TPTP Problem File: SCT170+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT170+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 204, 100 axioms selected
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla11]
% Names : arrow_100_fofmg_l204 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 327 ( 98 unt; 0 def)
% Number of atoms : 852 ( 113 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 609 ( 84 ~; 3 |; 71 &)
% ( 44 <=>; 407 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 0 prp; 1-2 aty)
% Number of functors : 186 ( 186 usr; 48 con; 0-3 aty)
% Number of variables : 816 ( 805 !; 11 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:30:34
% : Encoded with monomorphized guards.
%------------------------------------------------------------------------------
%----Explicit typings (83)
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OIIA,axiom,
is_fun631676118l_bool(arrow_1212118780le_IIA) ).
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OLin,axiom,
is_fun432044380l_bool(arrow_1239002508le_Lin) ).
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_OProf,axiom,
is_fun959573582l_bool(arrow_413697182e_Prof) ).
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_Oabove,axiom,
! [B_1_1,B_2_1,B_3_1] :
( ( is_fun282293932t_bool(B_1_1)
& is_Arr553848933le_alt(B_2_1)
& is_Arr553848933le_alt(B_3_1) )
=> is_fun282293932t_bool(arrow_812378712_above(B_1_1,B_2_1,B_3_1)) ) ).
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_Omkbot,axiom,
! [B_1_1,B_2_1] :
( ( is_fun282293932t_bool(B_1_1)
& is_Arr553848933le_alt(B_2_1) )
=> is_fun282293932t_bool(arrow_2077223396_mkbot(B_1_1,B_2_1)) ) ).
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_Omktop,axiom,
! [B_1_1,B_2_1] :
( ( is_fun282293932t_bool(B_1_1)
& is_Arr553848933le_alt(B_2_1) )
=> is_fun282293932t_bool(arrow_78446834_mktop(B_1_1,B_2_1)) ) ).
fof(gsy_c_Arrow__Order__Mirabelle__fjewxadnqg_Ounanimity,axiom,
is_fun631676118l_bool(arrow_467566751nimity) ).
fof(gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_000,axiom,
! [B_1_1,B_2_1,B_3_1] :
( ( is_fun282293932t_bool(B_1_1)
& is_Arr553848933le_alt(B_2_1)
& is_Arr553848933le_alt(B_3_1) )
=> is_bool(in_rel76448514le_alt(B_1_1,B_2_1,B_3_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc_,axiom,
! [B_1_1,B_2_1] :
( is_fun917378774i_bool(B_1_1)
=> is_fun959573582l_bool(pi_Arr688267935t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oin,axiom,
! [B_1_1,B_2_1] :
( is_fun959573582l_bool(B_1_1)
=> is_fun631676118l_bool(pi_fun433100839t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oa,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_1_1)
=> is_fun432044380l_bool(pi_Pro2135156861t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt,axiom,
is_Arr553848933le_alt(undefi1301554228le_alt(arrow_1812558424le_alt)) ).
fof(gsy_c_HOL_Oundefined_000tc__HOL__Obool,axiom,
is_bool(undefined_bool(bool)) ).
fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj,axiom,
is_fun282293932t_bool(undefi802509179t_bool(fun(product_prod(arrow_1812558424le_alt,arrow_1812558424le_alt),bool))) ).
fof(gsy_c_HOL_Oundefined_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg_,axiom,
is_Pro1340026148le_alt(undefi1858141461le_alt(product_prod(arrow_1812558424le_alt,arrow_1812558424le_alt))) ).
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_fun917378774i_bool(top_to1256827021i_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_fun959573582l_bool(top_to1194196741l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde,axiom,
is_fun631676118l_bool(top_to40512653l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord,axiom,
is_fun432044380l_bool(top_to2005687013l_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir,axiom,
is_fun282293932t_bool(top_to2034604131t_bool) ).
fof(gsy_c_Product__Type_OPair_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt,hypothesis,
! [B_1_1,B_2_1] :
( ( is_Arr553848933le_alt(B_1_1)
& is_Arr553848933le_alt(B_2_1) )
=> is_Pro1340026148le_alt(produc171383831le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_Product__Type_Ocurry_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oal,axiom,
! [B_1_1,B_2_1,B_3_1] :
( ( is_fun282293932t_bool(B_1_1)
& is_Arr553848933le_alt(B_2_1)
& is_Arr553848933le_alt(B_3_1) )
=> is_bool(produc362057470t_bool(B_1_1,B_2_1,B_3_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi,axiom,
! [B_1_1] :
( is_fun917378774i_bool(B_1_1)
=> is_fun917378774i_bool(collec45183100e_indi(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oi,axiom,
! [B_1_1] :
( is_fun959573582l_bool(B_1_1)
=> is_fun959573582l_bool(collec1580242420t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewx,axiom,
! [B_1_1] :
( is_fun631676118l_bool(B_1_1)
=> is_fun631676118l_bool(collec1520786044t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjew,axiom,
! [B_1_1] :
( is_fun432044380l_bool(B_1_1)
=> is_fun432044380l_bool(collec874260222t_bool(B_1_1)) ) ).
fof(gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O,axiom,
! [B_1_1] :
( is_fun282293932t_bool(B_1_1)
=> is_fun282293932t_bool(collec1711870802le_alt(B_1_1)) ) ).
fof(gsy_c_fFalse,axiom,
is_bool(fFalse) ).
fof(gsy_c_fTrue,axiom,
is_bool(fTrue) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_000tc__fun_Itc,hypothesis,
! [B_1_1,B_2_1] :
( is_Arr553848933le_alt(B_2_1)
=> is_fun282293932t_bool(hAPP_A619995676t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__HOL__O,axiom,
! [B_1_1,B_2_1] :
( is_fun917378774i_bool(B_1_1)
=> is_bool(hAPP_A1466488369i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It,axiom,
! [B_1_1,B_2_1] : is_fun959573582l_bool(hAPP_A1912483895l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_001,axiom,
! [B_1_1,B_2_1] : is_fun631676118l_bool(hAPP_A1964572607l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_002,axiom,
! [B_1_1,B_2_1] : is_fun432044380l_bool(hAPP_A1944296755l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__fun_It_003,hypothesis,
! [B_1_1,B_2_1] : is_fun282293932t_bool(hAPP_A1374816149t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__prod_I,axiom,
! [B_1_1,B_2_1] : is_Pro1340026148le_alt(hAPP_A1736628091le_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____fjew,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_fun917378774i_bool(hAPP_b1018211123i_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_fun959573582l_bool(hAPP_b1719629739l_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_fun631676118l_bool(hAPP_b990649139l_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_fun432044380l_bool(hAPP_b1965422783l_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_fun282293932t_bool(hAPP_b1024867081t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabelle____fje,axiom,
! [B_1_1,B_2_1] :
( is_bool(B_2_1)
=> is_Pro1340026148le_alt(hAPP_b1817367815le_alt(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__List__Olist_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oa,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_l1656811191t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc_,axiom,
! [B_1_1,B_2_1] :
( is_fun917378774i_bool(B_2_1)
=> is_bool(hAPP_f919661787l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__004,axiom,
! [B_1_1,B_2_1] :
( is_fun959573582l_bool(B_1_1)
=> is_bool(hAPP_f1636546729l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__005,axiom,
! [B_1_1,B_2_1] : is_fun917378774i_bool(hAPP_f749892423i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__006,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_f313042899l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__007,axiom,
! [B_1_1,B_2_1] : is_fun432044380l_bool(hAPP_f861484971l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_Mtc__008,axiom,
! [B_1_1,B_2_1] : is_fun282293932t_bool(hAPP_f695124765t_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__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f204273237l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_009,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1012384989l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_010,axiom,
! [B_1_1,B_2_1] :
( is_fun959573582l_bool(B_2_1)
=> is_bool(hAPP_f453661011l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_011,axiom,
! [B_1_1,B_2_1] :
( is_fun631676118l_bool(B_1_1)
=> is_bool(hAPP_f785543729l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_012,axiom,
! [B_1_1,B_2_1] : is_fun917378774i_bool(hAPP_f355113919i_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_013,axiom,
! [B_1_1,B_2_1] : is_fun_bool_bool(hAPP_f497468491l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__O_014,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f483434675l_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_f1018082273l_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_f1271180905l_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_f1550037191l_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_f1895985727l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f234874197l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_015,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f500145249l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fjew_016,axiom,
! [B_1_1,B_2_1] :
( is_fun631676118l_bool(B_2_1)
=> is_bool(hAPP_f213304539l_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_f1766869725l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_017,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f1279200745l_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_f592909149l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_018,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f526292585l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_f460310451l_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fje_019,axiom,
! [B_1_1,B_2_1] :
( is_fun432044380l_bool(B_2_1)
=> is_bool(hAPP_f503012287l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__,hypothesis,
! [B_1_1,B_2_1] :
( ( is_fun432044380l_bool(B_1_1)
& is_fun282293932t_bool(B_2_1) )
=> is_bool(hAPP_f745298353l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___020,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_2_1)
=> is_fun917378774i_bool(hAPP_f352490559i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___021,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_2_1)
=> is_fun_bool_bool(hAPP_f417299659l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc_,axiom,
! [B_1_1,B_2_1] :
( ( is_fun282293932t_bool(B_1_1)
& is_Pro1340026148le_alt(B_2_1) )
=> is_bool(hAPP_P2075002375t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__022,axiom,
! [B_1_1,B_2_1] :
( is_Pro1340026148le_alt(B_2_1)
=> is_fun917378774i_bool(hAPP_P907763049i_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__023,axiom,
! [B_1_1,B_2_1] :
( is_Pro1340026148le_alt(B_2_1)
=> is_fun_bool_bool(hAPP_P2127852789l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_member_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mt,hypothesis,
! [B_1_1] :
( is_Pro1340026148le_alt(B_1_1)
=> is_fun432044380l_bool(member1056080916le_alt(B_1_1)) ) ).
fof(gsy_v_a____,hypothesis,
is_Arr553848933le_alt(a) ).
fof(gsy_v_b____,hypothesis,
is_Arr553848933le_alt(b) ).
fof(gsy_v_c____,hypothesis,
is_Arr553848933le_alt(c) ).
%----Relevant facts (216)
fof(fact_0__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(p),arrow_413697182e_Prof)) ).
fof(fact_1_assms_I3_J,axiom,
hBOOL(hAPP_f785543729l_bool(arrow_1212118780le_IIA,f)) ).
fof(fact_2_u,axiom,
hBOOL(hAPP_f785543729l_bool(arrow_467566751nimity,f)) ).
fof(fact_3__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_4_dist,axiom,
hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,cons_A2055670914le_alt(a,cons_A2055670914le_alt(b,cons_A2055670914le_alt(c,nil_Ar965638354le_alt))))) ).
fof(fact_5_iff,axiom,
! [I] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(a,b)),hAPP_A1374816149t_bool(p,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),hAPP_A1374816149t_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_Arr553848933le_alt(C)
=> ~ hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,cons_A2055670914le_alt(a,cons_A2055670914le_alt(b,cons_A2055670914le_alt(C,nil_Ar965638354le_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_f453661011l_bool(member1277417654t_bool(cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_2120977260_below,cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_2120977260_below,p),c),b)),b),a)),arrow_413697182e_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_f453661011l_bool(member1277417654t_bool(cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_2120977260_below,cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_2120977260_below,cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_2120977260_below,p),c),b)),b),a)),a),c)),arrow_413697182e_Prof)) ).
fof(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_2120977260_below,p),c),b)),arrow_413697182e_Prof)) ).
fof(fact_10_in__mkbot,axiom,
! [X_1,Y,L_1,Z] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y)
& is_Arr553848933le_alt(Z) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),arrow_2077223396_mkbot(L_1,Z)))
<=> ( Y != Z
& ( X_1 = Z
=> X_1 != Y )
& ( X_1 != Z
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),L_1)) ) ) ) ) ).
fof(fact_11_in__mktop,axiom,
! [X_1,Y,L_1,Z] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y)
& is_Arr553848933le_alt(Z) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),arrow_78446834_mktop(L_1,Z)))
<=> ( X_1 != Z
& ( Y = Z
=> X_1 != Y )
& ( Y != Z
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),L_1)) ) ) ) ) ).
fof(fact_12_in__below,axiom,
! [X_1,Y,L_1,Aa,Ba] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_2120977260_below,L_1),Aa),Ba)))
<=> ( X_1 != Y
& ( Y = Aa
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Ba)),L_1)) )
& ( Y != Aa
=> ( ( X_1 = Aa
=> ( Y = Ba
| hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Y)),L_1)) ) )
& ( X_1 != Aa
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),L_1)) ) ) ) ) ) ) ) ) ).
fof(fact_13_split__paired__All,axiom,
! [Pa] :
( ! [X1] :
( is_Pro1340026148le_alt(X1)
=> hBOOL(hAPP_P2075002375t_bool(Pa,X1)) )
<=> ! [A_1,B] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B) )
=> hBOOL(hAPP_P2075002375t_bool(Pa,produc171383831le_alt(A_1,B))) ) ) ).
fof(fact_14_Pair__eq,axiom,
! [Aa,Ba,A_3,B_3] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba)
& is_Arr553848933le_alt(A_3)
& is_Arr553848933le_alt(B_3) )
=> ( produc171383831le_alt(Aa,Ba) = produc171383831le_alt(A_3,B_3)
<=> ( Aa = A_3
& Ba = B_3 ) ) ) ).
fof(fact_15_Pair__inject,axiom,
! [A_7,B_5,A_6,B_4] :
( ( is_Arr553848933le_alt(A_7)
& is_Arr553848933le_alt(B_5)
& is_Arr553848933le_alt(A_6)
& is_Arr553848933le_alt(B_4) )
=> ( produc171383831le_alt(A_7,B_5) = produc171383831le_alt(A_6,B_4)
=> ~ ( A_7 = A_6
=> B_5 != B_4 ) ) ) ).
fof(fact_16_in__rel__def,axiom,
! [R_1,X_1,Y] :
( hBOOL(in_rel76448514le_alt(R_1,X_1,Y))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),R_1)) ) ).
fof(fact_17_below__Lin,axiom,
! [L_1,X_1,Y] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y) )
=> ( X_1 != Y
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_2120977260_below,L_1),X_1),Y)),arrow_1239002508le_Lin)) ) ) ) ).
fof(fact_18__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(p_1),arrow_413697182e_Prof)) ).
fof(fact_19__C1_C,axiom,
! [P_a,Pa,A_3,B_3,Aa,Ba] :
( ( is_Arr553848933le_alt(A_3)
& is_Arr553848933le_alt(B_3)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( A_3 != B_3
=> ( Aa != B_3
=> ( Ba != A_3
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_a),arrow_413697182e_Prof))
=> ( ! [I] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_3,B_3)),hAPP_A1374816149t_bool(P_a,I))) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa)))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_3,B_3)),hAPP_f695124765t_bool(f,P_a))) ) ) ) ) ) ) ) ) ) ).
fof(fact_20__C2_C,axiom,
! [P_a,Pa,A_3,B_3,Aa,Ba] :
( ( is_Arr553848933le_alt(A_3)
& is_Arr553848933le_alt(B_3)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( A_3 != B_3
=> ( Aa != B_3
=> ( Ba != A_3
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_a),arrow_413697182e_Prof))
=> ( ! [I] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_3,B_3)),hAPP_A1374816149t_bool(P_a,I))) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_3,B_3)),hAPP_f695124765t_bool(f,P_a))) ) ) ) ) ) ) ) ) ) ).
fof(fact_21_assms_I1_J,axiom,
hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(f),pi_fun433100839t_bool(arrow_413697182e_Prof,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,arrow_1239002508le_Lin)))) ).
fof(fact_22_const__Lin__Prof,axiom,
! [L_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,L_1)),arrow_413697182e_Prof)) ) ).
fof(fact_23_mkbot__Lin,axiom,
! [X_1,L_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(arrow_2077223396_mkbot(L_1,X_1)),arrow_1239002508le_Lin)) ) ).
fof(fact_24_mktop__Lin,axiom,
! [X_1,L_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(arrow_78446834_mktop(L_1,X_1)),arrow_1239002508le_Lin)) ) ).
fof(fact_25_Lin__irrefl,axiom,
! [Aa,Ba,L_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),L_1))
=> ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),L_1)) ) ) ).
fof(fact_26_notin__Lin__iff,axiom,
! [X_1,Y,L_1] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y) )
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> ( X_1 != Y
=> ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),L_1))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Y,X_1)),L_1)) ) ) ) ) ).
fof(fact_27_third__alt,axiom,
! [A_5,B_2] :
( ( is_Arr553848933le_alt(A_5)
& is_Arr553848933le_alt(B_2) )
=> ( A_5 != B_2
=> ? [C] :
( is_Arr553848933le_alt(C)
& hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,cons_A2055670914le_alt(A_5,cons_A2055670914le_alt(B_2,cons_A2055670914le_alt(C,nil_Ar965638354le_alt))))) ) ) ) ).
fof(fact_28_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP_f785543729l_bool(arrow_1212118780le_IIA,Fa))
<=> ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),arrow_413697182e_Prof))
=> ! [Xa] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Xa),arrow_413697182e_Prof))
=> ! [A_1,B] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B) )
=> ( ! [I] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_A1374816149t_bool(X,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_A1374816149t_bool(Xa,I))) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_f695124765t_bool(Fa,X)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_f695124765t_bool(Fa,Xa))) ) ) ) ) ) ) ).
fof(fact_29_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP_f785543729l_bool(arrow_467566751nimity,Fa))
<=> ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),arrow_413697182e_Prof))
=> ! [A_1,B] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B) )
=> ( ! [I] : hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_A1374816149t_bool(X,I)))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_f695124765t_bool(Fa,X))) ) ) ) ) ).
fof(fact_30_complete__Lin,axiom,
! [Aa,Ba] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ? [X] :
( is_fun282293932t_bool(X)
& hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),arrow_1239002508le_Lin))
& hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),X)) ) ) ) ).
fof(fact_31_in__above,axiom,
! [X_1,Y,L_1,Aa,Ba] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),arrow_812378712_above(L_1,Aa,Ba)))
<=> ( X_1 != Y
& ( X_1 = Ba
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Y)),L_1)) )
& ( X_1 != Ba
=> ( ( Y = Ba
=> ( X_1 = Aa
| hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Aa)),L_1)) ) )
& ( Y != Ba
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Y)),L_1)) ) ) ) ) ) ) ) ) ).
fof(fact_32_distinct_Osimps_I1_J,axiom,
hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,nil_Ar965638354le_alt)) ).
fof(fact_33_list_Osimps_I2_J,axiom,
! [A_4,List_4] : nil_Ar965638354le_alt != cons_A2055670914le_alt(A_4,List_4) ).
fof(fact_34_list_Oinject,axiom,
! [Aa,List_3,A_3,List_2] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(A_3) )
=> ( cons_A2055670914le_alt(Aa,List_3) = cons_A2055670914le_alt(A_3,List_2)
<=> ( Aa = A_3
& List_3 = List_2 ) ) ) ).
fof(fact_35_not__Cons__self2,axiom,
! [X_7,Xs_7] : cons_A2055670914le_alt(X_7,Xs_7) != Xs_7 ).
fof(fact_36_not__Cons__self,axiom,
! [Xs_6,X_6] : Xs_6 != cons_A2055670914le_alt(X_6,Xs_6) ).
fof(fact_37_above__Lin,axiom,
! [L_1,X_1,Y] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Y) )
=> ( X_1 != Y
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L_1),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(arrow_812378712_above(L_1,X_1,Y)),arrow_1239002508le_Lin)) ) ) ) ).
fof(fact_38_list_Osimps_I3_J,axiom,
! [A_2,List_1] : cons_A2055670914le_alt(A_2,List_1) != nil_Ar965638354le_alt ).
fof(fact_39_dictatorI,axiom,
! [I_1,Fa] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(Fa),pi_fun433100839t_bool(arrow_413697182e_Prof,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,arrow_1239002508le_Lin))))
=> ( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),arrow_413697182e_Prof))
=> ! [A_1,B] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B) )
=> ( A_1 != B
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_A1374816149t_bool(X,I_1)))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B)),hAPP_f695124765t_bool(Fa,X))) ) ) ) )
=> hBOOL(hAPP_A1466488369i_bool(hAPP_f355113919i_bool(arrow_2061665457ctator,Fa),I_1)) ) ) ).
fof(fact_40_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_1)),hAPP_P2127852789l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A)) ) ) ).
fof(fact_41_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B_1)))
=> ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_1)),hAPP_A1374816149t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A)) ) ) ).
fof(fact_42_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B_1)))
=> ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_1)),hAPP_b1024867081t_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
fof(fact_43_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_1)),hAPP_A1912483895l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A)) ) ) ).
fof(fact_44_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_1)),hAPP_b1719629739l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
fof(fact_45_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_1)),hAPP_b1965422783l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
fof(fact_46_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_1)),hAPP_A1964572607l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A)) ) ) ).
fof(fact_47_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_1)),hAPP_b990649139l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A)) ) ) ).
fof(fact_48_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_1)),hAPP_P907763049i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A)) ) ) ).
fof(fact_49_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_1)),hAPP_f749892423i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A)) ) ) ).
fof(fact_50_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_1)),hAPP_f313042899l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A)) ) ) ).
fof(fact_51_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_1)),hAPP_f352490559i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A)) ) ) ).
fof(fact_52_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_1)),hAPP_f417299659l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A)) ) ) ).
fof(fact_53_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B_1)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_1)),hAPP_f355113919i_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A)) ) ) ).
fof(fact_54_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_1)),hAPP_f497468491l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A)) ) ) ).
fof(fact_55_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_1)),hAPP_f861484971l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A)) ) ) ).
fof(fact_56_PiE,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B_1)))
=> ( ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_1)),hAPP_A1944296755l_bool(B_1,X_1)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A)) ) ) ).
fof(fact_57_list_Oexhaust,axiom,
! [Y_4] :
( Y_4 != nil_Ar965638354le_alt
=> ~ ! [A_1,List] :
( is_Arr553848933le_alt(A_1)
=> Y_4 != cons_A2055670914le_alt(A_1,List) ) ) ).
fof(fact_58_neq__Nil__conv,axiom,
! [Xs] :
( Xs != nil_Ar965638354le_alt
<=> ? [Y_1,Ys_2] :
( is_Arr553848933le_alt(Y_1)
& Xs = cons_A2055670914le_alt(Y_1,Ys_2) ) ) ).
fof(fact_59_alt3,axiom,
? [A_1,B,C] :
( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B)
& is_Arr553848933le_alt(C)
& hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,cons_A2055670914le_alt(A_1,cons_A2055670914le_alt(B,cons_A2055670914le_alt(C,nil_Ar965638354le_alt))))) ) ).
fof(fact_60_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B_1)))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_1)),hAPP_P2127852789l_bool(B_1,X_1))) ) ) ).
fof(fact_61_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B_1)))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_1)),hAPP_P907763049i_bool(B_1,X_1))) ) ) ).
fof(fact_62_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B_1)))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_1)),hAPP_f749892423i_bool(B_1,X_1))) ) ) ).
fof(fact_63_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B_1)))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_1)),hAPP_f313042899l_bool(B_1,X_1))) ) ) ).
fof(fact_64_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B_1)))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_1)),hAPP_f352490559i_bool(B_1,X_1))) ) ) ).
fof(fact_65_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B_1)))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_1)),hAPP_f417299659l_bool(B_1,X_1))) ) ) ).
fof(fact_66_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B_1)))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_1)),hAPP_f355113919i_bool(B_1,X_1))) ) ) ).
fof(fact_67_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B_1)))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_1)),hAPP_f497468491l_bool(B_1,X_1))) ) ) ).
fof(fact_68_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B_1)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_1)),hAPP_A1374816149t_bool(B_1,X_1))) ) ) ).
fof(fact_69_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_1)),hAPP_b1024867081t_bool(B_1,X_1))) ) ) ).
fof(fact_70_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B_1)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_1)),hAPP_A1912483895l_bool(B_1,X_1))) ) ) ).
fof(fact_71_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_1)),hAPP_b1719629739l_bool(B_1,X_1))) ) ) ).
fof(fact_72_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_1)),hAPP_b1965422783l_bool(B_1,X_1))) ) ) ).
fof(fact_73_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B_1)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_1)),hAPP_A1964572607l_bool(B_1,X_1))) ) ) ).
fof(fact_74_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B_1)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_1)),hAPP_b990649139l_bool(B_1,X_1))) ) ) ).
fof(fact_75_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B_1)))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_1)),hAPP_f861484971l_bool(B_1,X_1))) ) ) ).
fof(fact_76_Pi__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B_1)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_1)),hAPP_A1944296755l_bool(B_1,X_1))) ) ) ).
fof(fact_77_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,B_1))))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_78_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,hAPP_f1970593179i_bool(cOMBK_100791596le_alt,B_1))))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_79_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,hAPP_f681113465i_bool(cOMBK_454107598t_bool,B_1))))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_80_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,hAPP_f219827985l_bool(cOMBK_886533338t_bool,B_1))))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_1)),B_1)) ) ) ).
fof(fact_81_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,hAPP_f1903519657i_bool(cOMBK_2076140708t_bool,B_1))))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_82_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,hAPP_f1667233577l_bool(cOMBK_1015076504t_bool,B_1))))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_1)),B_1)) ) ) ).
fof(fact_83_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,hAPP_f1677452273i_bool(cOMBK_1372975190t_bool,B_1))))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_1)),B_1)) ) ) ).
fof(fact_84_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,hAPP_f1235573641l_bool(cOMBK_1072228194t_bool,B_1))))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_1)),B_1)) ) ) ).
fof(fact_85_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,B_1))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_86_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,hAPP_f1520552209t_bool(cOMBK_697786936l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_1)),B_1)) ) ) ).
fof(fact_87_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,hAPP_f813556705l_bool(cOMBK_116240846e_indi,B_1))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_88_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,hAPP_f371807573l_bool(cOMBK_697604314l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_89_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,hAPP_f2135750719l_bool(cOMBK_971068024l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_90_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,hAPP_f1697527281l_bool(cOMBK_1292462166e_indi,B_1))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_91_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,hAPP_f448497509l_bool(cOMBK_1268833122l_bool,B_1))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_92_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,B_1))))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_93_funcset__mem,axiom,
! [X_1,F,A,B_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,B_1))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_1)),B_1)) ) ) ).
fof(fact_94_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP_A1466488369i_bool(hAPP_f355113919i_bool(arrow_2061665457ctator,Fa),I_1))
<=> ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),arrow_413697182e_Prof))
=> hAPP_f695124765t_bool(Fa,X) = hAPP_A1374816149t_bool(X,I_1) ) ) ).
fof(fact_95_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_Pro1340026148le_alt(X)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X)),hAPP_P907763049i_bool(B_1,X))) ) )
=> hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B_1))) ) ).
fof(fact_96_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X)),hAPP_f749892423i_bool(B_1,X))) )
=> hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B_1))) ) ).
fof(fact_97_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X)),hAPP_f313042899l_bool(B_1,X))) )
=> hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B_1))) ) ).
fof(fact_98_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_fun282293932t_bool(X)
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X)),hAPP_f352490559i_bool(B_1,X))) ) )
=> hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B_1))) ) ).
fof(fact_99_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_fun282293932t_bool(X)
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X)),hAPP_f417299659l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B_1))) ) ).
fof(fact_100_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X)),hAPP_f355113919i_bool(B_1,X))) )
=> hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B_1))) ) ).
fof(fact_101_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X)),hAPP_f497468491l_bool(B_1,X))) )
=> hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B_1))) ) ).
fof(fact_102_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X)),hAPP_A1374816149t_bool(B_1,X))) )
=> hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B_1))) ) ).
fof(fact_103_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X)),hAPP_b1024867081t_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B_1))) ) ).
fof(fact_104_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X)),hAPP_A1912483895l_bool(B_1,X))) )
=> hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B_1))) ) ).
fof(fact_105_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X)),hAPP_b1719629739l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B_1))) ) ).
fof(fact_106_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X)),hAPP_b1965422783l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B_1))) ) ).
fof(fact_107_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X)),hAPP_A1964572607l_bool(B_1,X))) )
=> hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B_1))) ) ).
fof(fact_108_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X)),hAPP_b990649139l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B_1))) ) ).
fof(fact_109_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( is_Pro1340026148le_alt(X)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X)),hAPP_P2127852789l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B_1))) ) ).
fof(fact_110_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X)),hAPP_f861484971l_bool(B_1,X))) )
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B_1))) ) ).
fof(fact_111_Pi__I,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X)),hAPP_A1944296755l_bool(B_1,X))) )
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B_1))) ) ).
fof(fact_112_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_Pro1340026148le_alt(X)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X)),B_1)) ) )
=> hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,hAPP_f1970593179i_bool(cOMBK_100791596le_alt,B_1)))) ) ).
fof(fact_113_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X)),B_1)) )
=> hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,hAPP_f681113465i_bool(cOMBK_454107598t_bool,B_1)))) ) ).
fof(fact_114_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,hAPP_f219827985l_bool(cOMBK_886533338t_bool,B_1)))) ) ).
fof(fact_115_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_fun282293932t_bool(X)
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X)),B_1)) ) )
=> hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,hAPP_f1903519657i_bool(cOMBK_2076140708t_bool,B_1)))) ) ).
fof(fact_116_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_fun282293932t_bool(X)
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X)),B_1)) ) )
=> hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,hAPP_f1667233577l_bool(cOMBK_1015076504t_bool,B_1)))) ) ).
fof(fact_117_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X)),B_1)) )
=> hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,hAPP_f1677452273i_bool(cOMBK_1372975190t_bool,B_1)))) ) ).
fof(fact_118_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,hAPP_f1235573641l_bool(cOMBK_1072228194t_bool,B_1)))) ) ).
fof(fact_119_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X)),B_1)) )
=> hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,B_1)))) ) ).
fof(fact_120_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X)),B_1)) ) )
=> hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,hAPP_f1520552209t_bool(cOMBK_697786936l_bool,B_1)))) ) ).
fof(fact_121_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,hAPP_f813556705l_bool(cOMBK_116240846e_indi,B_1)))) ) ).
fof(fact_122_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X)),B_1)) ) )
=> hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,hAPP_f371807573l_bool(cOMBK_697604314l_bool,B_1)))) ) ).
fof(fact_123_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X)),B_1)) ) )
=> hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,hAPP_f2135750719l_bool(cOMBK_971068024l_bool,B_1)))) ) ).
fof(fact_124_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,hAPP_f1697527281l_bool(cOMBK_1292462166e_indi,B_1)))) ) ).
fof(fact_125_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X)),B_1)) ) )
=> hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,hAPP_f448497509l_bool(cOMBK_1268833122l_bool,B_1)))) ) ).
fof(fact_126_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( is_Pro1340026148le_alt(X)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X)),B_1)) ) )
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,B_1)))) ) ).
fof(fact_127_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,B_1)))) ) ).
fof(fact_128_funcsetI,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X)),B_1)) )
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,B_1)))) ) ).
fof(fact_129_linear__alt,axiom,
? [L] :
( is_fun282293932t_bool(L)
& hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin)) ) ).
fof(fact_130_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_Pro1340026148le_alt(X)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X)),hAPP_P907763049i_bool(B_1,X))) ) )
=> hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B_1))) ) ).
fof(fact_131_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X)),hAPP_f749892423i_bool(B_1,X))) )
=> hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B_1))) ) ).
fof(fact_132_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X)),hAPP_f313042899l_bool(B_1,X))) )
=> hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B_1))) ) ).
fof(fact_133_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_fun282293932t_bool(X)
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X)),hAPP_f352490559i_bool(B_1,X))) ) )
=> hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B_1))) ) ).
fof(fact_134_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_fun282293932t_bool(X)
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X)),hAPP_f417299659l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B_1))) ) ).
fof(fact_135_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X)),hAPP_f355113919i_bool(B_1,X))) )
=> hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B_1))) ) ).
fof(fact_136_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X)),hAPP_f497468491l_bool(B_1,X))) )
=> hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B_1))) ) ).
fof(fact_137_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X)),hAPP_A1374816149t_bool(B_1,X))) )
=> hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B_1))) ) ).
fof(fact_138_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X)),hAPP_b1024867081t_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B_1))) ) ).
fof(fact_139_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X)),hAPP_A1912483895l_bool(B_1,X))) )
=> hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B_1))) ) ).
fof(fact_140_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X)),hAPP_b1719629739l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B_1))) ) ).
fof(fact_141_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X)),hAPP_b1965422783l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B_1))) ) ).
fof(fact_142_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X)),hAPP_A1964572607l_bool(B_1,X))) )
=> hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B_1))) ) ).
fof(fact_143_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_bool(X)
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X)),hAPP_b990649139l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B_1))) ) ).
fof(fact_144_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( is_Pro1340026148le_alt(X)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X)),hAPP_P2127852789l_bool(B_1,X))) ) )
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B_1))) ) ).
fof(fact_145_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X)),hAPP_f861484971l_bool(B_1,X))) )
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B_1))) ) ).
fof(fact_146_Pi__I_H,axiom,
! [F,B_1,A] :
( ! [X] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X)),hAPP_A1944296755l_bool(B_1,X))) )
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B_1))) ) ).
fof(fact_147_Pi__cong,axiom,
! [B_1,G,F,A] :
( ! [W] :
( is_Pro1340026148le_alt(W)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(W),A))
=> ( hBOOL(hAPP_P2075002375t_bool(F,W))
<=> hBOOL(hAPP_P2075002375t_bool(G,W)) ) ) )
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B_1)))
<=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(G),pi_Pro2135156861t_bool(A,B_1))) ) ) ).
fof(fact_148_Pi__cong,axiom,
! [B_1,F,G,A] :
( ! [W] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(W),A))
=> hAPP_f695124765t_bool(F,W) = hAPP_f695124765t_bool(G,W) )
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B_1)))
<=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(G),pi_fun433100839t_bool(A,B_1))) ) ) ).
fof(fact_149_Pi__cong,axiom,
! [B_1,F,G,A] :
( ! [W] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(W),A))
=> hAPP_A1374816149t_bool(F,W) = hAPP_A1374816149t_bool(G,W) )
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B_1)))
<=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(G),pi_Arr688267935t_bool(A,B_1))) ) ) ).
fof(fact_150_splice_Osimps_I2_J,axiom,
! [V,Va] : splice1200342693le_alt(cons_A2055670914le_alt(V,Va),nil_Ar965638354le_alt) = cons_A2055670914le_alt(V,Va) ).
fof(fact_151_splice_Osimps_I3_J,axiom,
! [X_5,Xs_5,Y_3,Ys_1] : splice1200342693le_alt(cons_A2055670914le_alt(X_5,Xs_5),cons_A2055670914le_alt(Y_3,Ys_1)) = cons_A2055670914le_alt(X_5,cons_A2055670914le_alt(Y_3,splice1200342693le_alt(Xs_5,Ys_1))) ).
fof(fact_152_splice_Osimps_I1_J,axiom,
! [Ys] : splice1200342693le_alt(nil_Ar965638354le_alt,Ys) = Ys ).
fof(fact_153_splice__Nil2,axiom,
! [Xs_4] : splice1200342693le_alt(Xs_4,nil_Ar965638354le_alt) = Xs_4 ).
fof(fact_154_pred__equals__eq2,axiom,
! [S,R_1] :
( ( is_fun282293932t_bool(S)
& is_fun282293932t_bool(R_1) )
=> ( ! [X,Xa] :
( ( is_Arr553848933le_alt(X)
& is_Arr553848933le_alt(Xa) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X,Xa)),R_1))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X,Xa)),S)) ) )
<=> R_1 = S ) ) ).
fof(fact_155_prod_Oexhaust,axiom,
! [Y_2] :
( is_Pro1340026148le_alt(Y_2)
=> ~ ! [A_1,B] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B) )
=> Y_2 != produc171383831le_alt(A_1,B) ) ) ).
fof(fact_156_PairE,axiom,
! [P_1] :
( is_Pro1340026148le_alt(P_1)
=> ~ ! [X,Y_1] :
( ( is_Arr553848933le_alt(X)
& is_Arr553848933le_alt(Y_1) )
=> P_1 != produc171383831le_alt(X,Y_1) ) ) ).
fof(fact_157_split__paired__Ex,axiom,
! [Pa] :
( ? [X1] :
( is_Pro1340026148le_alt(X1)
& hBOOL(hAPP_P2075002375t_bool(Pa,X1)) )
<=> ? [A_1,B] :
( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B)
& hBOOL(hAPP_P2075002375t_bool(Pa,produc171383831le_alt(A_1,B))) ) ) ).
fof(fact_158_insert__Nil,axiom,
! [X_4] : insert1800010984le_alt(X_4,nil_Ar965638354le_alt) = cons_A2055670914le_alt(X_4,nil_Ar965638354le_alt) ).
fof(fact_159_distinct__insert,axiom,
! [X_3,Xs_3] :
( hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,Xs_3))
=> hBOOL(hAPP_l1656811191t_bool(distin2063252165le_alt,insert1800010984le_alt(X_3,Xs_3))) ) ).
fof(fact_160_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
<=> hBOOL(hAPP_A1466488369i_bool(A,X_1)) ) ).
fof(fact_161_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X_1),A))
<=> hBOOL(hAPP_bool_bool(A,X_1)) ) ).
fof(fact_162_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),A))
<=> hBOOL(hAPP_P2075002375t_bool(A,X_1)) ) ).
fof(fact_163_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),A))
<=> hBOOL(hAPP_f1636546729l_bool(A,X_1)) ) ).
fof(fact_164_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),A))
<=> hBOOL(hAPP_f745298353l_bool(A,X_1)) ) ).
fof(fact_165_mem__def,axiom,
! [X_1,A] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),A))
<=> hBOOL(hAPP_f785543729l_bool(A,X_1)) ) ).
fof(fact_166_Collect__def,axiom,
! [Pa] :
( is_fun917378774i_bool(Pa)
=> collec45183100e_indi(Pa) = Pa ) ).
fof(fact_167_list__nonempty__induct,axiom,
! [Pa,Xs] :
( Xs != nil_Ar965638354le_alt
=> ( ! [X] :
( is_Arr553848933le_alt(X)
=> hBOOL(hAPP_l1656811191t_bool(Pa,cons_A2055670914le_alt(X,nil_Ar965638354le_alt))) )
=> ( ! [X,Xs_2] :
( is_Arr553848933le_alt(X)
=> ( Xs_2 != nil_Ar965638354le_alt
=> ( hBOOL(hAPP_l1656811191t_bool(Pa,Xs_2))
=> hBOOL(hAPP_l1656811191t_bool(Pa,cons_A2055670914le_alt(X,Xs_2))) ) ) )
=> hBOOL(hAPP_l1656811191t_bool(Pa,Xs)) ) ) ) ).
fof(fact_168_curry__def,axiom,
! [X,Xa,Xb] :
( hBOOL(produc362057470t_bool(X,Xa,Xb))
<=> hBOOL(hAPP_P2075002375t_bool(X,produc171383831le_alt(Xa,Xb))) ) ).
fof(fact_169_curryI,axiom,
! [F,Aa,Ba] :
( hBOOL(hAPP_P2075002375t_bool(F,produc171383831le_alt(Aa,Ba)))
=> hBOOL(produc362057470t_bool(F,Aa,Ba)) ) ).
fof(fact_170_curryE,axiom,
! [F,Aa,Ba] :
( hBOOL(produc362057470t_bool(F,Aa,Ba))
=> hBOOL(hAPP_P2075002375t_bool(F,produc171383831le_alt(Aa,Ba))) ) ).
fof(fact_171_curryD,axiom,
! [F,Aa,Ba] :
( hBOOL(produc362057470t_bool(F,Aa,Ba))
=> hBOOL(hAPP_P2075002375t_bool(F,produc171383831le_alt(Aa,Ba))) ) ).
fof(fact_172_curry__conv,axiom,
! [F,Aa,Ba] :
( hBOOL(produc362057470t_bool(F,Aa,Ba))
<=> hBOOL(hAPP_P2075002375t_bool(F,produc171383831le_alt(Aa,Ba))) ) ).
fof(fact_173_eq__Nil__null,axiom,
! [Xs] :
( Xs = nil_Ar965638354le_alt
<=> hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,Xs)) ) ).
fof(fact_174_List_Onull__def,axiom,
! [Xs] :
( hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,Xs))
<=> Xs = nil_Ar965638354le_alt ) ).
fof(fact_175_null__rec_I1_J,axiom,
! [X_2,Xs_1] : ~ hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,cons_A2055670914le_alt(X_2,Xs_1))) ).
fof(fact_176_null__rec_I2_J,axiom,
hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,nil_Ar965638354le_alt)) ).
fof(fact_177_equal__Nil__null,axiom,
! [Xs] :
( hBOOL(hAPP_l1656811191t_bool(equal_35123829le_alt(Xs),nil_Ar965638354le_alt))
<=> hBOOL(hAPP_l1656811191t_bool(null_A1200409306le_alt,Xs)) ) ).
fof(fact_178_Prof__def,axiom,
arrow_413697182e_Prof = pi_Arr688267935t_bool(top_to1256827021i_bool,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,arrow_1239002508le_Lin)) ).
fof(fact_179_top1I,axiom,
! [X_1] : hBOOL(hAPP_f785543729l_bool(top_to40512653l_bool,X_1)) ).
fof(fact_180_top1I,axiom,
! [X_1] : hBOOL(hAPP_f745298353l_bool(top_to2005687013l_bool,X_1)) ).
fof(fact_181_top1I,axiom,
! [X_1] : hBOOL(hAPP_f1636546729l_bool(top_to1194196741l_bool,X_1)) ).
fof(fact_182_top1I,axiom,
! [X_1] : hBOOL(hAPP_P2075002375t_bool(top_to2034604131t_bool,X_1)) ).
fof(fact_183_top1I,axiom,
! [X_1] : hBOOL(hAPP_A1466488369i_bool(top_to1256827021i_bool,X_1)) ).
fof(fact_184_Pi__UNIV,axiom,
! [A] : pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,top_to1647826457l_bool)) = top_to2005687013l_bool ).
fof(fact_185_Pi__UNIV,axiom,
! [A] : pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,top_to2005687013l_bool)) = top_to40512653l_bool ).
fof(fact_186_Pi__UNIV,axiom,
! [A] : pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,top_to2005687013l_bool)) = top_to1194196741l_bool ).
fof(fact_187_equal__list__def,axiom,
! [X_1,Y] :
( hBOOL(hAPP_l1656811191t_bool(equal_35123829le_alt(X_1),Y))
<=> X_1 = Y ) ).
fof(fact_188_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f387058535l_bool(member_bool(X_1),top_to1647826457l_bool)) ).
fof(fact_189_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),top_to1256827021i_bool)) ).
fof(fact_190_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),top_to2034604131t_bool)) ).
fof(fact_191_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),top_to1194196741l_bool)) ).
fof(fact_192_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),top_to2005687013l_bool)) ).
fof(fact_193_iso__tuple__UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),top_to40512653l_bool)) ).
fof(fact_194_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f387058535l_bool(member_bool(X_1),top_to1647826457l_bool)) ).
fof(fact_195_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),top_to1256827021i_bool)) ).
fof(fact_196_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_1),top_to2034604131t_bool)) ).
fof(fact_197_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),top_to1194196741l_bool)) ).
fof(fact_198_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),top_to2005687013l_bool)) ).
fof(fact_199_UNIV__I,axiom,
! [X_1] : hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_1),top_to40512653l_bool)) ).
fof(fact_200_UNIV__def,axiom,
top_to40512653l_bool = collec1520786044t_bool(hAPP_b990649139l_bool(cOMBK_580911210t_bool,fTrue)) ).
fof(fact_201_UNIV__def,axiom,
top_to2005687013l_bool = collec874260222t_bool(hAPP_b1965422783l_bool(cOMBK_977355664t_bool,fTrue)) ).
fof(fact_202_UNIV__def,axiom,
top_to1194196741l_bool = collec1580242420t_bool(hAPP_b1719629739l_bool(cOMBK_789167586t_bool,fTrue)) ).
fof(fact_203_UNIV__def,axiom,
top_to2034604131t_bool = collec1711870802le_alt(hAPP_b1024867081t_bool(cOMBK_2069093696le_alt,fTrue)) ).
fof(fact_204_UNIV__def,axiom,
top_to1256827021i_bool = collec45183100e_indi(hAPP_b1018211123i_bool(cOMBK_1157044842e_indi,fTrue)) ).
fof(fact_205_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_f785543729l_bool(top_to40512653l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_206_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_f745298353l_bool(top_to2005687013l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_207_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_f1636546729l_bool(top_to1194196741l_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_208_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_P2075002375t_bool(top_to2034604131t_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_209_top__apply,axiom,
! [X_1] :
( hBOOL(hAPP_A1466488369i_bool(top_to1256827021i_bool,X_1))
<=> hBOOL(top_top_bool) ) ).
fof(fact_210_UNIV__eq__I,axiom,
! [A] :
( is_fun_bool_bool(A)
=> ( ! [X] :
( is_bool(X)
=> hBOOL(hAPP_f387058535l_bool(member_bool(X),A)) )
=> top_to1647826457l_bool = A ) ) ).
fof(fact_211_UNIV__eq__I,axiom,
! [A] :
( is_fun917378774i_bool(A)
=> ( ! [X] : hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X),A))
=> top_to1256827021i_bool = A ) ) ).
fof(fact_212_UNIV__eq__I,axiom,
! [A] :
( is_fun282293932t_bool(A)
=> ( ! [X] :
( is_Pro1340026148le_alt(X)
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X),A)) )
=> top_to2034604131t_bool = A ) ) ).
fof(fact_213_UNIV__eq__I,axiom,
! [A] :
( is_fun959573582l_bool(A)
=> ( ! [X] : hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X),A))
=> top_to1194196741l_bool = A ) ) ).
fof(fact_214_UNIV__eq__I,axiom,
! [A] :
( is_fun432044380l_bool(A)
=> ( ! [X] :
( is_fun282293932t_bool(X)
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X),A)) )
=> top_to2005687013l_bool = A ) ) ).
fof(fact_215_UNIV__eq__I,axiom,
! [A] :
( is_fun631676118l_bool(A)
=> ( ! [X] : hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X),A))
=> top_to40512653l_bool = A ) ) ).
%----Helper facts (27)
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_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____fje,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_A1466488369i_bool(hAPP_b1018211123i_bool(cOMBK_1157044842e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_P2075002375t_bool(hAPP_b1024867081t_bool(cOMBK_2069093696le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f745298353l_bool(hAPP_b1965422783l_bool(cOMBK_977355664t_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_P2127852789l_bool(hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj,axiom,
! [P,Q] :
( is_fun282293932t_bool(P)
=> hAPP_b1024867081t_bool(hAPP_f1520552209t_bool(cOMBK_697786936l_bool,P),Q) = P ) ).
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_f417299659l_bool(hAPP_f1667233577l_bool(cOMBK_1015076504t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe,axiom,
! [P,Q] :
( is_fun432044380l_bool(P)
=> hAPP_b1965422783l_bool(hAPP_f2135750719l_bool(cOMBK_971068024l_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg__,axiom,
! [P,Q] :
( is_fun917378774i_bool(P)
=> hAPP_P907763049i_bool(hAPP_f1970593179i_bool(cOMBK_100791596le_alt,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj_024,axiom,
! [P,Q] :
( is_fun282293932t_bool(P)
=> hAPP_A1374816149t_bool(hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,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_f1636546729l_bool(hAPP_b1719629739l_bool(cOMBK_789167586t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___025,axiom,
! [P,Q] :
( is_fun917378774i_bool(P)
=> hAPP_f352490559i_bool(hAPP_f1903519657i_bool(cOMBK_2076140708t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_026,axiom,
! [P,Q] :
( is_fun432044380l_bool(P)
=> hAPP_A1944296755l_bool(hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_027,axiom,
! [P,Q] :
( is_fun_bool_bool(P)
=> hAPP_f313042899l_bool(hAPP_f219827985l_bool(cOMBK_886533338t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje,axiom,
! [P,Q] :
( is_fun959573582l_bool(P)
=> hAPP_b1719629739l_bool(hAPP_f371807573l_bool(cOMBK_697604314l_bool,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000,axiom,
! [P,Q,R] : hAPP_A1374816149t_bool(cOMBC_1778077589t_bool(P,Q),R) = hAPP_A619995676t_bool(hAPP_A702630576t_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___028,axiom,
! [P,Q] :
( is_fun917378774i_bool(P)
=> hAPP_f749892423i_bool(hAPP_f681113465i_bool(cOMBK_454107598t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____fje_029,axiom,
! [P,Q] :
( is_fun959573582l_bool(P)
=> hAPP_A1912483895l_bool(hAPP_f813556705l_bool(cOMBK_116240846e_indi,P),Q) = P ) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_030,axiom,
! [P,Q,R] : hAPP_A702630576t_bool(cOMBC_493523632t_bool(P,Q),R) = hAPP_A384644407t_bool(hAPP_A460042315t_bool(P,R),Q) ).
fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__,axiom,
! [P,Q] :
( is_bool(P)
=> hAPP_f785543729l_bool(hAPP_b990649139l_bool(cOMBK_580911210t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_031,axiom,
! [P,Q] :
( is_fun432044380l_bool(P)
=> hAPP_f861484971l_bool(hAPP_f20355883l_bool(cOMBK_1088865252t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc_032,axiom,
! [P,Q] :
( is_fun_bool_bool(P)
=> hAPP_f497468491l_bool(hAPP_f1235573641l_bool(cOMBK_1072228194t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel,axiom,
! [P,Q] :
( is_fun631676118l_bool(P)
=> hAPP_b990649139l_bool(hAPP_f448497509l_bool(cOMBK_1268833122l_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___033,axiom,
! [P,Q] :
( is_fun917378774i_bool(P)
=> hAPP_f355113919i_bool(hAPP_f1677452273i_bool(cOMBK_1372975190t_bool,P),Q) = P ) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabel_034,axiom,
! [P,Q] :
( is_fun631676118l_bool(P)
=> hAPP_A1964572607l_bool(hAPP_f1697527281l_bool(cOMBK_1292462166e_indi,P),Q) = P ) ).
fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj,axiom,
! [P,Q,R] : hAPP_A460042315t_bool(cOMBB_69933763e_indi(P,Q),R) = hAPP_f1336478923t_bool(P,hAPP_A1374816149t_bool(Q,R)) ).
%----Conjectures (1)
fof(conj_0,conjecture,
! [I] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(a,b)),hAPP_A1374816149t_bool(p,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(a,c)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_2120977260_below,hAPP_A1374816149t_bool(p,I)),c),b))) ) ).
%------------------------------------------------------------------------------