(hAPP_f87553445l_bool(hAPP_A86021709l_bool(member2080870050le_alt,X_2),set_Ar426477344le_alt(Xs)))
& hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) )
=> ~ ! [Ys,X_2] :
( is_Arr723427730le_alt(X_2)
=> ( ? [Zs] : Xs = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(append28105492le_alt,Ys),hAPP_l372964747le_alt(hAPP_A1660609715le_alt(cons_A77766063le_alt,X_2),Zs))
=> ~ hBOOL(hAPP_A1120018583t_bool(Pa,X_2)) ) ) ) ).
fof(fact_648_in__set__conv__decomp,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f560517119l_bool(hAPP_f1332197581l_bool(member1704306684t_bool,X_1),set_fu444796538t_bool(Xs)))
<=> ? [Ys,Zs] : Xs = hAPP_l342779967t_bool(hAPP_l1392153600t_bool(append2131097198t_bool,Ys),hAPP_l342779967t_bool(hAPP_f1916337549t_bool(cons_f476294153t_bool,X_1),Zs)) ) ).
fof(fact_649_in__set__conv__decomp,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f147218624l_bool(hAPP_f621397159l_bool(member1265098019t_bool,X_1),set_fu222164517t_bool(Xs)))
<=> ? [Ys,Zs] : Xs = hAPP_l1130749077t_bool(hAPP_l1438053435t_bool(append352340785t_bool,Ys),hAPP_l1130749077t_bool(hAPP_f1337535236t_bool(cons_f160345174t_bool,X_1),Zs)) ) ).
fof(fact_650_in__set__conv__decomp,axiom,
! [X_1,Xs] :
( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,X_1),set_Pr2031705942le_alt(Xs)))
<=> ? [Ys,Zs] : Xs = hAPP_l850073941le_alt(hAPP_l595508106le_alt(append1735936098le_alt,Ys),hAPP_l850073941le_alt(hAPP_P465197523le_alt(cons_P272751751le_alt,X_1),Zs)) ) ).
fof(fact_651_termination__basic__simps_I5_J,axiom,
! [X,Y] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ) ).
fof(fact_652_lessI,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),suc(N_1))) ).
fof(fact_653_Suc__mono,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),suc(N_1))) ) ).
fof(fact_654_n__not__Suc__n,axiom,
! [N_1] : N_1 != suc(N_1) ).
fof(fact_655_Suc__n__not__n,axiom,
! [N_1] : suc(N_1) != N_1 ).
fof(fact_656_nat_Oinject,axiom,
! [Nat_1,Nat] :
( suc(Nat_1) = suc(Nat)
<=> Nat_1 = Nat ) ).
fof(fact_657_Suc__inject,axiom,
! [X,Y] :
( suc(X) = suc(Y)
=> X = Y ) ).
fof(fact_658_less__not__refl,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).
fof(fact_659_nat__neq__iff,axiom,
! [M,N] :
( M != N
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M)) ) ) ).
fof(fact_660_linorder__neqE__nat,axiom,
! [X,Y] :
( X != Y
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ) ).
fof(fact_661_less__irrefl__nat,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),N_1)) ).
fof(fact_662_less__not__refl2,axiom,
! [N_1,M_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))
=> M_1 != N_1 ) ).
fof(fact_663_less__not__refl3,axiom,
! [S,T] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
=> S != T ) ).
fof(fact_664_nat__less__cases,axiom,
! [Pa,M,N] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
=> ( ( M = N
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,N),M)) ) ) ) ).
fof(fact_665_le__refl,axiom,
! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)) ).
fof(fact_666_nat__le__linear,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1)) ) ).
fof(fact_667_eq__imp__le,axiom,
! [M_1,N_1] :
( M_1 = N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_668_le__trans,axiom,
! [K,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K)) ) ) ).
fof(fact_669_le__antisym,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_1))
=> M_1 = N_1 ) ) ).
fof(fact_670_Suc__less__SucD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),suc(N_1)))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).
fof(fact_671_Suc__lessD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).
fof(fact_672_less__SucE,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> M_1 = N_1 ) ) ).
fof(fact_673_less__trans__Suc,axiom,
! [K,I_1,J] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(I_1)),K)) ) ) ).
fof(fact_674_Suc__lessI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> ( suc(M_1) != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M_1)),N_1)) ) ) ).
fof(fact_675_less__SucI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1))) ) ).
fof(fact_676_less__antisym,axiom,
! [N_1,M_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),M_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N_1),suc(M_1)))
=> M_1 = N_1 ) ) ).
fof(fact_677_not__less__less__Suc__eq,axiom,
! [N,M] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M)))
<=> N = M ) ) ).
fof(fact_678_Suc__less__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,suc(M)),suc(N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_679_less__Suc__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),suc(N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
| M = N ) ) ).
fof(fact_680_not__less__eq,axiom,
! [M,N] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M))) ) ).
fof(fact_681_Suc__n__not__le__n,axiom,
! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N_1)),N_1)) ).
fof(fact_682_not__less__eq__eq,axiom,
! [M,N] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),M)) ) ).
fof(fact_683_le__Suc__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),suc(N)))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
| M = suc(N) ) ) ).
fof(fact_684_Suc__le__mono,axiom,
! [N,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),suc(M)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M)) ) ).
fof(fact_685_le__SucI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),suc(N_1))) ) ).
fof(fact_686_le__SucE,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),suc(N_1)))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> M_1 = suc(N_1) ) ) ).
fof(fact_687_Suc__leD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_688_less__or__eq__imp__le,axiom,
! [M_1,N_1] :
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
| M_1 = N_1 )
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_689_le__neq__implies__less,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> ( M_1 != N_1
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ) ).
fof(fact_690_less__imp__le__nat,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1)) ) ).
fof(fact_691_le__eq__less__or__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
| M = N ) ) ).
fof(fact_692_nat__less__le,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
& M != N ) ) ).
fof(fact_693_Suc__le__lessD,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1)) ) ).
fof(fact_694_le__less__Suc__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),suc(M)))
<=> N = M ) ) ).
fof(fact_695_Suc__leI,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M_1)),N_1)) ) ).
fof(fact_696_le__imp__less__Suc,axiom,
! [M_1,N_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N_1))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),suc(N_1))) ) ).
fof(fact_697_Suc__le__eq,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(M)),N))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),N)) ) ).
fof(fact_698_less__Suc__eq__le,axiom,
! [M,N] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),suc(N)))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),N)) ) ).
fof(fact_699_less__eq__Suc__le,axiom,
! [N,M] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M))
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,suc(N)),M)) ) ).
%----Helper facts (107)
fof(help_fNot_1_1_U,axiom,
! [P] :
( ~ hBOOL(hAPP_bool_bool(fNot,P))
| ~ hBOOL(P) ) ).
fof(help_fNot_2_1_U,axiom,
! [P] :
( hBOOL(P)
| hBOOL(hAPP_bool_bool(fNot,P)) ) ).
fof(help_fTrue_1_1_U,axiom,
hBOOL(fTrue) ).
fof(help_fTrue_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fequal_1_1_fequal_000tc__HOL__Obool_T,axiom,
! [X,Y] :
( ( is_bool(X)
& is_bool(Y) )
=> ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__HOL__Obool_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fequal_bool,X),Y)) ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_bool_bool(hAPP_f961197973l_bool(hAPP_f1172769267l_bool(cOMBB_bool_bool_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_bool_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
! [P,Q,R] : hAPP_bool_bool(hAPP_b589554111l_bool(hAPP_f1897201897l_bool(cOMBC_bool_bool_bool,P),Q),R) = hAPP_bool_bool(hAPP_b589554111l_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_T,axiom,
! [X,Y] :
( ( is_Arr723427730le_alt(X)
& is_Arr723427730le_alt(Y) )
=> ( ~ hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(fequal21574094le_alt,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(fequal21574094le_alt,X),Y)) ) ).
fof(help_fequal_1_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_T,axiom,
! [X,Y] :
( ( is_Arr859726945e_indi(X)
& is_Arr859726945e_indi(Y) )
=> ( ~ hBOOL(hAPP_A416869060i_bool(hAPP_A1609075839i_bool(fequal2012472101e_indi,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_A416869060i_bool(hAPP_A1609075839i_bool(fequal2012472101e_indi,X),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_A1120018583t_bool(hAPP_b287951269t_bool(cOMBK_507931254le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl_087,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_A416869060i_bool(hAPP_b2116075462i_bool(cOMBK_1391252605e_indi,P),Q) = P ) ).
fof(help_fequal_1_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(fequal1028827333le_alt,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_l300482276t_bool(hAPP_l2066632447t_bool(fequal1028827333le_alt,X),Y)) ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order__,axiom,
! [P,Q,R] : hAPP_A1120018583t_bool(hAPP_f246757773t_bool(hAPP_f1211148133t_bool(cOMBB_966447723le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_A1120018583t_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Arrow____Order___088,axiom,
! [P,Q,R] : hAPP_A416869060i_bool(hAPP_f1282033109i_bool(hAPP_f1765349427i_bool(cOMBB_1957128648e_indi,P),Q),R) = hAPP_bool_bool(P,hAPP_A416869060i_bool(Q,R)) ).
fof(help_fequal_1_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmt,axiom,
! [X,Y] :
( ( is_Pro1004667236le_alt(X)
& is_Pro1004667236le_alt(Y) )
=> ( ~ hBOOL(hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(fequal1881358376le_alt,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmt,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(fequal1881358376le_alt,X),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t,axiom,
! [P,Q,R] : hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(hAPP_f271508829t_bool(cOMBC_2032358938t_bool,P),Q),R) = hAPP_A1120018583t_bool(hAPP_A1781286015t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000,axiom,
! [P,Q,R] : hAPP_A416869060i_bool(hAPP_A1609075839i_bool(hAPP_f791932009i_bool(cOMBC_553632464i_bool,P),Q),R) = hAPP_A416869060i_bool(hAPP_A1609075839i_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_P1813625415t_bool(hAPP_b763490121t_bool(cOMBK_1733734784le_alt,P),Q) = P ) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,axiom,
! [X,Y] :
( ( is_fun20916972t_bool(X)
& is_fun20916972t_bool(Y) )
=> ( ~ hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(fequal318101288t_bool,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(fequal318101288t_bool,X),Y)) ) ).
fof(help_If_1_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
! [X,Y] : hAPP_P2096362161le_alt(hAPP_P1891191097le_alt(if_Pro1659200999le_alt(fTrue),X),Y) = X ).
fof(help_If_2_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
! [X,Y] : hAPP_P2096362161le_alt(hAPP_P1891191097le_alt(if_Pro1659200999le_alt(fFalse),X),Y) = Y ).
fof(help_If_3_1_If_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabelle____,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__Arrow_,axiom,
! [P,Q,R] : hAPP_P1813625415t_bool(hAPP_f137597973t_bool(hAPP_f2063770867t_bool(cOMBB_1860605643le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P1813625415t_bool(Q,R)) ).
fof(help_fequal_1_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(fequal1025934616le_alt,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirab,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(fequal1025934616le_alt,X),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__List__Olist_Itc__Arrow____Order____,axiom,
! [P,Q,R] : hAPP_n2108195705le_alt(hAPP_l1244209582le_alt(hAPP_f1660378693le_alt(cOMBC_1158490499le_alt,P),Q),R) = hAPP_l372964747le_alt(hAPP_n344665784le_alt(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1733357041l_bool(hAPP_b805997823l_bool(cOMBK_715978704t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
! [P,Q] :
( is_fun_bool_bool(P)
=> hAPP_P1122857141l_bool(hAPP_f719005683l_bool(cOMBK_1673635960le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [P,Q] :
( is_fun20916972t_bool(P)
=> hAPP_b763490121t_bool(hAPP_f581841297t_bool(cOMBK_1685845624l_bool,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__prod_It,axiom,
! [P,Q,R] : hAPP_f1733357041l_bool(hAPP_f574392641l_bool(hAPP_f2007076633l_bool(cOMBB_1517321413t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f1733357041l_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
! [P,Q] :
( is_fun_bool_bool(P)
=> hAPP_f812095627l_bool(hAPP_f2062029545l_bool(cOMBK_753699544t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_b805997823l_bool(hAPP_f118515775l_bool(cOMBK_1028572856l_bool,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__prod_Itc__List__,axiom,
! [P,Q,R] : hAPP_P1373277879t_bool(hAPP_f2073680917t_bool(hAPP_f2036795507t_bool(cOMBB_1957338939le_alt,P),Q),R) = hAPP_bool_bool(P,hAPP_P1373277879t_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [P,Q] :
( is_fun1651000642t_bool(P)
=> hAPP_P1116266031t_bool(hAPP_f342341961t_bool(cOMBK_980874600le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_089,axiom,
! [P,Q] :
( is_fun20916972t_bool(P)
=> hAPP_A1014090479t_bool(hAPP_f102394819t_bool(cOMBK_78615028le_alt,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_090,axiom,
! [P,Q,R] : hAPP_A1849759038le_alt(hAPP_l1693669363le_alt(hAPP_f18365135le_alt(cOMBC_1169281096le_alt,P),Q),R) = hAPP_l372964747le_alt(hAPP_A1660609715le_alt(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___091,axiom,
! [P,Q] :
( is_fun2015243113i_bool(P)
=> hAPP_P957402556i_bool(hAPP_f3439105i_bool(cOMBK_520250367le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_092,axiom,
! [P,Q] :
( is_fun20916972t_bool(P)
=> hAPP_A340536322t_bool(hAPP_f590186314t_bool(cOMBK_776703103e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
! [P,Q] : hAPP_A1660609715le_alt(hAPP_f921948995le_alt(cOMBK_1825575856le_alt,P),Q) = P ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb,axiom,
! [X,Y] :
( ( is_fun1264457267t_bool(X)
& is_fun1264457267t_bool(Y) )
=> ( ~ hBOOL(hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(fequal1289369847t_bool,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(fequal1289369847t_bool,X),Y)) ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_093,axiom,
! [P,Q,R] : hAPP_A1120018583t_bool(hAPP_f1068593625t_bool(hAPP_f372913425t_bool(cOMBC_943734388l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_A433435097l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [P,Q,R] : hAPP_l372964747le_alt(hAPP_l1390889510le_alt(hAPP_f268020663le_alt(cOMBC_168079159le_alt,P),Q),R) = hAPP_l372964747le_alt(hAPP_l1390889510le_alt(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___094,axiom,
! [P,Q] :
( is_fun1651000642t_bool(P)
=> hAPP_f1068593625t_bool(hAPP_f391873743t_bool(cOMBK_339579368t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_095,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_A433435097l_bool(hAPP_f1954218281l_bool(cOMBK_549130676le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f1378099862l_bool(hAPP_b1461182872l_bool(cOMBK_776847951t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___096,axiom,
! [P,Q] :
( is_fun2015243113i_bool(P)
=> hAPP_f431432850i_bool(hAPP_f1077635369i_bool(cOMBK_1399131793t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_097,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_A659996934l_bool(hAPP_f1639180358l_bool(cOMBK_350223551e_indi,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Arrow__,axiom,
! [P,Q,R] : hAPP_f1378099862l_bool(hAPP_f189058133l_bool(hAPP_f2048491699l_bool(cOMBB_1376111258t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f1378099862l_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_098,axiom,
! [P,Q] :
( is_fun_bool_bool(P)
=> hAPP_f591334822l_bool(hAPP_f498119908l_bool(cOMBK_874213703t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [P,Q] :
( is_fun701126715l_bool(P)
=> hAPP_b1461182872l_bool(hAPP_f1768325679l_bool(cOMBK_391161927l_bool,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_099,axiom,
! [P,Q,R] : hAPP_A340536322t_bool(hAPP_A630236912t_bool(hAPP_f832306437t_bool(cOMBC_325526267t_bool,P),Q),R) = hAPP_A1014090479t_bool(hAPP_A85603248t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
! [P,Q,R] : hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(hAPP_f1381403369t_bool(cOMBC_518322134t_bool,P),Q),R) = hAPP_P1813625415t_bool(hAPP_P1999019327t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_100,axiom,
! [P,Q,R] : hAPP_l300482276t_bool(hAPP_f4315714t_bool(hAPP_f921250311t_bool(cOMBC_1827582133l_bool,P),Q),R) = hAPP_f890578273l_bool(hAPP_l1493471510l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_101,axiom,
! [P,Q,R] : hAPP_A1781286015t_bool(hAPP_f1840820673t_bool(hAPP_f775987425t_bool(cOMBC_441619036t_bool,P),Q),R) = hAPP_f1068593625t_bool(hAPP_A64811457t_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [P,Q,R] : hAPP_A1660609715le_alt(hAPP_f904937452le_alt(hAPP_f239458941le_alt(cOMBB_521986850le_alt,P),Q),R) = hAPP_l1390889510le_alt(P,hAPP_A1849759038le_alt(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___102,axiom,
! [P,Q] :
( is_fun1651000642t_bool(P)
=> hAPP_f3167870t_bool(hAPP_f1698272152t_bool(cOMBK_242036279t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl_103,axiom,
! [P,Q] :
( is_fun701126715l_bool(P)
=> hAPP_A1745457982l_bool(hAPP_f1973254019l_bool(cOMBK_1744976613le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___104,axiom,
! [P,Q] :
( is_fun2015243113i_bool(P)
=> hAPP_f1570138413i_bool(hAPP_f1274922098i_bool(cOMBK_948333518t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl_105,axiom,
! [P,Q] :
( is_fun701126715l_bool(P)
=> hAPP_A701636433l_bool(hAPP_f1932802664l_bool(cOMBK_1217667022e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_106,axiom,
! [P,Q] :
( is_fun20916972t_bool(P)
=> hAPP_P651748559t_bool(hAPP_f1737373975t_bool(cOMBK_1925322610le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order__,axiom,
! [P,Q] : hAPP_P1436281263t_bool(hAPP_f2022891751t_bool(cOMBK_1634281074le_alt,P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_107,axiom,
! [P,Q,R] : hAPP_l591780830le_alt(hAPP_f1216999144le_alt(hAPP_f879032165le_alt(cOMBB_1303549321le_alt,P),Q),R) = hAPP_l591780830le_alt(P,hAPP_l372964747le_alt(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [P,Q,R] : hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(hAPP_f574303429l_bool(cOMBC_906425754l_bool,P),Q),R) = hAPP_f1733357041l_bool(hAPP_f1344932147l_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_108,axiom,
! [P,Q,R] : hAPP_A85603248t_bool(hAPP_A711952286t_bool(hAPP_f114580065t_bool(cOMBC_1377016489t_bool,P),Q),R) = hAPP_A28770973t_bool(hAPP_A1202525278t_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_109,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_P467353593l_bool(hAPP_f905851705l_bool(cOMBK_740566962le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___110,axiom,
! [P,Q] : hAPP_f1681297285t_bool(hAPP_f684471657t_bool(cOMBK_509674590t_bool,P),Q) = P ).
fof(help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q,R] : hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(hAPP_f1542885353t_bool(cOMBC_1094121654t_bool,P),Q),R) = hAPP_P1373277879t_bool(hAPP_P1133336895t_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_,axiom,
! [P,Q,R] : hAPP_A433435097l_bool(hAPP_f1656652505l_bool(hAPP_f1585690341l_bool(cOMBB_711698847le_alt,P),Q),R) = hAPP_P1151433609l_bool(P,hAPP_A1561816353le_alt(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_111,axiom,
! [P,Q,R] : hAPP_l2066632447t_bool(hAPP_f1895633847t_bool(hAPP_f1997384703t_bool(cOMBC_1696964078t_bool,P),Q),R) = hAPP_f4315714t_bool(hAPP_l2144750563t_bool(P,R),Q) ).
fof(help_fequal_1_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____w,axiom,
! [X,Y] :
( ( is_fun48324065t_bool(X)
& is_fun48324065t_bool(Y) )
=> ( ~ hBOOL(hAPP_f446648900l_bool(hAPP_f656614015l_bool(fequal547890341t_bool,X),Y))
| X = Y ) ) ).
fof(help_fequal_2_1_fequal_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____w,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_f446648900l_bool(hAPP_f656614015l_bool(fequal547890341t_bool,X),Y)) ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f446648900l_bool(hAPP_b651754310l_bool(cOMBK_577652221t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_112,axiom,
! [P,Q] :
( is_fun1420103068l_bool(P)
=> hAPP_f1895971544l_bool(hAPP_f633903640l_bool(cOMBK_1918246033t_bool,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_113,axiom,
! [P,Q,R] : hAPP_l1148780281le_alt(hAPP_f670565125le_alt(hAPP_f1124725731le_alt(cOMBB_1236261828le_alt,P),Q),R) = hAPP_l1148780281le_alt(P,hAPP_l372964747le_alt(Q,R)) ).
fof(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls,axiom,
! [P,Q,R] : hAPP_l591780830le_alt(hAPP_f1427069397le_alt(hAPP_f1928725626le_alt(cOMBS_1626428525le_alt,P),Q),R) = hAPP_P2096362161le_alt(hAPP_l1791846092le_alt(P,R),hAPP_l591780830le_alt(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl_114,axiom,
! [P,Q] :
( is_fun701126715l_bool(P)
=> hAPP_P2049543454l_bool(hAPP_f978113205l_bool(cOMBK_1549622337le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___115,axiom,
! [P,Q] : hAPP_f1329247136t_bool(hAPP_f303195352t_bool(cOMBK_1264040257t_bool,P),Q) = P ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc,axiom,
! [P,Q,R] : hAPP_f446648900l_bool(hAPP_f1028172757l_bool(hAPP_f920654899l_bool(cOMBB_410960200t_bool,P),Q),R) = hAPP_bool_bool(P,hAPP_f446648900l_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_116,axiom,
! [P,Q] :
( is_fun_bool_bool(P)
=> hAPP_f721327224l_bool(hAPP_f1459432374l_bool(cOMBK_1068969205t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q] :
( is_fun292781289l_bool(P)
=> hAPP_b651754310l_bool(hAPP_f1756719499l_bool(cOMBK_1377637877l_bool,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [P,Q,R] : hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(hAPP_f576161641l_bool(cOMBC_1887456628l_bool,P),Q),R) = hAPP_f1378099862l_bool(hAPP_f1901083135l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q,R] : hAPP_l1493471510l_bool(hAPP_f622637325l_bool(hAPP_f1224738111l_bool(cOMBB_1407335828le_alt,P),Q),R) = hAPP_P2032392041l_bool(P,hAPP_l591780830le_alt(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___117,axiom,
! [P,Q] :
( is_fun1651000642t_bool(P)
=> hAPP_f1741989420t_bool(hAPP_f1300833606t_bool(cOMBK_1961253349t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_118,axiom,
! [P,Q] :
( is_fun292781289l_bool(P)
=> hAPP_A990651116l_bool(hAPP_f1136405251l_bool(cOMBK_1435997879le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___119,axiom,
! [P,Q] :
( is_fun2015243113i_bool(P)
=> hAPP_f783549695i_bool(hAPP_f1377869636i_bool(cOMBK_1847391868t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_120,axiom,
! [P,Q] :
( is_fun292781289l_bool(P)
=> hAPP_A955165183l_bool(hAPP_f206814660l_bool(cOMBK_472365180e_indi,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_121,axiom,
! [P,Q,R] : hAPP_l1148780281le_alt(hAPP_f670565125le_alt(hAPP_f351228915le_alt(cOMBC_72147604le_alt,P),Q),R) = hAPP_f1216999144le_alt(hAPP_l486475401le_alt(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__,axiom,
! [P,Q,R] : hAPP_A643475905l_bool(hAPP_f1747206697l_bool(hAPP_f274832101l_bool(cOMBB_885534287le_alt,P),Q),R) = hAPP_f1656652505l_bool(P,hAPP_A1171966089le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy,axiom,
! [P,Q,R] : hAPP_A1202525278t_bool(hAPP_f1044120523t_bool(hAPP_f2020174441t_bool(cOMBB_930893948e_indi,P),Q),R) = hAPP_f684072049t_bool(P,hAPP_A340536322t_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___122,axiom,
! [P,Q,R] : hAPP_A64811457t_bool(hAPP_f1092358369t_bool(hAPP_f1682340965t_bool(cOMBB_333235735le_alt,P),Q),R) = hAPP_f372913425t_bool(P,hAPP_A643475905l_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_123,axiom,
! [P,Q] :
( is_fun292781289l_bool(P)
=> hAPP_P1533476044l_bool(hAPP_f1197671953l_bool(cOMBK_165199855le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Arrow____Order___124,axiom,
! [P,Q] : hAPP_f1114489970t_bool(hAPP_f1228246954t_bool(cOMBK_906927855t_bool,P),Q) = P ).
fof(help_COMBS_1_1_COMBS_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____wyls_125,axiom,
! [P,Q,R] : hAPP_l1148780281le_alt(hAPP_f794134621le_alt(hAPP_f2122335314le_alt(cOMBS_1569784209le_alt,P),Q),R) = hAPP_f1427069397le_alt(hAPP_l486097526le_alt(P,R),hAPP_l1148780281le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Arrow____Order____Mirabel_126,axiom,
! [P,Q,R] : hAPP_l1791846092le_alt(hAPP_f1291634731le_alt(hAPP_f1654251593le_alt(cOMBB_1675847172le_alt,P),Q),R) = hAPP_P1891191097le_alt(P,hAPP_l591780830le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell,axiom,
! [P,Q,R] : hAPP_l1748807729l_bool(hAPP_f1893731349l_bool(hAPP_f1418100887l_bool(cOMBB_1150645560le_alt,P),Q),R) = hAPP_f622637325l_bool(P,hAPP_l1148780281le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_127,axiom,
! [P,Q,R] : hAPP_l2144750563t_bool(hAPP_f1837837439t_bool(hAPP_f1503353479t_bool(cOMBB_1326560562le_alt,P),Q),R) = hAPP_f921250311t_bool(P,hAPP_l1748807729l_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_128,axiom,
! [P,Q,R] : hAPP_l486475401le_alt(hAPP_f593033837le_alt(hAPP_f332249751le_alt(cOMBB_96247696le_alt,P),Q),R) = hAPP_f879032165le_alt(P,hAPP_l1148780281le_alt(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_129,axiom,
! [P,Q,R] : hAPP_l436896263le_alt(hAPP_f1504748473le_alt(hAPP_f1949171529le_alt(cOMBB_215060470le_alt,P),Q),R) = hAPP_f1291634731le_alt(P,hAPP_l1148780281le_alt(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl,axiom,
! [P,Q,R] : hAPP_f446648900l_bool(hAPP_f656614015l_bool(hAPP_f1031027817l_bool(cOMBC_921123792l_bool,P),Q),R) = hAPP_f446648900l_bool(hAPP_f656614015l_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__Arrow____Order____Mirabell_130,axiom,
! [P,Q,R] : hAPP_l486097526le_alt(hAPP_f310101886le_alt(hAPP_f1558754397le_alt(cOMBB_1988247237le_alt,P),Q),R) = hAPP_f1928725626le_alt(P,hAPP_l436896263le_alt(Q,R)) ).
%----Conjectures (1)
fof(conj_0,conjecture,
! [I] :
( is_Arr859726945e_indi(I)
=> ( hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),b)),hAPP_A340536322t_bool(p,I)))
<=> hBOOL(hAPP_f1733357041l_bool(hAPP_P1151433609l_bool(member720722004le_alt,hAPP_A1561816353le_alt(hAPP_A1171966089le_alt(produc1456060119le_alt,a),c)),hAPP_A1014090479t_bool(hAPP_A28770973t_bool(hAPP_f684072049t_bool(arrow_207701375_below,hAPP_A340536322t_bool(p,I)),c),b))) ) ) ).
%------------------------------------------------------------------------------