TPTP Problem File: SCT170_10.p
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%------------------------------------------------------------------------------
% File : SCT170_10 : TPTP v8.2.0. Released v8.2.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 204, 100 axioms selected
% Version : SCT170_1 with the conjecture removed
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [TPTP]
% Names :
% Status : Satisfiable
% Rating : 1.00 v8.2.0
% Syntax : Number of formulae : 515 ( 80 unt; 272 typ; 0 def)
% Number of atoms : 585 ( 113 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 426 ( 84 ~; 3 |; 13 &)
% ( 43 <=>; 283 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 94 ( 93 usr)
% Number of type conns : 242 ( 133 >; 109 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 178 ( 178 usr; 46 con; 0-3 aty)
% Number of variables : 692 ( 681 !; 11 ?; 692 :)
% SPC : TF0_SAT_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:28:26
%------------------------------------------------------------------------------
%----Should-be-implicit typings (93)
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%----Explicit typings (179)
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tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oi_105,type,
hAPP_f748921117l_bool: ( fun_fu1904749695l_bool * fun_fu2085524157t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____Mi,type,
hAPP_f1481710327l_bool: ( fun_fu376055641l_bool * fun_fu132047767l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Or,type,
hAPP_f759862099l_bool: ( fun_fu1037822389l_bool * fun_fu1655311859l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____O,type,
hAPP_f639792199l_bool: ( fun_fu664235509l_bool * fun_fu897278719l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____M,type,
hAPP_f899216831l_bool: ( fun_fu582883361l_bool * fun_fu2114498143t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr,type,
hAPP_f243652437l_bool: ( fun_fu881806519l_bool * fun_fu1884117237i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_106,type,
hAPP_f1394256759l_bool: ( fun_fu288602073l_bool * fun_fu386577431l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_107,type,
hAPP_f1435434693l_bool: ( fun_fu304973171l_bool * fun_fu1251737213l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_108,type,
hAPP_f544895323l_bool: ( fun_fu1740763529l_bool * fun_fu1251737213l_bool ) > fun_Ar884201459l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrr_109,type,
hAPP_f989466937l_bool: ( fun_fu1786351335l_bool * fun_fu1251737213l_bool ) > fun_bo2138151889l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle,type,
hAPP_f174050481l_bool: ( fun_fu595758099l_bool * fun_fu1123909713i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle_110,type,
hAPP_f1827424979l_bool: ( fun_fu2105385269l_bool * fun_fu304973171l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabell,type,
hAPP_f359017159l_bool: ( fun_fu1655733109l_bool * fun_fu1083074431i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabell_111,type,
hAPP_f1347377641l_bool: ( fun_fu1371820951l_bool * fun_fu2011759009l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr,type,
hAPP_f1270259485l_bool: ( fun_fu278604415l_bool * fun_fu662212797i_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_112,type,
hAPP_f180608831l_bool: ( fun_fu2011759009l_bool * fun_fu383145951l_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_113,type,
hAPP_f1651042461l_bool: ( fun_fu491357777l_bool * fun_fu383145951l_bool ) > fun_Ar1821573119l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_114,type,
hAPP_f71505983l_bool: ( fun_fu1479273075l_bool * fun_fu383145951l_bool ) > fun_bo1803678369l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvr_115,type,
hAPP_f459175489l_bool: ( fun_fu890127093l_bool * fun_fu383145951l_bool ) > fun_fu746839971l_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O,type,
hAPP_f671542927e_indi: ( fun_fu334384573e_indi * fun_Pr1639951081t_bool ) > arrow_501706939e_indi ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_116,type,
hAPP_f1944886577l_bool: ( fun_fu383145951l_bool * fun_Pr1639951081t_bool ) > bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_117,type,
hAPP_f1560118175t_bool: ( fun_fu193278215t_bool * fun_Pr1639951081t_bool ) > fun_Ar154839667t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_118,type,
hAPP_f906860201i_bool: ( fun_fu1867632401i_bool * fun_Pr1639951081t_bool ) > fun_Ar1871347069i_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_119,type,
hAPP_f1172974131t_bool: ( fun_fu1917018721t_bool * fun_Pr1639951081t_bool ) > fun_Ar2047178847t_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_120,type,
hAPP_f2128533835l_bool: ( fun_fu1903211571l_bool * fun_Pr1639951081t_bool ) > fun_bool_bool ).
tff(sy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__O_121,type,
hAPP_f1758973969t_bool: ( fun_fu1008469439t_bool * fun_Pr1639951081t_bool ) > fun_bo230129725t_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc__,type,
hAPP_P163170789e_indi: ( fun_Pr506339783e_indi * produc624534567le_alt ) > arrow_501706939e_indi ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc___122,type,
hAPP_P751176071t_bool: ( fun_Pr1639951081t_bool * produc624534567le_alt ) > bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc___123,type,
hAPP_P259956691i_bool: ( fun_Pr123985543i_bool * produc624534567le_alt ) > fun_Ar1871347069i_bool ).
tff(sy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc___124,type,
hAPP_P2005668213l_bool: ( fun_Pr534938793l_bool * produc624534567le_alt ) > fun_bool_bool ).
tff(sy_c_hBOOL,type,
hBOOL: bool > $o ).
tff(sy_c_member_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi,type,
member1124131880e_indi: arrow_501706939e_indi > fun_fu350122099l_bool ).
tff(sy_c_member_000tc__HOL__Obool,type,
member_bool: bool > fun_fu1255657237l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc,type,
member1701178322t_bool: fun_Ar1200683263t_bool > fun_fu243829175l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc_125,type,
member2069173038t_bool: fun_Ar1570071899t_bool > fun_fu1019918867l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc_126,type,
member558395596t_bool: fun_Ar2047178847t_bool > fun_fu386577431l_bool ).
tff(sy_c_member_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_Mtc_127,type,
member844573594le_alt: fun_Ar795681735le_alt > fun_fu1904749695l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____Mirabelle,type,
member1494646772t_bool: fun_bo478202017t_bool > fun_fu376055641l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____Order____,type,
member1211611472t_bool: fun_bo2136393469t_bool > fun_fu1037822389l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____Order___,type,
member2079888426t_bool: fun_bo230129725t_bool > fun_fu664235509l_bool ).
tff(sy_c_member_000tc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____Mirabell,type,
member158436796le_alt: fun_bo1156530537le_alt > fun_fu582883361l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__,type,
member422031058e_indi: fun_fu2069019647e_indi > fun_fu881806519l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___128,type,
member1120178292l_bool: fun_fu103733537l_bool > fun_fu288602073l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___129,type,
member256508712t_bool: fun_fu50365883t_bool > fun_fu304973171l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv,type,
member95348014e_indi: fun_fu1743730523e_indi > fun_fu595758099l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv_130,type,
member326955216l_bool: fun_fu1251737213l_bool > fun_fu2105385269l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf,type,
member993084970e_indi: fun_fu334384573e_indi > fun_fu1655733109l_bool ).
tff(sy_c_member_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_131,type,
member85421004l_bool: fun_fu383145951l_bool > fun_fu1371820951l_bool ).
tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb_,type,
member555231642e_indi: fun_Pr506339783e_indi > fun_fu278604415l_bool ).
tff(sy_c_member_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__132,type,
member641857340t_bool: fun_Pr1639951081t_bool > fun_fu2011759009l_bool ).
tff(sy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oalt_Mtc,type,
member1484933012le_alt: produc624534567le_alt > fun_fu383145951l_bool ).
tff(sy_v_F,type,
f: fun_fu50365883t_bool ).
tff(sy_v_P_H____,type,
p_1: fun_Ar2047178847t_bool ).
tff(sy_v_P____,type,
p: fun_Ar2047178847t_bool ).
tff(sy_v_a____,type,
a: arrow_1621810872le_alt ).
tff(sy_v_b____,type,
b: arrow_1621810872le_alt ).
tff(sy_v_c____,type,
c: arrow_1621810872le_alt ).
%----Relevant facts (216)
tff(fact_0__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(p),arrow_1880704820e_Prof)) ).
tff(fact_1_assms_I3_J,axiom,
hBOOL(hAPP_f725100827l_bool(arrow_981905126le_IIA,f)) ).
tff(fact_2_u,axiom,
hBOOL(hAPP_f725100827l_bool(arrow_807483785nimity,f)) ).
tff(fact_3__096a_A_126_061_Ab_096,axiom,
a != b ).
tff(fact_4_dist,axiom,
hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,cons_A1375194904le_alt(a,cons_A1375194904le_alt(b,cons_A1375194904le_alt(c,nil_Ar285162344le_alt))))) ).
tff(fact_5_iff,axiom,
! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(a,b)),hAPP_A2044747691t_bool(p,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(b,a)),hAPP_A2044747691t_bool(p_1,I))) ) ).
tff(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: arrow_1621810872le_alt] : ~ hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,cons_A1375194904le_alt(a,cons_A1375194904le_alt(b,cons_A1375194904le_alt(C,nil_Ar285162344le_alt))))) ).
tff(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_f1237345129l_bool(member558395596t_bool(cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_1170304598_below,cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_1170304598_below,p),c),b)),b),a)),arrow_1880704820e_Prof)) ).
tff(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_f1237345129l_bool(member558395596t_bool(cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_1170304598_below,cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_1170304598_below,cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_1170304598_below,p),c),b)),b),a)),a),c)),arrow_1880704820e_Prof)) ).
tff(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(cOMBC_377836265t_bool(cOMBC_1994570734t_bool(cOMBB_715840641e_indi(arrow_1170304598_below,p),c),b)),arrow_1880704820e_Prof)) ).
tff(fact_10_in__mkbot,axiom,
! [X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool,Z: arrow_1621810872le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),arrow_1126550734_mkbot(L_1,Z)))
<=> ( ( Y != Z )
& ( ( X_1 = Z )
=> ( X_1 != Y ) )
& ( ( X_1 != Z )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),L_1)) ) ) ) ).
tff(fact_11_in__mktop,axiom,
! [X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool,Z: arrow_1621810872le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),arrow_1275257820_mktop(L_1,Z)))
<=> ( ( X_1 != Z )
& ( ( Y = Z )
=> ( X_1 != Y ) )
& ( ( Y != Z )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),L_1)) ) ) ) ).
tff(fact_12_in__below,axiom,
! [X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_1170304598_below,L_1),Aa),Ba)))
<=> ( ( X_1 != Y )
& ( ( Y = Aa )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Ba)),L_1)) )
& ( ( Y != Aa )
=> ( ( ( X_1 = Aa )
=> ( ( Y = Ba )
| hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Y)),L_1)) ) )
& ( ( X_1 != Aa )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),L_1)) ) ) ) ) ) ) ) ).
tff(fact_13_split__paired__All,axiom,
! [Pa: fun_Pr1639951081t_bool] :
( ! [X1: produc624534567le_alt] : hBOOL(hAPP_P751176071t_bool(Pa,X1))
<=> ! [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt] : hBOOL(hAPP_P751176071t_bool(Pa,produc170576535le_alt(A_1,B))) ) ).
tff(fact_14_Pair__eq,axiom,
! [Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt,A_3: arrow_1621810872le_alt,B_3: arrow_1621810872le_alt] :
( ( produc170576535le_alt(Aa,Ba) = produc170576535le_alt(A_3,B_3) )
<=> ( ( Aa = A_3 )
& ( Ba = B_3 ) ) ) ).
tff(fact_15_Pair__inject,axiom,
! [A_7: arrow_1621810872le_alt,B_5: arrow_1621810872le_alt,A_6: arrow_1621810872le_alt,B_4: arrow_1621810872le_alt] :
( ( produc170576535le_alt(A_7,B_5) = produc170576535le_alt(A_6,B_4) )
=> ~ ( ( A_7 = A_6 )
=> ( B_5 != B_4 ) ) ) ).
tff(fact_16_in__rel__def,axiom,
! [R_1: fun_Pr1639951081t_bool,X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt] :
( hBOOL(in_rel75641218le_alt(R_1,X_1,Y))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),R_1)) ) ).
tff(fact_17_below__Lin,axiom,
! [L_1: fun_Pr1639951081t_bool,X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt] :
( ( X_1 != Y )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_1170304598_below,L_1),X_1),Y)),arrow_1008788854le_Lin)) ) ) ).
tff(fact_18__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(p_1),arrow_1880704820e_Prof)) ).
tff(fact_19__C1_C,axiom,
! [P_a: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,A_3: arrow_1621810872le_alt,B_3: arrow_1621810872le_alt,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( ( A_3 != B_3 )
=> ( ( Aa != B_3 )
=> ( ( Ba != A_3 )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_a),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_3,B_3)),hAPP_A2044747691t_bool(P_a,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_3,B_3)),hAPP_f718157575t_bool(f,P_a))) ) ) ) ) ) ) ) ) ).
tff(fact_20__C2_C,axiom,
! [P_a: fun_Ar2047178847t_bool,Pa: fun_Ar2047178847t_bool,A_3: arrow_1621810872le_alt,B_3: arrow_1621810872le_alt,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( ( A_3 != B_3 )
=> ( ( Aa != B_3 )
=> ( ( Ba != A_3 )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Pa),arrow_1880704820e_Prof))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(P_a),arrow_1880704820e_Prof))
=> ( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_A2044747691t_bool(Pa,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_3,B_3)),hAPP_A2044747691t_bool(P_a,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),hAPP_f718157575t_bool(f,Pa)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_3,B_3)),hAPP_f718157575t_bool(f,P_a))) ) ) ) ) ) ) ) ) ).
tff(fact_21_assms_I1_J,axiom,
hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(f),pi_fun456133649t_bool(arrow_1880704820e_Prof,hAPP_f459175489l_bool(cOMBK_639770490t_bool,arrow_1008788854le_Lin)))) ).
tff(fact_22_const__Lin__Prof,axiom,
! [L_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_f1172974131t_bool(cOMBK_164791446e_indi,L_1)),arrow_1880704820e_Prof)) ) ).
tff(fact_23_mkbot__Lin,axiom,
! [X_1: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(arrow_1126550734_mkbot(L_1,X_1)),arrow_1008788854le_Lin)) ) ).
tff(fact_24_mktop__Lin,axiom,
! [X_1: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(arrow_1275257820_mktop(L_1,X_1)),arrow_1008788854le_Lin)) ) ).
tff(fact_25_Lin__irrefl,axiom,
! [Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),L_1))
=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Ba,Aa)),L_1)) ) ) ).
tff(fact_26_notin__Lin__iff,axiom,
! [X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> ( ( X_1 != Y )
=> ( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),L_1))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Y,X_1)),L_1)) ) ) ) ).
tff(fact_27_third__alt,axiom,
! [A_5: arrow_1621810872le_alt,B_2: arrow_1621810872le_alt] :
( ( A_5 != B_2 )
=> ? [C: arrow_1621810872le_alt] : hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,cons_A1375194904le_alt(A_5,cons_A1375194904le_alt(B_2,cons_A1375194904le_alt(C,nil_Ar285162344le_alt))))) ) ).
tff(fact_28_IIA__def,axiom,
! [Fa: fun_fu50365883t_bool] :
( hBOOL(hAPP_f725100827l_bool(arrow_981905126le_IIA,Fa))
<=> ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),arrow_1880704820e_Prof))
=> ! [Xa: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(Xa),arrow_1880704820e_Prof))
=> ! [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt] :
( ! [I: arrow_501706939e_indi] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_A2044747691t_bool(X,I)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_A2044747691t_bool(Xa,I))) )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_f718157575t_bool(Fa,X)))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_f718157575t_bool(Fa,Xa))) ) ) ) ) ) ).
tff(fact_29_unanimity__def,axiom,
! [Fa: fun_fu50365883t_bool] :
( hBOOL(hAPP_f725100827l_bool(arrow_807483785nimity,Fa))
<=> ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),arrow_1880704820e_Prof))
=> ! [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt] :
( ! [I: arrow_501706939e_indi] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_A2044747691t_bool(X,I)))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_f718157575t_bool(Fa,X))) ) ) ) ).
tff(fact_30_complete__Lin,axiom,
! [Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ? [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),arrow_1008788854le_Lin))
& hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Ba)),X)) ) ) ).
tff(fact_31_in__above,axiom,
! [X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt,L_1: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( ( Aa != Ba )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),arrow_2009189698_above(L_1,Aa,Ba)))
<=> ( ( X_1 != Y )
& ( ( X_1 = Ba )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(Aa,Y)),L_1)) )
& ( ( X_1 != Ba )
=> ( ( ( Y = Ba )
=> ( ( X_1 = Aa )
| hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Aa)),L_1)) ) )
& ( ( Y != Ba )
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X_1,Y)),L_1)) ) ) ) ) ) ) ) ).
tff(fact_32_distinct_Osimps_I1_J,axiom,
hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,nil_Ar285162344le_alt)) ).
tff(fact_33_list_Osimps_I2_J,axiom,
! [A_4: arrow_1621810872le_alt,List_4: list_A1414934253le_alt] : nil_Ar285162344le_alt != cons_A1375194904le_alt(A_4,List_4) ).
tff(fact_34_list_Oinject,axiom,
! [Aa: arrow_1621810872le_alt,List_3: list_A1414934253le_alt,A_3: arrow_1621810872le_alt,List_2: list_A1414934253le_alt] :
( ( cons_A1375194904le_alt(Aa,List_3) = cons_A1375194904le_alt(A_3,List_2) )
<=> ( ( Aa = A_3 )
& ( List_3 = List_2 ) ) ) ).
tff(fact_35_not__Cons__self2,axiom,
! [X_7: arrow_1621810872le_alt,Xs_7: list_A1414934253le_alt] : cons_A1375194904le_alt(X_7,Xs_7) != Xs_7 ).
tff(fact_36_not__Cons__self,axiom,
! [Xs_6: list_A1414934253le_alt,X_6: arrow_1621810872le_alt] : Xs_6 != cons_A1375194904le_alt(X_6,Xs_6) ).
tff(fact_37_above__Lin,axiom,
! [L_1: fun_Pr1639951081t_bool,X_1: arrow_1621810872le_alt,Y: arrow_1621810872le_alt] :
( ( X_1 != Y )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L_1),arrow_1008788854le_Lin))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(arrow_2009189698_above(L_1,X_1,Y)),arrow_1008788854le_Lin)) ) ) ).
tff(fact_38_list_Osimps_I3_J,axiom,
! [A_2: arrow_1621810872le_alt,List_1: list_A1414934253le_alt] : cons_A1375194904le_alt(A_2,List_1) != nil_Ar285162344le_alt ).
tff(fact_39_dictatorI,axiom,
! [I_1: arrow_501706939e_indi,Fa: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(Fa),pi_fun456133649t_bool(arrow_1880704820e_Prof,hAPP_f459175489l_bool(cOMBK_639770490t_bool,arrow_1008788854le_Lin))))
=> ( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),arrow_1880704820e_Prof))
=> ! [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt] :
( ( A_1 != B )
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_A2044747691t_bool(X,I_1)))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(A_1,B)),hAPP_f718157575t_bool(Fa,X))) ) ) )
=> hBOOL(hAPP_A1059798043i_bool(hAPP_f1559864639i_bool(arrow_1322316103ctator,Fa),I_1)) ) ) ).
tff(fact_40_PiE,axiom,
! [X_1: produc624534567le_alt,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool,B_1: fun_Pr534938793l_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X_1)),hAPP_P2005668213l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A)) ) ) ).
tff(fact_41_PiE,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar795681735le_alt,A: fun_Ar1871347069i_bool,B_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,B_1)))
=> ( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X_1)),hAPP_A2044747691t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A)) ) ) ).
tff(fact_42_PiE,axiom,
! [X_1: bool,F: fun_bo1156530537le_alt,A: fun_bool_bool,B_1: fun_bo230129725t_bool] :
( hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,B_1)))
=> ( ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X_1)),hAPP_b1848524425t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
tff(fact_43_PiE,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar1200683263t_bool,A: fun_Ar1871347069i_bool,B_1: fun_Ar1784032663l_bool] :
( hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X_1)),hAPP_A1790795747l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A)) ) ) ).
tff(fact_44_PiE,axiom,
! [X_1: bool,F: fun_bo478202017t_bool,A: fun_bool_bool,B_1: fun_bo1613497205l_bool] :
( hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X_1)),hAPP_b1178471617l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
tff(fact_45_PiE,axiom,
! [X_1: bool,F: fun_bo230129725t_bool,A: fun_bool_bool,B_1: fun_bo1803678369l_bool] :
( hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X_1)),hAPP_b1017527359l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
tff(fact_46_PiE,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar1570071899t_bool,A: fun_Ar1871347069i_bool,B_1: fun_Ar884201459l_bool] :
( hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X_1)),hAPP_A107624255l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A)) ) ) ).
tff(fact_47_PiE,axiom,
! [X_1: bool,F: fun_bo2136393469t_bool,A: fun_bool_bool,B_1: fun_bo2138151889l_bool] :
( hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X_1)),hAPP_b930206237l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
tff(fact_48_PiE,axiom,
! [X_1: produc624534567le_alt,F: fun_Pr506339783e_indi,A: fun_Pr1639951081t_bool,B_1: fun_Pr123985543i_bool] :
( hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X_1)),hAPP_P259956691i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A)) ) ) ).
tff(fact_49_PiE,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu2069019647e_indi,A: fun_fu103733537l_bool,B_1: fun_fu23838287i_bool] :
( hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X_1)),hAPP_f1511451035i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A)) ) ) ).
tff(fact_50_PiE,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu103733537l_bool,A: fun_fu103733537l_bool,B_1: fun_fu658952305l_bool] :
( hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X_1)),hAPP_f1418708797l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A)) ) ) ).
tff(fact_51_PiE,axiom,
! [X_1: fun_Pr1639951081t_bool,F: fun_fu334384573e_indi,A: fun_fu383145951l_bool,B_1: fun_fu1867632401i_bool] :
( hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X_1)),hAPP_f906860201i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A)) ) ) ).
tff(fact_52_PiE,axiom,
! [X_1: fun_Pr1639951081t_bool,F: fun_fu383145951l_bool,A: fun_fu383145951l_bool,B_1: fun_fu1903211571l_bool] :
( hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X_1)),hAPP_f2128533835l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A)) ) ) ).
tff(fact_53_PiE,axiom,
! [X_1: fun_fu50365883t_bool,F: fun_fu1743730523e_indi,A: fun_fu1251737213l_bool,B_1: fun_fu1950461939i_bool] :
( hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X_1)),hAPP_f1559864639i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A)) ) ) ).
tff(fact_54_PiE,axiom,
! [X_1: fun_fu50365883t_bool,F: fun_fu1251737213l_bool,A: fun_fu1251737213l_bool,B_1: fun_fu1734842389l_bool] :
( hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X_1)),hAPP_f626809057l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A)) ) ) ).
tff(fact_55_PiE,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu50365883t_bool,A: fun_fu103733537l_bool,B_1: fun_fu746839971l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X_1)),hAPP_f1265202753l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A)) ) ) ).
tff(fact_56_PiE,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool,B_1: fun_Ar1821573119l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X_1)),hAPP_A1710743709l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A)) ) ) ).
tff(fact_57_list_Oexhaust,axiom,
! [Y_4: list_A1414934253le_alt] :
( ( Y_4 != nil_Ar285162344le_alt )
=> ~ ! [A_1: arrow_1621810872le_alt,List: list_A1414934253le_alt] : Y_4 != cons_A1375194904le_alt(A_1,List) ) ).
tff(fact_58_neq__Nil__conv,axiom,
! [Xs: list_A1414934253le_alt] :
( ( Xs != nil_Ar285162344le_alt )
<=> ? [Y_1: arrow_1621810872le_alt,Ys_2: list_A1414934253le_alt] : Xs = cons_A1375194904le_alt(Y_1,Ys_2) ) ).
tff(fact_59_alt3,axiom,
? [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt,C: arrow_1621810872le_alt] : hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,cons_A1375194904le_alt(A_1,cons_A1375194904le_alt(B,cons_A1375194904le_alt(C,nil_Ar285162344le_alt))))) ).
tff(fact_60_Pi__mem,axiom,
! [X_1: produc624534567le_alt,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool,B_1: fun_Pr534938793l_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B_1)))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X_1)),hAPP_P2005668213l_bool(B_1,X_1))) ) ) ).
tff(fact_61_Pi__mem,axiom,
! [X_1: produc624534567le_alt,F: fun_Pr506339783e_indi,A: fun_Pr1639951081t_bool,B_1: fun_Pr123985543i_bool] :
( hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,B_1)))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X_1)),hAPP_P259956691i_bool(B_1,X_1))) ) ) ).
tff(fact_62_Pi__mem,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu2069019647e_indi,A: fun_fu103733537l_bool,B_1: fun_fu23838287i_bool] :
( hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,B_1)))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X_1)),hAPP_f1511451035i_bool(B_1,X_1))) ) ) ).
tff(fact_63_Pi__mem,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu103733537l_bool,A: fun_fu103733537l_bool,B_1: fun_fu658952305l_bool] :
( hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,B_1)))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X_1)),hAPP_f1418708797l_bool(B_1,X_1))) ) ) ).
tff(fact_64_Pi__mem,axiom,
! [X_1: fun_Pr1639951081t_bool,F: fun_fu334384573e_indi,A: fun_fu383145951l_bool,B_1: fun_fu1867632401i_bool] :
( hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,B_1)))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X_1)),hAPP_f906860201i_bool(B_1,X_1))) ) ) ).
tff(fact_65_Pi__mem,axiom,
! [X_1: fun_Pr1639951081t_bool,F: fun_fu383145951l_bool,A: fun_fu383145951l_bool,B_1: fun_fu1903211571l_bool] :
( hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,B_1)))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X_1)),hAPP_f2128533835l_bool(B_1,X_1))) ) ) ).
tff(fact_66_Pi__mem,axiom,
! [X_1: fun_fu50365883t_bool,F: fun_fu1743730523e_indi,A: fun_fu1251737213l_bool,B_1: fun_fu1950461939i_bool] :
( hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,B_1)))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X_1)),hAPP_f1559864639i_bool(B_1,X_1))) ) ) ).
tff(fact_67_Pi__mem,axiom,
! [X_1: fun_fu50365883t_bool,F: fun_fu1251737213l_bool,A: fun_fu1251737213l_bool,B_1: fun_fu1734842389l_bool] :
( hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,B_1)))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X_1)),hAPP_f626809057l_bool(B_1,X_1))) ) ) ).
tff(fact_68_Pi__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar795681735le_alt,A: fun_Ar1871347069i_bool,B_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,B_1)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X_1)),hAPP_A2044747691t_bool(B_1,X_1))) ) ) ).
tff(fact_69_Pi__mem,axiom,
! [X_1: bool,F: fun_bo1156530537le_alt,A: fun_bool_bool,B_1: fun_bo230129725t_bool] :
( hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X_1)),hAPP_b1848524425t_bool(B_1,X_1))) ) ) ).
tff(fact_70_Pi__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar1200683263t_bool,A: fun_Ar1871347069i_bool,B_1: fun_Ar1784032663l_bool] :
( hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,B_1)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X_1)),hAPP_A1790795747l_bool(B_1,X_1))) ) ) ).
tff(fact_71_Pi__mem,axiom,
! [X_1: bool,F: fun_bo478202017t_bool,A: fun_bool_bool,B_1: fun_bo1613497205l_bool] :
( hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X_1)),hAPP_b1178471617l_bool(B_1,X_1))) ) ) ).
tff(fact_72_Pi__mem,axiom,
! [X_1: bool,F: fun_bo230129725t_bool,A: fun_bool_bool,B_1: fun_bo1803678369l_bool] :
( hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X_1)),hAPP_b1017527359l_bool(B_1,X_1))) ) ) ).
tff(fact_73_Pi__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar1570071899t_bool,A: fun_Ar1871347069i_bool,B_1: fun_Ar884201459l_bool] :
( hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,B_1)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X_1)),hAPP_A107624255l_bool(B_1,X_1))) ) ) ).
tff(fact_74_Pi__mem,axiom,
! [X_1: bool,F: fun_bo2136393469t_bool,A: fun_bool_bool,B_1: fun_bo2138151889l_bool] :
( hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X_1)),hAPP_b930206237l_bool(B_1,X_1))) ) ) ).
tff(fact_75_Pi__mem,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu50365883t_bool,A: fun_fu103733537l_bool,B_1: fun_fu746839971l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B_1)))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X_1)),hAPP_f1265202753l_bool(B_1,X_1))) ) ) ).
tff(fact_76_Pi__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool,B_1: fun_Ar1821573119l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B_1)))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X_1)),hAPP_A1710743709l_bool(B_1,X_1))) ) ) ).
tff(fact_77_funcset__mem,axiom,
! [X_1: produc624534567le_alt,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool,B_1: fun_bool_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,hAPP_f1601816755l_bool(cOMBK_290363320le_alt,B_1))))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_78_funcset__mem,axiom,
! [X_1: produc624534567le_alt,F: fun_Pr506339783e_indi,A: fun_Pr1639951081t_bool,B_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,hAPP_f1561296623i_bool(cOMBK_328807062le_alt,B_1))))
=> ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X_1)),B_1)) ) ) ).
tff(fact_79_funcset__mem,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu2069019647e_indi,A: fun_fu103733537l_bool,B_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,hAPP_f823592631i_bool(cOMBK_269839822t_bool,B_1))))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X_1)),B_1)) ) ) ).
tff(fact_80_funcset__mem,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu103733537l_bool,A: fun_fu103733537l_bool,B_1: fun_bool_bool] :
( hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,hAPP_f1325493883l_bool(cOMBK_167511280t_bool,B_1))))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X_1)),B_1)) ) ) ).
tff(fact_81_funcset__mem,axiom,
! [X_1: fun_Pr1639951081t_bool,F: fun_fu334384573e_indi,A: fun_fu383145951l_bool,B_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,hAPP_f1364159657i_bool(cOMBK_1207925178t_bool,B_1))))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X_1)),B_1)) ) ) ).
tff(fact_82_funcset__mem,axiom,
! [X_1: fun_Pr1639951081t_bool,F: fun_fu383145951l_bool,A: fun_fu383145951l_bool,B_1: fun_bool_bool] :
( hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,hAPP_f1230984105l_bool(cOMBK_1838733848t_bool,B_1))))
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X_1)),B_1)) ) ) ).
tff(fact_83_funcset__mem,axiom,
! [X_1: fun_fu50365883t_bool,F: fun_fu1743730523e_indi,A: fun_fu1251737213l_bool,B_1: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,hAPP_f1224613979i_bool(cOMBK_519762474t_bool,B_1))))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X_1)),B_1)) ) ) ).
tff(fact_84_funcset__mem,axiom,
! [X_1: fun_fu50365883t_bool,F: fun_fu1251737213l_bool,A: fun_fu1251737213l_bool,B_1: fun_bool_bool] :
( hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,hAPP_f1364914207l_bool(cOMBK_1853791052t_bool,B_1))))
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X_1)),B_1)) ) ) ).
tff(fact_85_funcset__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar795681735le_alt,A: fun_Ar1871347069i_bool,B_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,hAPP_f1172974131t_bool(cOMBK_164791446e_indi,B_1))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X_1)),B_1)) ) ) ).
tff(fact_86_funcset__mem,axiom,
! [X_1: bool,F: fun_bo1156530537le_alt,A: fun_bool_bool,B_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,hAPP_f1758973969t_bool(cOMBK_1897375160l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X_1)),B_1)) ) ) ).
tff(fact_87_funcset__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar1200683263t_bool,A: fun_Ar1871347069i_bool,B_1: fun_fu103733537l_bool] :
( hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,hAPP_f466810275l_bool(cOMBK_30438862e_indi,B_1))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_88_funcset__mem,axiom,
! [X_1: bool,F: fun_bo478202017t_bool,A: fun_bool_bool,B_1: fun_fu103733537l_bool] :
( hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,hAPP_f2013855105l_bool(cOMBK_1481288432l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_89_funcset__mem,axiom,
! [X_1: bool,F: fun_bo230129725t_bool,A: fun_bool_bool,B_1: fun_fu383145951l_bool] :
( hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,hAPP_f71505983l_bool(cOMBK_648664568l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_90_funcset__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar1570071899t_bool,A: fun_Ar1871347069i_bool,B_1: fun_fu1251737213l_bool] :
( hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,hAPP_f544895323l_bool(cOMBK_869185066e_indi,B_1))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_91_funcset__mem,axiom,
! [X_1: bool,F: fun_bo2136393469t_bool,A: fun_bool_bool,B_1: fun_fu1251737213l_bool] :
( hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,hAPP_f989466937l_bool(cOMBK_343479628l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_92_funcset__mem,axiom,
! [X_1: fun_Ar2047178847t_bool,F: fun_fu50365883t_bool,A: fun_fu103733537l_bool,B_1: fun_fu383145951l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,hAPP_f459175489l_bool(cOMBK_639770490t_bool,B_1))))
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_93_funcset__mem,axiom,
! [X_1: arrow_501706939e_indi,F: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool,B_1: fun_fu383145951l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,B_1))))
=> ( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X_1)),B_1)) ) ) ).
tff(fact_94_dictator__def,axiom,
! [Fa: fun_fu50365883t_bool,I_1: arrow_501706939e_indi] :
( hBOOL(hAPP_A1059798043i_bool(hAPP_f1559864639i_bool(arrow_1322316103ctator,Fa),I_1))
<=> ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),arrow_1880704820e_Prof))
=> ( hAPP_f718157575t_bool(Fa,X) = hAPP_A2044747691t_bool(X,I_1) ) ) ) ).
tff(fact_95_Pi__I,axiom,
! [F: fun_Pr506339783e_indi,B_1: fun_Pr123985543i_bool,A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X)),hAPP_P259956691i_bool(B_1,X))) )
=> hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,B_1))) ) ).
tff(fact_96_Pi__I,axiom,
! [F: fun_fu2069019647e_indi,B_1: fun_fu23838287i_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X)),hAPP_f1511451035i_bool(B_1,X))) )
=> hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,B_1))) ) ).
tff(fact_97_Pi__I,axiom,
! [F: fun_fu103733537l_bool,B_1: fun_fu658952305l_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X)),hAPP_f1418708797l_bool(B_1,X))) )
=> hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,B_1))) ) ).
tff(fact_98_Pi__I,axiom,
! [F: fun_fu334384573e_indi,B_1: fun_fu1867632401i_bool,A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X)),hAPP_f906860201i_bool(B_1,X))) )
=> hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,B_1))) ) ).
tff(fact_99_Pi__I,axiom,
! [F: fun_fu383145951l_bool,B_1: fun_fu1903211571l_bool,A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X)),hAPP_f2128533835l_bool(B_1,X))) )
=> hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,B_1))) ) ).
tff(fact_100_Pi__I,axiom,
! [F: fun_fu1743730523e_indi,B_1: fun_fu1950461939i_bool,A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X)),hAPP_f1559864639i_bool(B_1,X))) )
=> hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,B_1))) ) ).
tff(fact_101_Pi__I,axiom,
! [F: fun_fu1251737213l_bool,B_1: fun_fu1734842389l_bool,A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X)),hAPP_f626809057l_bool(B_1,X))) )
=> hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,B_1))) ) ).
tff(fact_102_Pi__I,axiom,
! [F: fun_Ar795681735le_alt,B_1: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X)),hAPP_A2044747691t_bool(B_1,X))) )
=> hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,B_1))) ) ).
tff(fact_103_Pi__I,axiom,
! [F: fun_bo1156530537le_alt,B_1: fun_bo230129725t_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X)),hAPP_b1848524425t_bool(B_1,X))) )
=> hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,B_1))) ) ).
tff(fact_104_Pi__I,axiom,
! [F: fun_Ar1200683263t_bool,B_1: fun_Ar1784032663l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X)),hAPP_A1790795747l_bool(B_1,X))) )
=> hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,B_1))) ) ).
tff(fact_105_Pi__I,axiom,
! [F: fun_bo478202017t_bool,B_1: fun_bo1613497205l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X)),hAPP_b1178471617l_bool(B_1,X))) )
=> hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,B_1))) ) ).
tff(fact_106_Pi__I,axiom,
! [F: fun_bo230129725t_bool,B_1: fun_bo1803678369l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X)),hAPP_b1017527359l_bool(B_1,X))) )
=> hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,B_1))) ) ).
tff(fact_107_Pi__I,axiom,
! [F: fun_Ar1570071899t_bool,B_1: fun_Ar884201459l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X)),hAPP_A107624255l_bool(B_1,X))) )
=> hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,B_1))) ) ).
tff(fact_108_Pi__I,axiom,
! [F: fun_bo2136393469t_bool,B_1: fun_bo2138151889l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X)),hAPP_b930206237l_bool(B_1,X))) )
=> hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,B_1))) ) ).
tff(fact_109_Pi__I,axiom,
! [F: fun_Pr1639951081t_bool,B_1: fun_Pr534938793l_bool,A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X)),hAPP_P2005668213l_bool(B_1,X))) )
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B_1))) ) ).
tff(fact_110_Pi__I,axiom,
! [F: fun_fu50365883t_bool,B_1: fun_fu746839971l_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X)),hAPP_f1265202753l_bool(B_1,X))) )
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B_1))) ) ).
tff(fact_111_Pi__I,axiom,
! [F: fun_Ar2047178847t_bool,B_1: fun_Ar1821573119l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X)),hAPP_A1710743709l_bool(B_1,X))) )
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B_1))) ) ).
tff(fact_112_funcsetI,axiom,
! [F: fun_Pr506339783e_indi,B_1: fun_Ar1871347069i_bool,A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X)),B_1)) )
=> hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,hAPP_f1561296623i_bool(cOMBK_328807062le_alt,B_1)))) ) ).
tff(fact_113_funcsetI,axiom,
! [F: fun_fu2069019647e_indi,B_1: fun_Ar1871347069i_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X)),B_1)) )
=> hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,hAPP_f823592631i_bool(cOMBK_269839822t_bool,B_1)))) ) ).
tff(fact_114_funcsetI,axiom,
! [F: fun_fu103733537l_bool,B_1: fun_bool_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,hAPP_f1325493883l_bool(cOMBK_167511280t_bool,B_1)))) ) ).
tff(fact_115_funcsetI,axiom,
! [F: fun_fu334384573e_indi,B_1: fun_Ar1871347069i_bool,A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X)),B_1)) )
=> hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,hAPP_f1364159657i_bool(cOMBK_1207925178t_bool,B_1)))) ) ).
tff(fact_116_funcsetI,axiom,
! [F: fun_fu383145951l_bool,B_1: fun_bool_bool,A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,hAPP_f1230984105l_bool(cOMBK_1838733848t_bool,B_1)))) ) ).
tff(fact_117_funcsetI,axiom,
! [F: fun_fu1743730523e_indi,B_1: fun_Ar1871347069i_bool,A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X)),B_1)) )
=> hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,hAPP_f1224613979i_bool(cOMBK_519762474t_bool,B_1)))) ) ).
tff(fact_118_funcsetI,axiom,
! [F: fun_fu1251737213l_bool,B_1: fun_bool_bool,A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,hAPP_f1364914207l_bool(cOMBK_1853791052t_bool,B_1)))) ) ).
tff(fact_119_funcsetI,axiom,
! [F: fun_Ar795681735le_alt,B_1: fun_Pr1639951081t_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X)),B_1)) )
=> hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,hAPP_f1172974131t_bool(cOMBK_164791446e_indi,B_1)))) ) ).
tff(fact_120_funcsetI,axiom,
! [F: fun_bo1156530537le_alt,B_1: fun_Pr1639951081t_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X)),B_1)) )
=> hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,hAPP_f1758973969t_bool(cOMBK_1897375160l_bool,B_1)))) ) ).
tff(fact_121_funcsetI,axiom,
! [F: fun_Ar1200683263t_bool,B_1: fun_fu103733537l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,hAPP_f466810275l_bool(cOMBK_30438862e_indi,B_1)))) ) ).
tff(fact_122_funcsetI,axiom,
! [F: fun_bo478202017t_bool,B_1: fun_fu103733537l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,hAPP_f2013855105l_bool(cOMBK_1481288432l_bool,B_1)))) ) ).
tff(fact_123_funcsetI,axiom,
! [F: fun_bo230129725t_bool,B_1: fun_fu383145951l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,hAPP_f71505983l_bool(cOMBK_648664568l_bool,B_1)))) ) ).
tff(fact_124_funcsetI,axiom,
! [F: fun_Ar1570071899t_bool,B_1: fun_fu1251737213l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,hAPP_f544895323l_bool(cOMBK_869185066e_indi,B_1)))) ) ).
tff(fact_125_funcsetI,axiom,
! [F: fun_bo2136393469t_bool,B_1: fun_fu1251737213l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,hAPP_f989466937l_bool(cOMBK_343479628l_bool,B_1)))) ) ).
tff(fact_126_funcsetI,axiom,
! [F: fun_Pr1639951081t_bool,B_1: fun_bool_bool,A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,hAPP_f1601816755l_bool(cOMBK_290363320le_alt,B_1)))) ) ).
tff(fact_127_funcsetI,axiom,
! [F: fun_fu50365883t_bool,B_1: fun_fu383145951l_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,hAPP_f459175489l_bool(cOMBK_639770490t_bool,B_1)))) ) ).
tff(fact_128_funcsetI,axiom,
! [F: fun_Ar2047178847t_bool,B_1: fun_fu383145951l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,B_1)))) ) ).
tff(fact_129_linear__alt,axiom,
? [L: fun_Pr1639951081t_bool] : hBOOL(hAPP_f180608831l_bool(member641857340t_bool(L),arrow_1008788854le_Lin)) ).
tff(fact_130_Pi__I_H,axiom,
! [F: fun_Pr506339783e_indi,B_1: fun_Pr123985543i_bool,A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_P163170789e_indi(F,X)),hAPP_P259956691i_bool(B_1,X))) )
=> hBOOL(hAPP_f1270259485l_bool(member555231642e_indi(F),pi_Pro723839835e_indi(A,B_1))) ) ).
tff(fact_131_Pi__I_H,axiom,
! [F: fun_fu2069019647e_indi,B_1: fun_fu23838287i_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f1631746589e_indi(F,X)),hAPP_f1511451035i_bool(B_1,X))) )
=> hBOOL(hAPP_f243652437l_bool(member422031058e_indi(F),pi_fun1549517203e_indi(A,B_1))) ) ).
tff(fact_132_Pi__I_H,axiom,
! [F: fun_fu103733537l_bool,B_1: fun_fu658952305l_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1095388607l_bool(F,X)),hAPP_f1418708797l_bool(B_1,X))) )
=> hBOOL(hAPP_f1394256759l_bool(member1120178292l_bool(F),pi_fun953636405l_bool(A,B_1))) ) ).
tff(fact_133_Pi__I_H,axiom,
! [F: fun_fu334384573e_indi,B_1: fun_fu1867632401i_bool,A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f671542927e_indi(F,X)),hAPP_f906860201i_bool(B_1,X))) )
=> hBOOL(hAPP_f359017159l_bool(member993084970e_indi(F),pi_fun2132478361e_indi(A,B_1))) ) ).
tff(fact_134_Pi__I_H,axiom,
! [F: fun_fu383145951l_bool,B_1: fun_fu1903211571l_bool,A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1944886577l_bool(F,X)),hAPP_f2128533835l_bool(B_1,X))) )
=> hBOOL(hAPP_f1347377641l_bool(member85421004l_bool(F),pi_fun779925307l_bool(A,B_1))) ) ).
tff(fact_135_Pi__I_H,axiom,
! [F: fun_fu1743730523e_indi,B_1: fun_fu1950461939i_bool,A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(hAPP_f87993209e_indi(F,X)),hAPP_f1559864639i_bool(B_1,X))) )
=> hBOOL(hAPP_f174050481l_bool(member95348014e_indi(F),pi_fun1545124079e_indi(A,B_1))) ) ).
tff(fact_136_Pi__I_H,axiom,
! [F: fun_fu1251737213l_bool,B_1: fun_fu1734842389l_bool,A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f725100827l_bool(F,X)),hAPP_f626809057l_bool(B_1,X))) )
=> hBOOL(hAPP_f1827424979l_bool(member326955216l_bool(F),pi_fun465500049l_bool(A,B_1))) ) ).
tff(fact_137_Pi__I_H,axiom,
! [F: fun_Ar795681735le_alt,B_1: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_A2034733541le_alt(F,X)),hAPP_A2044747691t_bool(B_1,X))) )
=> hBOOL(hAPP_f748921117l_bool(member844573594le_alt(F),pi_Arr447918939le_alt(A,B_1))) ) ).
tff(fact_138_Pi__I_H,axiom,
! [F: fun_bo1156530537le_alt,B_1: fun_bo230129725t_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(hAPP_b98736263le_alt(F,X)),hAPP_b1848524425t_bool(B_1,X))) )
=> hBOOL(hAPP_f899216831l_bool(member158436796le_alt(F),pi_boo158890749le_alt(A,B_1))) ) ).
tff(fact_139_Pi__I_H,axiom,
! [F: fun_Ar1200683263t_bool,B_1: fun_Ar1784032663l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_A1159468061t_bool(F,X)),hAPP_A1790795747l_bool(B_1,X))) )
=> hBOOL(hAPP_f1753158741l_bool(member1701178322t_bool(F),pi_Arr1077238675t_bool(A,B_1))) ) ).
tff(fact_140_Pi__I_H,axiom,
! [F: fun_bo478202017t_bool,B_1: fun_bo1613497205l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(hAPP_b114674879t_bool(F,X)),hAPP_b1178471617l_bool(B_1,X))) )
=> hBOOL(hAPP_f1481710327l_bool(member1494646772t_bool(F),pi_boo2120406325t_bool(A,B_1))) ) ).
tff(fact_141_Pi__I_H,axiom,
! [F: fun_bo230129725t_bool,B_1: fun_bo1803678369l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_b1848524425t_bool(F,X)),hAPP_b1017527359l_bool(B_1,X))) )
=> hBOOL(hAPP_f639792199l_bool(member2079888426t_bool(F),pi_boo683563155t_bool(A,B_1))) ) ).
tff(fact_142_Pi__I_H,axiom,
! [F: fun_Ar1570071899t_bool,B_1: fun_Ar884201459l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_A1168502649t_bool(F,X)),hAPP_A107624255l_bool(B_1,X))) )
=> hBOOL(hAPP_f598211249l_bool(member2069173038t_bool(F),pi_Arr478149871t_bool(A,B_1))) ) ).
tff(fact_143_Pi__I_H,axiom,
! [F: fun_bo2136393469t_bool,B_1: fun_bo2138151889l_bool,A: fun_bool_bool] :
( ! [X: bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(hAPP_b1112685083t_bool(F,X)),hAPP_b930206237l_bool(B_1,X))) )
=> hBOOL(hAPP_f759862099l_bool(member1211611472t_bool(F),pi_boo853084305t_bool(A,B_1))) ) ).
tff(fact_144_Pi__I_H,axiom,
! [F: fun_Pr1639951081t_bool,B_1: fun_Pr534938793l_bool,A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P751176071t_bool(F,X)),hAPP_P2005668213l_bool(B_1,X))) )
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B_1))) ) ).
tff(fact_145_Pi__I_H,axiom,
! [F: fun_fu50365883t_bool,B_1: fun_fu746839971l_bool,A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_f718157575t_bool(F,X)),hAPP_f1265202753l_bool(B_1,X))) )
=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B_1))) ) ).
tff(fact_146_Pi__I_H,axiom,
! [F: fun_Ar2047178847t_bool,B_1: fun_Ar1821573119l_bool,A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(hAPP_A2044747691t_bool(F,X)),hAPP_A1710743709l_bool(B_1,X))) )
=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B_1))) ) ).
tff(fact_147_Pi__cong,axiom,
! [B_1: fun_Pr534938793l_bool,G: fun_Pr1639951081t_bool,F: fun_Pr1639951081t_bool,A: fun_Pr1639951081t_bool] :
( ! [W: produc624534567le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(W),A))
=> ( hBOOL(hAPP_P751176071t_bool(F,W))
<=> hBOOL(hAPP_P751176071t_bool(G,W)) ) )
=> ( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(F),pi_Pro811330557t_bool(A,B_1)))
<=> hBOOL(hAPP_f180608831l_bool(member641857340t_bool(G),pi_Pro811330557t_bool(A,B_1))) ) ) ).
tff(fact_148_Pi__cong,axiom,
! [B_1: fun_fu746839971l_bool,F: fun_fu50365883t_bool,G: fun_fu50365883t_bool,A: fun_fu103733537l_bool] :
( ! [W: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(W),A))
=> ( hAPP_f718157575t_bool(F,W) = hAPP_f718157575t_bool(G,W) ) )
=> ( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(F),pi_fun456133649t_bool(A,B_1)))
<=> hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(G),pi_fun456133649t_bool(A,B_1))) ) ) ).
tff(fact_149_Pi__cong,axiom,
! [B_1: fun_Ar1821573119l_bool,F: fun_Ar2047178847t_bool,G: fun_Ar2047178847t_bool,A: fun_Ar1871347069i_bool] :
( ! [W: arrow_501706939e_indi] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(W),A))
=> ( hAPP_A2044747691t_bool(F,W) = hAPP_A2044747691t_bool(G,W) ) )
=> ( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(F),pi_Arr1358199477t_bool(A,B_1)))
<=> hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(G),pi_Arr1358199477t_bool(A,B_1))) ) ) ).
tff(fact_150_splice_Osimps_I2_J,axiom,
! [V: arrow_1621810872le_alt,Va: list_A1414934253le_alt] : splice519866683le_alt(cons_A1375194904le_alt(V,Va),nil_Ar285162344le_alt) = cons_A1375194904le_alt(V,Va) ).
tff(fact_151_splice_Osimps_I3_J,axiom,
! [X_5: arrow_1621810872le_alt,Xs_5: list_A1414934253le_alt,Y_3: arrow_1621810872le_alt,Ys_1: list_A1414934253le_alt] : splice519866683le_alt(cons_A1375194904le_alt(X_5,Xs_5),cons_A1375194904le_alt(Y_3,Ys_1)) = cons_A1375194904le_alt(X_5,cons_A1375194904le_alt(Y_3,splice519866683le_alt(Xs_5,Ys_1))) ).
tff(fact_152_splice_Osimps_I1_J,axiom,
! [Ys: list_A1414934253le_alt] : splice519866683le_alt(nil_Ar285162344le_alt,Ys) = Ys ).
tff(fact_153_splice__Nil2,axiom,
! [Xs_4: list_A1414934253le_alt] : splice519866683le_alt(Xs_4,nil_Ar285162344le_alt) = Xs_4 ).
tff(fact_154_pred__equals__eq2,axiom,
! [S: fun_Pr1639951081t_bool,R_1: fun_Pr1639951081t_bool] :
( ! [X: arrow_1621810872le_alt,Xa: arrow_1621810872le_alt] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X,Xa)),R_1))
<=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(X,Xa)),S)) )
<=> ( R_1 = S ) ) ).
tff(fact_155_prod_Oexhaust,axiom,
! [Y_2: produc624534567le_alt] :
~ ! [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt] : Y_2 != produc170576535le_alt(A_1,B) ).
tff(fact_156_PairE,axiom,
! [P_1: produc624534567le_alt] :
~ ! [X: arrow_1621810872le_alt,Y_1: arrow_1621810872le_alt] : P_1 != produc170576535le_alt(X,Y_1) ).
tff(fact_157_split__paired__Ex,axiom,
! [Pa: fun_Pr1639951081t_bool] :
( ? [X1: produc624534567le_alt] : hBOOL(hAPP_P751176071t_bool(Pa,X1))
<=> ? [A_1: arrow_1621810872le_alt,B: arrow_1621810872le_alt] : hBOOL(hAPP_P751176071t_bool(Pa,produc170576535le_alt(A_1,B))) ) ).
tff(fact_158_insert__Nil,axiom,
! [X_4: arrow_1621810872le_alt] : insert1119534974le_alt(X_4,nil_Ar285162344le_alt) = cons_A1375194904le_alt(X_4,nil_Ar285162344le_alt) ).
tff(fact_159_distinct__insert,axiom,
! [X_3: arrow_1621810872le_alt,Xs_3: list_A1414934253le_alt] :
( hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,Xs_3))
=> hBOOL(hAPP_l1367475021t_bool(distin1382776155le_alt,insert1119534974le_alt(X_3,Xs_3))) ) ).
tff(fact_160_mem__def,axiom,
! [X_1: arrow_501706939e_indi,A: fun_Ar1871347069i_bool] :
( hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),A))
<=> hBOOL(hAPP_A1059798043i_bool(A,X_1)) ) ).
tff(fact_161_mem__def,axiom,
! [X_1: bool,A: fun_bool_bool] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
<=> hBOOL(hAPP_bool_bool(A,X_1)) ) ).
tff(fact_162_mem__def,axiom,
! [X_1: produc624534567le_alt,A: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),A))
<=> hBOOL(hAPP_P751176071t_bool(A,X_1)) ) ).
tff(fact_163_mem__def,axiom,
! [X_1: fun_Ar2047178847t_bool,A: fun_fu103733537l_bool] :
( hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),A))
<=> hBOOL(hAPP_f1095388607l_bool(A,X_1)) ) ).
tff(fact_164_mem__def,axiom,
! [X_1: fun_Pr1639951081t_bool,A: fun_fu383145951l_bool] :
( hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),A))
<=> hBOOL(hAPP_f1944886577l_bool(A,X_1)) ) ).
tff(fact_165_mem__def,axiom,
! [X_1: fun_fu50365883t_bool,A: fun_fu1251737213l_bool] :
( hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),A))
<=> hBOOL(hAPP_f725100827l_bool(A,X_1)) ) ).
tff(fact_166_Collect__def,axiom,
! [Pa: fun_Ar1871347069i_bool] : collec1241994086e_indi(Pa) = Pa ).
tff(fact_167_list__nonempty__induct,axiom,
! [Pa: fun_li1977348015t_bool,Xs: list_A1414934253le_alt] :
( ( Xs != nil_Ar285162344le_alt )
=> ( ! [X: arrow_1621810872le_alt] : hBOOL(hAPP_l1367475021t_bool(Pa,cons_A1375194904le_alt(X,nil_Ar285162344le_alt)))
=> ( ! [X: arrow_1621810872le_alt,Xs_2: list_A1414934253le_alt] :
( ( Xs_2 != nil_Ar285162344le_alt )
=> ( hBOOL(hAPP_l1367475021t_bool(Pa,Xs_2))
=> hBOOL(hAPP_l1367475021t_bool(Pa,cons_A1375194904le_alt(X,Xs_2))) ) )
=> hBOOL(hAPP_l1367475021t_bool(Pa,Xs)) ) ) ) ).
tff(fact_168_curry__def,axiom,
! [X: fun_Pr1639951081t_bool,Xa: arrow_1621810872le_alt,Xb: arrow_1621810872le_alt] :
( hBOOL(produc480181630t_bool(X,Xa,Xb))
<=> hBOOL(hAPP_P751176071t_bool(X,produc170576535le_alt(Xa,Xb))) ) ).
tff(fact_169_curryI,axiom,
! [F: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( hBOOL(hAPP_P751176071t_bool(F,produc170576535le_alt(Aa,Ba)))
=> hBOOL(produc480181630t_bool(F,Aa,Ba)) ) ).
tff(fact_170_curryE,axiom,
! [F: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( hBOOL(produc480181630t_bool(F,Aa,Ba))
=> hBOOL(hAPP_P751176071t_bool(F,produc170576535le_alt(Aa,Ba))) ) ).
tff(fact_171_curryD,axiom,
! [F: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( hBOOL(produc480181630t_bool(F,Aa,Ba))
=> hBOOL(hAPP_P751176071t_bool(F,produc170576535le_alt(Aa,Ba))) ) ).
tff(fact_172_curry__conv,axiom,
! [F: fun_Pr1639951081t_bool,Aa: arrow_1621810872le_alt,Ba: arrow_1621810872le_alt] :
( hBOOL(produc480181630t_bool(F,Aa,Ba))
<=> hBOOL(hAPP_P751176071t_bool(F,produc170576535le_alt(Aa,Ba))) ) ).
tff(fact_173_eq__Nil__null,axiom,
! [Xs: list_A1414934253le_alt] :
( ( Xs = nil_Ar285162344le_alt )
<=> hBOOL(hAPP_l1367475021t_bool(null_A519933296le_alt,Xs)) ) ).
tff(fact_174_List_Onull__def,axiom,
! [Xs: list_A1414934253le_alt] :
( hBOOL(hAPP_l1367475021t_bool(null_A519933296le_alt,Xs))
<=> ( Xs = nil_Ar285162344le_alt ) ) ).
tff(fact_175_null__rec_I1_J,axiom,
! [X_2: arrow_1621810872le_alt,Xs_1: list_A1414934253le_alt] : ~ hBOOL(hAPP_l1367475021t_bool(null_A519933296le_alt,cons_A1375194904le_alt(X_2,Xs_1))) ).
tff(fact_176_null__rec_I2_J,axiom,
hBOOL(hAPP_l1367475021t_bool(null_A519933296le_alt,nil_Ar285162344le_alt)) ).
tff(fact_177_equal__Nil__null,axiom,
! [Xs: list_A1414934253le_alt] :
( hBOOL(hAPP_l1367475021t_bool(equal_1931790859le_alt(Xs),nil_Ar285162344le_alt))
<=> hBOOL(hAPP_l1367475021t_bool(null_A519933296le_alt,Xs)) ) ).
tff(fact_178_Prof__def,axiom,
arrow_1880704820e_Prof = pi_Arr1358199477t_bool(top_to850136695i_bool,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,arrow_1008788854le_Lin)) ).
tff(fact_179_top1I,axiom,
! [X_1: fun_fu50365883t_bool] : hBOOL(hAPP_f725100827l_bool(top_to2127553399l_bool,X_1)) ).
tff(fact_180_top1I,axiom,
! [X_1: fun_Pr1639951081t_bool] : hBOOL(hAPP_f1944886577l_bool(top_to1057791589l_bool,X_1)) ).
tff(fact_181_top1I,axiom,
! [X_1: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1095388607l_bool(top_to653038619l_bool,X_1)) ).
tff(fact_182_top1I,axiom,
! [X_1: produc624534567le_alt] : hBOOL(hAPP_P751176071t_bool(top_to710777827t_bool,X_1)) ).
tff(fact_183_top1I,axiom,
! [X_1: arrow_501706939e_indi] : hBOOL(hAPP_A1059798043i_bool(top_to850136695i_bool,X_1)) ).
tff(fact_184_Pi__UNIV,axiom,
! [A: fun_Pr1639951081t_bool] : pi_Pro811330557t_bool(A,hAPP_f1601816755l_bool(cOMBK_290363320le_alt,top_to1647826457l_bool)) = top_to1057791589l_bool ).
tff(fact_185_Pi__UNIV,axiom,
! [A: fun_fu103733537l_bool] : pi_fun456133649t_bool(A,hAPP_f459175489l_bool(cOMBK_639770490t_bool,top_to1057791589l_bool)) = top_to2127553399l_bool ).
tff(fact_186_Pi__UNIV,axiom,
! [A: fun_Ar1871347069i_bool] : pi_Arr1358199477t_bool(A,hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,top_to1057791589l_bool)) = top_to653038619l_bool ).
tff(fact_187_equal__list__def,axiom,
! [X_1: list_A1414934253le_alt,Y: list_A1414934253le_alt] :
( hBOOL(hAPP_l1367475021t_bool(equal_1931790859le_alt(X_1),Y))
<=> ( X_1 = Y ) ) ).
tff(fact_188_iso__tuple__UNIV__I,axiom,
! [X_1: bool] : hBOOL(hAPP_f387058535l_bool(member_bool(X_1),top_to1647826457l_bool)) ).
tff(fact_189_iso__tuple__UNIV__I,axiom,
! [X_1: arrow_501706939e_indi] : hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),top_to850136695i_bool)) ).
tff(fact_190_iso__tuple__UNIV__I,axiom,
! [X_1: produc624534567le_alt] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),top_to710777827t_bool)) ).
tff(fact_191_iso__tuple__UNIV__I,axiom,
! [X_1: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),top_to653038619l_bool)) ).
tff(fact_192_iso__tuple__UNIV__I,axiom,
! [X_1: fun_Pr1639951081t_bool] : hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),top_to1057791589l_bool)) ).
tff(fact_193_iso__tuple__UNIV__I,axiom,
! [X_1: fun_fu50365883t_bool] : hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),top_to2127553399l_bool)) ).
tff(fact_194_UNIV__I,axiom,
! [X_1: bool] : hBOOL(hAPP_f387058535l_bool(member_bool(X_1),top_to1647826457l_bool)) ).
tff(fact_195_UNIV__I,axiom,
! [X_1: arrow_501706939e_indi] : hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X_1),top_to850136695i_bool)) ).
tff(fact_196_UNIV__I,axiom,
! [X_1: produc624534567le_alt] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X_1),top_to710777827t_bool)) ).
tff(fact_197_UNIV__I,axiom,
! [X_1: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X_1),top_to653038619l_bool)) ).
tff(fact_198_UNIV__I,axiom,
! [X_1: fun_Pr1639951081t_bool] : hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X_1),top_to1057791589l_bool)) ).
tff(fact_199_UNIV__I,axiom,
! [X_1: fun_fu50365883t_bool] : hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X_1),top_to2127553399l_bool)) ).
tff(fact_200_UNIV__def,axiom,
top_to2127553399l_bool = collec154865254t_bool(hAPP_b930206237l_bool(cOMBK_1362474068t_bool,fTrue)) ).
tff(fact_201_UNIV__def,axiom,
top_to1057791589l_bool = collec1697917566t_bool(hAPP_b1017527359l_bool(cOMBK_1801013008t_bool,fTrue)) ).
tff(fact_202_UNIV__def,axiom,
top_to653038619l_bool = collec861220362t_bool(hAPP_b1178471617l_bool(cOMBK_70145528t_bool,fTrue)) ).
tff(fact_203_UNIV__def,axiom,
top_to710777827t_bool = collec2140722898le_alt(hAPP_b1848524425t_bool(cOMBK_350462144le_alt,fTrue)) ).
tff(fact_204_UNIV__def,axiom,
top_to850136695i_bool = collec1241994086e_indi(hAPP_b611520797i_bool(cOMBK_206372180e_indi,fTrue)) ).
tff(fact_205_top__apply,axiom,
! [X_1: fun_fu50365883t_bool] :
( hBOOL(hAPP_f725100827l_bool(top_to2127553399l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
tff(fact_206_top__apply,axiom,
! [X_1: fun_Pr1639951081t_bool] :
( hBOOL(hAPP_f1944886577l_bool(top_to1057791589l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
tff(fact_207_top__apply,axiom,
! [X_1: fun_Ar2047178847t_bool] :
( hBOOL(hAPP_f1095388607l_bool(top_to653038619l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
tff(fact_208_top__apply,axiom,
! [X_1: produc624534567le_alt] :
( hBOOL(hAPP_P751176071t_bool(top_to710777827t_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
tff(fact_209_top__apply,axiom,
! [X_1: arrow_501706939e_indi] :
( hBOOL(hAPP_A1059798043i_bool(top_to850136695i_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
tff(fact_210_UNIV__eq__I,axiom,
! [A: fun_bool_bool] :
( ! [X: bool] : hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> ( top_to1647826457l_bool = A ) ) ).
tff(fact_211_UNIV__eq__I,axiom,
! [A: fun_Ar1871347069i_bool] :
( ! [X: arrow_501706939e_indi] : hBOOL(hAPP_f90330565l_bool(member1124131880e_indi(X),A))
=> ( top_to850136695i_bool = A ) ) ).
tff(fact_212_UNIV__eq__I,axiom,
! [A: fun_Pr1639951081t_bool] :
( ! [X: produc624534567le_alt] : hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(X),A))
=> ( top_to710777827t_bool = A ) ) ).
tff(fact_213_UNIV__eq__I,axiom,
! [A: fun_fu103733537l_bool] :
( ! [X: fun_Ar2047178847t_bool] : hBOOL(hAPP_f1237345129l_bool(member558395596t_bool(X),A))
=> ( top_to653038619l_bool = A ) ) ).
tff(fact_214_UNIV__eq__I,axiom,
! [A: fun_fu383145951l_bool] :
( ! [X: fun_Pr1639951081t_bool] : hBOOL(hAPP_f180608831l_bool(member641857340t_bool(X),A))
=> ( top_to1057791589l_bool = A ) ) ).
tff(fact_215_UNIV__eq__I,axiom,
! [A: fun_fu1251737213l_bool] :
( ! [X: fun_fu50365883t_bool] : hBOOL(hAPP_f1435434693l_bool(member256508712t_bool(X),A))
=> ( top_to2127553399l_bool = A ) ) ).
%----Helper facts (27)
tff(help_fTrue_1_1_U,axiom,
hBOOL(fTrue) ).
tff(help_fTrue_1_1_T,axiom,
! [P: bool] :
( ( P = fTrue )
| ( P = fFalse ) ) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____yfv,axiom,
! [P: bool,Q: arrow_501706939e_indi] : hAPP_A1059798043i_bool(hAPP_b611520797i_bool(cOMBK_206372180e_indi,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P: bool,Q: produc624534567le_alt] : hAPP_P751176071t_bool(hAPP_b1848524425t_bool(cOMBK_350462144le_alt,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
! [P: bool,Q: fun_Pr1639951081t_bool] : hAPP_f1944886577l_bool(hAPP_b1017527359l_bool(cOMBK_1801013008t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It,axiom,
! [P: fun_bool_bool,Q: produc624534567le_alt] : hAPP_P2005668213l_bool(hAPP_f1601816755l_bool(cOMBK_290363320le_alt,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf,axiom,
! [P: fun_Pr1639951081t_bool,Q: bool] : hAPP_b1848524425t_bool(hAPP_f1758973969t_bool(cOMBK_1897375160l_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc,axiom,
! [P: fun_bool_bool,Q: fun_Pr1639951081t_bool] : hAPP_f2128533835l_bool(hAPP_f1230984105l_bool(cOMBK_1838733848t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P: fun_fu383145951l_bool,Q: bool] : hAPP_b1017527359l_bool(hAPP_f71505983l_bool(cOMBK_648664568l_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb__,axiom,
! [P: fun_Ar1871347069i_bool,Q: produc624534567le_alt] : hAPP_P259956691i_bool(hAPP_f1561296623i_bool(cOMBK_328807062le_alt,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf_133,axiom,
! [P: fun_Pr1639951081t_bool,Q: arrow_501706939e_indi] : hAPP_A2044747691t_bool(hAPP_f1172974131t_bool(cOMBK_164791446e_indi,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P: bool,Q: fun_Ar2047178847t_bool] : hAPP_f1095388607l_bool(hAPP_b1178471617l_bool(cOMBK_70145528t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___134,axiom,
! [P: fun_Ar1871347069i_bool,Q: fun_Pr1639951081t_bool] : hAPP_f906860201i_bool(hAPP_f1364159657i_bool(cOMBK_1207925178t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_135,axiom,
! [P: fun_fu383145951l_bool,Q: arrow_501706939e_indi] : hAPP_A1710743709l_bool(hAPP_f1651042461l_bool(cOMBK_2098615510e_indi,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_136,axiom,
! [P: fun_bool_bool,Q: fun_Ar2047178847t_bool] : hAPP_f1418708797l_bool(hAPP_f1325493883l_bool(cOMBK_167511280t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv,axiom,
! [P: fun_fu103733537l_bool,Q: bool] : hAPP_b1178471617l_bool(hAPP_f2013855105l_bool(cOMBK_1481288432l_bool,P),Q) = P ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000,axiom,
! [P: fun_Ar1757019876t_bool,Q: arrow_1621810872le_alt,R: arrow_501706939e_indi] : hAPP_A2044747691t_bool(cOMBC_377836265t_bool(P,Q),R) = hAPP_A476679046t_bool(hAPP_A711829680t_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___137,axiom,
! [P: fun_Ar1871347069i_bool,Q: fun_Ar2047178847t_bool] : hAPP_f1511451035i_bool(hAPP_f823592631i_bool(cOMBK_269839822t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____yfv_138,axiom,
! [P: fun_fu103733537l_bool,Q: arrow_501706939e_indi] : hAPP_A1790795747l_bool(hAPP_f466810275l_bool(cOMBK_30438862e_indi,P),Q) = P ).
tff(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____yfvrrhwpeb__Oindi_000_139,axiom,
! [P: fun_Ar2079322857t_bool,Q: arrow_1621810872le_alt,R: arrow_501706939e_indi] : hAPP_A711829680t_bool(cOMBC_1994570734t_bool(P,Q),R) = hAPP_A272835723t_bool(hAPP_A784015157t_bool(P,R),Q) ).
tff(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
! [P: bool,Q: fun_fu50365883t_bool] : hAPP_f725100827l_bool(hAPP_b930206237l_bool(cOMBK_1362474068t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_140,axiom,
! [P: fun_fu383145951l_bool,Q: fun_Ar2047178847t_bool] : hAPP_f1265202753l_bool(hAPP_f459175489l_bool(cOMBK_639770490t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_141,axiom,
! [P: fun_bool_bool,Q: fun_fu50365883t_bool] : hAPP_f626809057l_bool(hAPP_f1364914207l_bool(cOMBK_1853791052t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P: fun_fu1251737213l_bool,Q: bool] : hAPP_b930206237l_bool(hAPP_f989466937l_bool(cOMBK_343479628l_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____yfvrrhwpeb___142,axiom,
! [P: fun_Ar1871347069i_bool,Q: fun_fu50365883t_bool] : hAPP_f1559864639i_bool(hAPP_f1224613979i_bool(cOMBK_519762474t_bool,P),Q) = P ).
tff(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_143,axiom,
! [P: fun_fu1251737213l_bool,Q: arrow_501706939e_indi] : hAPP_A107624255l_bool(hAPP_f544895323l_bool(cOMBK_869185066e_indi,P),Q) = P ).
tff(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____yf,axiom,
! [P: fun_fu193278215t_bool,Q: fun_Ar2047178847t_bool,R: arrow_501706939e_indi] : hAPP_A784015157t_bool(cOMBB_715840641e_indi(P,Q),R) = hAPP_f1560118175t_bool(P,hAPP_A2044747691t_bool(Q,R)) ).
%----Conjectures (1)
% tff(conj_0,conjecture,
% ! [I: arrow_501706939e_indi] :
% ( hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(a,b)),hAPP_A2044747691t_bool(p,I)))
% <=> hBOOL(hAPP_f1944886577l_bool(member1484933012le_alt(produc170576535le_alt(a,c)),hAPP_A476679046t_bool(hAPP_A272835723t_bool(hAPP_f1560118175t_bool(arrow_1170304598_below,hAPP_A2044747691t_bool(p,I)),c),b))) ) ).
%------------------------------------------------------------------------------