TPTP Problem File: SCT171+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SCT171+1 : TPTP v8.2.0. Released v5.3.0.
% Domain : Social Choice Theory
% Problem : Arrow's Impossibility Theorem line 309, 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_l309 [Bla11]
% Status : Theorem
% Rating : 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.08 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0
% Syntax : Number of formulae : 322 ( 119 unt; 0 def)
% Number of atoms : 793 ( 145 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 588 ( 117 ~; 9 |; 57 &)
% ( 50 <=>; 355 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 0 prp; 1-2 aty)
% Number of functors : 217 ( 217 usr; 62 con; 0-2 aty)
% Number of variables : 685 ( 684 !; 1 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 15:47:39
% : 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_Ounanimity,axiom,
is_fun631676118l_bool(arrow_467566751nimity) ).
fof(gsy_c_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc__Nat__,axiom,
! [B_1_1,B_2_1] : is_fun917378774i_bool(cOMBC_277798809t_bool(B_1_1,B_2_1)) ).
fof(gsy_c_Fun_Oinj__on_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000tc,axiom,
! [B_1_1,B_2_1] :
( is_fun917378774i_bool(B_2_1)
=> is_bool(inj_on24934938di_nat(B_1_1,B_2_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__Arrow____Order____Mirabelle____fjewxadnqg__Oindi,axiom,
is_Arr625519182e_indi(undefi818645567e_indi(arrow_2110637339e_indi)) ).
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_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____fjewxadnq,axiom,
! [B_1_1,B_2_1] :
( is_fun917378774i_bool(B_1_1)
=> is_fun1016509681e_indi(hilber1792103167di_nat(B_1_1,B_2_1)) ) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool,axiom,
is_bool(top_top_bool) ).
fof(gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____,axiom,
is_fun917378774i_bool(top_to1256827021i_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_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,axiom,
! [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_Arr625519182e_indi(B_2_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_Arr625519182e_indi(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_Arr625519182e_indi(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_Arr625519182e_indi(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,axiom,
! [B_1_1,B_2_1] :
( is_Arr625519182e_indi(B_2_1)
=> is_fun282293932t_bool(hAPP_A1374816149t_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_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__Nat__Onat_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oi,axiom,
! [B_1_1,B_2_1] :
( is_fun1016509681e_indi(B_1_1)
=> is_Arr625519182e_indi(hAPP_n385347014e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,axiom,
! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____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_Arr625519182e_indi(hAPP_f1818473245e_indi(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_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__006,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__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,hypothesis,
! [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_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_Arr625519182e_indi(hAPP_f618619045e_indi(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_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_013,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_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__,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_2_1)
=> is_Arr625519182e_indi(hAPP_f1659504677e_indi(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___020,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___021,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___022,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_2_1)
=> is_fun432044380l_bool(hAPP_f2056167603l_bool(B_1_1,B_2_1)) ) ).
fof(gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg___023,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_2_1)
=> is_fun282293932t_bool(hAPP_f1673487381t_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_Arr625519182e_indi(hAPP_P2024088443e_indi(B_1_1,B_2_1)) ).
fof(gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____fjewxadnqg__Oalt_Mtc__024,axiom,
! [B_1_1,B_2_1] :
( is_fun282293932t_bool(B_1_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__025,axiom,
! [B_1_1,B_2_1] : is_fun917378774i_bool(hAPP_P907763049i_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_fun432044380l_bool(member1056080916le_alt(B_1_1)) ).
fof(gsy_v_Lab____,axiom,
is_fun282293932t_bool(lab) ).
fof(gsy_v_Lba____,axiom,
is_fun282293932t_bool(lba) ).
fof(gsy_v_a____,axiom,
is_Arr553848933le_alt(a) ).
fof(gsy_v_b____,axiom,
is_Arr553848933le_alt(b) ).
fof(gsy_v_c____,hypothesis,
is_Arr553848933le_alt(c) ).
fof(gsy_v_d____,hypothesis,
is_Arr553848933le_alt(d) ).
fof(gsy_v_e____,axiom,
is_Arr553848933le_alt(e) ).
%----Relevant facts (198)
fof(fact_0_assms_I3_J,axiom,
hBOOL(hAPP_f785543729l_bool(arrow_1212118780le_IIA,f)) ).
fof(fact_1_u,axiom,
hBOOL(hAPP_f785543729l_bool(arrow_467566751nimity,f)) ).
fof(fact_2__096c_A_126_061_Ad_096,axiom,
c != d ).
fof(fact_3__096P_A_058_AProf_096,axiom,
hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(p),arrow_413697182e_Prof)) ).
fof(fact_4_in__mkbot,axiom,
! [X_2,Y_1,L,Z_1] :
( ( is_Arr553848933le_alt(X_2)
& is_Arr553848933le_alt(Y_1)
& is_Arr553848933le_alt(Z_1) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,L),Z_1)))
<=> ( Y_1 != Z_1
& ( X_2 = Z_1
=> X_2 != Y_1 )
& ( X_2 != Z_1
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L)) ) ) ) ) ).
fof(fact_5_in__mktop,axiom,
! [X_2,Y_1,L,Z_1] :
( ( is_Arr553848933le_alt(X_2)
& is_Arr553848933le_alt(Y_1)
& is_Arr553848933le_alt(Z_1) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,L),Z_1)))
<=> ( X_2 != Z_1
& ( Y_1 = Z_1
=> X_2 != Y_1 )
& ( Y_1 != Z_1
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L)) ) ) ) ) ).
fof(fact_6__C2_C,axiom,
! [P_1,Pa,A_8,B_8,Aa,Ba] :
( ( is_Arr553848933le_alt(A_8)
& is_Arr553848933le_alt(B_8)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( A_8 != B_8
=> ( Aa != B_8
=> ( Ba != A_8
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof))
=> ( ! [I] :
( is_Arr625519182e_indi(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_8,B_8)),hAPP_A1374816149t_bool(P_1,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_8,B_8)),hAPP_f695124765t_bool(f,P_1))) ) ) ) ) ) ) ) ) ) ).
fof(fact_7__C1_C,axiom,
! [P_1,Pa,A_8,B_8,Aa,Ba] :
( ( is_Arr553848933le_alt(A_8)
& is_Arr553848933le_alt(B_8)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( A_8 != B_8
=> ( Aa != B_8
=> ( Ba != A_8
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof))
=> ( ! [I] :
( is_Arr625519182e_indi(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_8,B_8)),hAPP_A1374816149t_bool(P_1,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_8,B_8)),hAPP_f695124765t_bool(f,P_1))) ) ) ) ) ) ) ) ) ) ).
fof(fact_8__C4_C,axiom,
! [P_1,Pa,Ca,Aa,Ba] :
( ( is_Arr553848933le_alt(Ca)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( Ba != Ca
=> ( Aa != Ca
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof))
=> ( ! [I] :
( is_Arr625519182e_indi(I)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Ca)),hAPP_A1374816149t_bool(P_1,I))) ) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Ca)),hAPP_f695124765t_bool(f,P_1))) ) ) ) ) ) ) ) ) ).
fof(fact_9_pairwise__neutrality,axiom,
! [P_1,Pa,A_8,B_8,Aa,Ba] :
( ( is_Arr553848933le_alt(A_8)
& is_Arr553848933le_alt(B_8)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( A_8 != B_8
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof))
=> ( ! [I] :
( is_Arr625519182e_indi(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_8,B_8)),hAPP_A1374816149t_bool(P_1,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_8,B_8)),hAPP_f695124765t_bool(f,P_1))) ) ) ) ) ) ) ) ).
fof(fact_10__C3_C,axiom,
! [P_1,Pa,Aa,Ba] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Pa),arrow_413697182e_Prof))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(P_1),arrow_413697182e_Prof))
=> ( ! [I] :
( is_Arr625519182e_indi(I)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_A1374816149t_bool(Pa,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),hAPP_A1374816149t_bool(P_1,I))) ) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),hAPP_f695124765t_bool(f,Pa)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),hAPP_f695124765t_bool(f,P_1))) ) ) ) ) ) ) ).
fof(fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J,axiom,
! [I] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A1374816149t_bool(p,I)))
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,hAPP_A1374816149t_bool(p,I)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n))
=> ( ( hAPP_A588601142di_nat(h,I) = n
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,hAPP_A1374816149t_bool(p,I)),c),e))) )
& ( hAPP_A588601142di_nat(h,I) != n
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,hAPP_A1374816149t_bool(p,I)),e))) ) ) ) ) ) ).
fof(fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_A1374816149t_bool(p,hAPP_n385347014e_indi(hilber1792103167di_nat(top_to1256827021i_bool,h),n)))) ).
fof(fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ).
fof(fact_14_PW,axiom,
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ) ).
fof(fact_15_split__paired__All,axiom,
! [Pa] :
( ! [X1] : hBOOL(hAPP_P2075002375t_bool(Pa,X1))
<=> ! [A_1,B_1] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B_1) )
=> hBOOL(hAPP_P2075002375t_bool(Pa,produc171383831le_alt(A_1,B_1))) ) ) ).
fof(fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai,axiom,
hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))),arrow_413697182e_Prof)) ).
fof(fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,e)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ).
fof(fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e)))))) ).
fof(fact_19_n_I1_J,axiom,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,n),finite120254591e_indi(top_to1256827021i_bool))) ).
fof(fact_20_injh,axiom,
hBOOL(inj_on24934938di_nat(h,top_to1256827021i_bool)) ).
fof(fact_21_Pair__inject,axiom,
! [A_10,B_10,A_9,B_9] :
( ( is_Arr553848933le_alt(A_10)
& is_Arr553848933le_alt(B_10)
& is_Arr553848933le_alt(A_9)
& is_Arr553848933le_alt(B_9) )
=> ( produc171383831le_alt(A_10,B_10) = produc171383831le_alt(A_9,B_9)
=> ~ ( A_10 = A_9
=> B_10 != B_9 ) ) ) ).
fof(fact_22_Pair__eq,axiom,
! [Aa,Ba,A_8,B_8] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba)
& is_Arr553848933le_alt(A_8)
& is_Arr553848933le_alt(B_8) )
=> ( produc171383831le_alt(Aa,Ba) = produc171383831le_alt(A_8,B_8)
<=> ( Aa = A_8
& Ba = B_8 ) ) ) ).
fof(fact_23_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP_f785543729l_bool(arrow_1212118780le_IIA,Fa))
<=> ! [X_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof))
=> ! [Xa] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(Xa),arrow_413697182e_Prof))
=> ! [A_1,B_1] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B_1) )
=> ( ! [I] :
( is_Arr625519182e_indi(I)
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(X_1,I)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(Xa,I))) ) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,X_1)))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,Xa))) ) ) ) ) ) ) ).
fof(fact_24_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP_f785543729l_bool(arrow_467566751nimity,Fa))
<=> ! [X_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof))
=> ! [A_1,B_1] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B_1) )
=> ( ! [I] :
( is_Arr625519182e_indi(I)
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(X_1,I))) )
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,X_1))) ) ) ) ) ).
fof(fact_25_top1I,axiom,
! [X_2] : hBOOL(hAPP_f745298353l_bool(top_to2005687013l_bool,X_2)) ).
fof(fact_26_top1I,axiom,
! [X_2] : hBOOL(hAPP_f1636546729l_bool(top_to1194196741l_bool,X_2)) ).
fof(fact_27_top1I,axiom,
! [X_2] : hBOOL(hAPP_f785543729l_bool(top_to40512653l_bool,X_2)) ).
fof(fact_28_top1I,axiom,
! [X_2] : hBOOL(hAPP_P2075002375t_bool(top_to2034604131t_bool,X_2)) ).
fof(fact_29_top1I,axiom,
! [X_2] : hBOOL(hAPP_A1466488369i_bool(top_to1256827021i_bool,X_2)) ).
fof(fact_30_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f387058535l_bool(member_bool(X_2),top_to1647826457l_bool)) ).
fof(fact_31_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),top_to1256827021i_bool)) ).
fof(fact_32_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),top_to2034604131t_bool)) ).
fof(fact_33_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),top_to1194196741l_bool)) ).
fof(fact_34_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),top_to40512653l_bool)) ).
fof(fact_35_UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),top_to2005687013l_bool)) ).
fof(fact_36_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f387058535l_bool(member_bool(X_2),top_to1647826457l_bool)) ).
fof(fact_37_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),top_to1256827021i_bool)) ).
fof(fact_38_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),top_to2034604131t_bool)) ).
fof(fact_39_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),top_to1194196741l_bool)) ).
fof(fact_40_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),top_to40512653l_bool)) ).
fof(fact_41_iso__tuple__UNIV__I,axiom,
! [X_2] : hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),top_to2005687013l_bool)) ).
fof(fact_42_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f745298353l_bool(top_to2005687013l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_43_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f1636546729l_bool(top_to1194196741l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_44_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_f785543729l_bool(top_to40512653l_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_45_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_P2075002375t_bool(top_to2034604131t_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_46_top__apply,axiom,
! [X_2] :
( hBOOL(hAPP_A1466488369i_bool(top_to1256827021i_bool,X_2))
<=> hBOOL(top_top_bool) ) ).
fof(fact_47_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f503012287l_bool(hAPP_f1669465919l_bool(ord_le272605321l_bool,top_to2005687013l_bool),Aa)) ).
fof(fact_48_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f453661011l_bool(hAPP_f1760255479l_bool(ord_le453141089l_bool,top_to1194196741l_bool),Aa)) ).
fof(fact_49_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f213304539l_bool(hAPP_f281286919l_bool(ord_le1480133609l_bool,top_to40512653l_bool),Aa)) ).
fof(fact_50_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,top_top_bool),Aa)) ).
fof(fact_51_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f745298353l_bool(hAPP_f2056167603l_bool(ord_le227393471t_bool,top_to2034604131t_bool),Aa)) ).
fof(fact_52_not__top__less,axiom,
! [Aa] : ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,top_to1256827021i_bool),Aa)) ).
fof(fact_53_linorder__cases,axiom,
! [X_14,Y_13] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_14),Y_13))
=> ( X_14 != Y_13
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_13),X_14)) ) ) ).
fof(fact_54_order__less__asym,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)) ) ).
fof(fact_55_order__less__asym,axiom,
! [X_13,Y_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_13),Y_12))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_12),X_13)) ) ).
fof(fact_56_xt1_I10_J,axiom,
! [Z_1,Y_1,X_2] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2))
=> ( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Z_1),Y_1))
=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Z_1),X_2)) ) ) ).
fof(fact_57_xt1_I10_J,axiom,
! [Z_2,Y_11,X_12] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_11),X_12))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),Y_11))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Z_2),X_12)) ) ) ).
fof(fact_58_order__less__trans,axiom,
! [Z_1,X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> ( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),Z_1))
=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Z_1)) ) ) ).
fof(fact_59_order__less__trans,axiom,
! [Z,X_11,Y_10] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Y_10))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_10),Z))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_11),Z)) ) ) ).
fof(fact_60_xt1_I2_J,axiom,
! [Ca,Ba,Aa] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Aa))
=> ( Ba = Ca
=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ca),Aa)) ) ) ).
fof(fact_61_xt1_I2_J,axiom,
! [C_3,B_7,A_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_7),A_7))
=> ( B_7 = C_3
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_3),A_7)) ) ) ).
fof(fact_62_ord__less__eq__trans,axiom,
! [Ca,Aa,Ba] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ba))
=> ( Ba = Ca
=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ca)) ) ) ).
fof(fact_63_ord__less__eq__trans,axiom,
! [C_2,A_6,B_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),B_6))
=> ( B_6 = C_2
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_6),C_2)) ) ) ).
fof(fact_64_xt1_I1_J,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ca),Ba))
=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ca),Aa)) ) ) ).
fof(fact_65_xt1_I1_J,axiom,
! [C_1,A_5,B_5] :
( A_5 = B_5
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_1),B_5))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,C_1),A_5)) ) ) ).
fof(fact_66_ord__eq__less__trans,axiom,
! [Ca,Aa,Ba] :
( Aa = Ba
=> ( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Ca))
=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ca)) ) ) ).
fof(fact_67_ord__eq__less__trans,axiom,
! [C,A_4,B_4] :
( A_4 = B_4
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_4),C))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_4),C)) ) ) ).
fof(fact_68_xt1_I9_J,axiom,
! [Ba,Aa] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Aa))
=> ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ba)) ) ).
fof(fact_69_xt1_I9_J,axiom,
! [B_3,A_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_3),A_3))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_3),B_3)) ) ).
fof(fact_70_order__less__asym_H,axiom,
! [Aa,Ba] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),Ba))
=> ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Ba),Aa)) ) ).
fof(fact_71_order__less__asym_H,axiom,
! [A_2,B_2] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_2))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,B_2),A_2)) ) ).
fof(fact_72_order__less__imp__triv,axiom,
! [Pa,X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> ( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_73_order__less__imp__triv,axiom,
! [Pa,X_2,Y_1] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2))
=> hBOOL(Pa) ) ) ).
fof(fact_74_order__less__imp__not__eq2,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> Y_1 != X_2 ) ).
fof(fact_75_order__less__imp__not__eq2,axiom,
! [X_10,Y_9] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_10),Y_9))
=> Y_9 != X_10 ) ).
fof(fact_76_order__less__imp__not__eq,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> X_2 != Y_1 ) ).
fof(fact_77_order__less__imp__not__eq,axiom,
! [X_9,Y_8] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_9),Y_8))
=> X_9 != Y_8 ) ).
fof(fact_78_order__less__imp__not__less,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)) ) ).
fof(fact_79_order__less__imp__not__less,axiom,
! [X_8,Y_7] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_8),Y_7))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_7),X_8)) ) ).
fof(fact_80_order__less__not__sym,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Y_1),X_2)) ) ).
fof(fact_81_order__less__not__sym,axiom,
! [X_7,Y_6] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_7),Y_6))
=> ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_6),X_7)) ) ).
fof(fact_82_less__imp__neq,axiom,
! [X_2,Y_1] :
( hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),Y_1))
=> X_2 != Y_1 ) ).
fof(fact_83_less__imp__neq,axiom,
! [X_6,Y_5] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_6),Y_5))
=> X_6 != Y_5 ) ).
fof(fact_84_linorder__neqE,axiom,
! [X_5,Y_4] :
( X_5 != Y_4
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_5),Y_4))
=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_4),X_5)) ) ) ).
fof(fact_85_linorder__antisym__conv3,axiom,
! [Y_1,X_2] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2))
=> ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
<=> X_2 = Y_1 ) ) ).
fof(fact_86_linorder__less__linear,axiom,
! [X_4,Y_3] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_4),Y_3))
| X_4 = Y_3
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_3),X_4)) ) ).
fof(fact_87_not__less__iff__gr__or__eq,axiom,
! [X_2,Y_1] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2))
| X_2 = Y_1 ) ) ).
fof(fact_88_linorder__neq__iff,axiom,
! [X_2,Y_1] :
( X_2 != Y_1
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Y_1))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y_1),X_2)) ) ) ).
fof(fact_89_order__less__irrefl,axiom,
! [X_2] : ~ hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,X_2),X_2)) ).
fof(fact_90_order__less__irrefl,axiom,
! [X_3] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_3),X_3)) ).
fof(fact_91_UNIV__def,axiom,
top_to2005687013l_bool = collec874260222t_bool(hAPP_b1965422783l_bool(cOMBK_977355664t_bool,fTrue)) ).
fof(fact_92_UNIV__def,axiom,
top_to1194196741l_bool = collec1580242420t_bool(hAPP_b1719629739l_bool(cOMBK_789167586t_bool,fTrue)) ).
fof(fact_93_UNIV__def,axiom,
top_to40512653l_bool = collec1520786044t_bool(hAPP_b990649139l_bool(cOMBK_580911210t_bool,fTrue)) ).
fof(fact_94_UNIV__def,axiom,
top_to2034604131t_bool = collec1711870802le_alt(hAPP_b1024867081t_bool(cOMBK_2069093696le_alt,fTrue)) ).
fof(fact_95_UNIV__def,axiom,
top_to1256827021i_bool = collec45183100e_indi(hAPP_b1018211123i_bool(cOMBK_1157044842e_indi,fTrue)) ).
fof(fact_96_pred__equals__eq2,axiom,
! [S,R_1] :
( ( is_fun282293932t_bool(S)
& is_fun282293932t_bool(R_1) )
=> ( ! [X_1,Xa] :
( ( is_Arr553848933le_alt(X_1)
& is_Arr553848933le_alt(Xa) )
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Xa)),R_1))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_1,Xa)),S)) ) )
<=> R_1 = S ) ) ).
fof(fact_97_less__top,axiom,
! [Aa] :
( is_fun432044380l_bool(Aa)
=> ( Aa != top_to2005687013l_bool
<=> hBOOL(hAPP_f503012287l_bool(hAPP_f1669465919l_bool(ord_le272605321l_bool,Aa),top_to2005687013l_bool)) ) ) ).
fof(fact_98_less__top,axiom,
! [Aa] :
( is_fun959573582l_bool(Aa)
=> ( Aa != top_to1194196741l_bool
<=> hBOOL(hAPP_f453661011l_bool(hAPP_f1760255479l_bool(ord_le453141089l_bool,Aa),top_to1194196741l_bool)) ) ) ).
fof(fact_99_less__top,axiom,
! [Aa] :
( is_fun631676118l_bool(Aa)
=> ( Aa != top_to40512653l_bool
<=> hBOOL(hAPP_f213304539l_bool(hAPP_f281286919l_bool(ord_le1480133609l_bool,Aa),top_to40512653l_bool)) ) ) ).
fof(fact_100_less__top,axiom,
! [Aa] :
( ~ ( hBOOL(Aa)
<=> hBOOL(top_top_bool) )
<=> hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_bool,Aa),top_top_bool)) ) ).
fof(fact_101_less__top,axiom,
! [Aa] :
( is_fun282293932t_bool(Aa)
=> ( Aa != top_to2034604131t_bool
<=> hBOOL(hAPP_f745298353l_bool(hAPP_f2056167603l_bool(ord_le227393471t_bool,Aa),top_to2034604131t_bool)) ) ) ).
fof(fact_102_less__top,axiom,
! [Aa] :
( is_fun917378774i_bool(Aa)
=> ( Aa != top_to1256827021i_bool
<=> hBOOL(hAPP_f919661787l_bool(hAPP_f1710416135l_bool(ord_le694128617i_bool,Aa),top_to1256827021i_bool)) ) ) ).
fof(fact_103_inv__f__eq,axiom,
! [X_2,Y_1,F] :
( is_Arr625519182e_indi(X_2)
=> ( hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool))
=> ( hAPP_A588601142di_nat(F,X_2) = Y_1
=> hAPP_n385347014e_indi(hilber1792103167di_nat(top_to1256827021i_bool,F),Y_1) = X_2 ) ) ) ).
fof(fact_104_inv__f__f,axiom,
! [X_2,F] :
( is_Arr625519182e_indi(X_2)
=> ( hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool))
=> hAPP_n385347014e_indi(hilber1792103167di_nat(top_to1256827021i_bool,F),hAPP_A588601142di_nat(F,X_2)) = X_2 ) ) ).
fof(fact_105_inv__into__f__f,axiom,
! [X_2,F,A] :
( is_Arr625519182e_indi(X_2)
=> ( hBOOL(inj_on24934938di_nat(F,A))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hAPP_n385347014e_indi(hilber1792103167di_nat(A,F),hAPP_A588601142di_nat(F,X_2)) = X_2 ) ) ) ).
fof(fact_106_inv__into__f__eq,axiom,
! [Y_1,X_2,F,A] :
( is_Arr625519182e_indi(X_2)
=> ( hBOOL(inj_on24934938di_nat(F,A))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> ( hAPP_A588601142di_nat(F,X_2) = Y_1
=> hAPP_n385347014e_indi(hilber1792103167di_nat(A,F),Y_1) = X_2 ) ) ) ) ).
fof(fact_107_inj__eq,axiom,
! [X_2,Y_1,F] :
( ( is_Arr625519182e_indi(X_2)
& is_Arr625519182e_indi(Y_1) )
=> ( hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool))
=> ( hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1)
<=> X_2 = Y_1 ) ) ) ).
fof(fact_108_inj__on__def,axiom,
! [F,A] :
( hBOOL(inj_on24934938di_nat(F,A))
<=> ! [X_1] :
( is_Arr625519182e_indi(X_1)
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_1),A))
=> ! [Xa] :
( is_Arr625519182e_indi(Xa)
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Xa),A))
=> ( hAPP_A588601142di_nat(F,X_1) = hAPP_A588601142di_nat(F,Xa)
=> X_1 = Xa ) ) ) ) ) ) ).
fof(fact_109_inj__on__contraD,axiom,
! [X_2,Y_1,F,A] :
( ( is_Arr625519182e_indi(X_2)
& is_Arr625519182e_indi(Y_1) )
=> ( hBOOL(inj_on24934938di_nat(F,A))
=> ( X_2 != Y_1
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Y_1),A))
=> hAPP_A588601142di_nat(F,X_2) != hAPP_A588601142di_nat(F,Y_1) ) ) ) ) ) ).
fof(fact_110_inj__on__iff,axiom,
! [Y_1,X_2,F,A] :
( ( is_Arr625519182e_indi(Y_1)
& is_Arr625519182e_indi(X_2) )
=> ( hBOOL(inj_on24934938di_nat(F,A))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Y_1),A))
=> ( hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1)
<=> X_2 = Y_1 ) ) ) ) ) ).
fof(fact_111_inj__onD,axiom,
! [X_2,Y_1,F,A] :
( ( is_Arr625519182e_indi(X_2)
& is_Arr625519182e_indi(Y_1) )
=> ( hBOOL(inj_on24934938di_nat(F,A))
=> ( hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1)
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(Y_1),A))
=> X_2 = Y_1 ) ) ) ) ) ).
fof(fact_112_injD,axiom,
! [X_2,Y_1,F] :
( ( is_Arr625519182e_indi(X_2)
& is_Arr625519182e_indi(Y_1) )
=> ( hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool))
=> ( hAPP_A588601142di_nat(F,X_2) = hAPP_A588601142di_nat(F,Y_1)
=> X_2 = Y_1 ) ) ) ).
fof(fact_113_inj__imp__inv__eq,axiom,
! [G,F] :
( is_fun1016509681e_indi(G)
=> ( hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool))
=> ( ! [X_1] : hAPP_A588601142di_nat(F,hAPP_n385347014e_indi(G,X_1)) = X_1
=> hilber1792103167di_nat(top_to1256827021i_bool,F) = G ) ) ) ).
fof(fact_114_injI,axiom,
! [F] :
( ! [X_1,Y_2] :
( ( is_Arr625519182e_indi(X_1)
& is_Arr625519182e_indi(Y_2) )
=> ( hAPP_A588601142di_nat(F,X_1) = hAPP_A588601142di_nat(F,Y_2)
=> X_1 = Y_2 ) )
=> hBOOL(inj_on24934938di_nat(F,top_to1256827021i_bool)) ) ).
fof(fact_115_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_116__096Lba_A_058_ALin_096,axiom,
hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(lba),arrow_1239002508le_Lin)) ).
fof(fact_117__096Lab_A_058_ALin_096,axiom,
hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(lab),arrow_1239002508le_Lin)) ).
fof(fact_118_Lin__irrefl,axiom,
! [Aa,Ba,L] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),L))
=> ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Ba,Aa)),L)) ) ) ).
fof(fact_119_notin__Lin__iff,axiom,
! [X_2,Y_1,L] :
( ( is_Arr553848933le_alt(X_2)
& is_Arr553848933le_alt(Y_1) )
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> ( X_2 != Y_1
=> ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Y_1,X_2)),L)) ) ) ) ) ).
fof(fact_120_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
<=> hBOOL(hAPP_A1466488369i_bool(A,X_2)) ) ).
fof(fact_121_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
<=> hBOOL(hAPP_bool_bool(A,X_2)) ) ).
fof(fact_122_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))
<=> hBOOL(hAPP_P2075002375t_bool(A,X_2)) ) ).
fof(fact_123_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
<=> hBOOL(hAPP_f1636546729l_bool(A,X_2)) ) ).
fof(fact_124_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))
<=> hBOOL(hAPP_f785543729l_bool(A,X_2)) ) ).
fof(fact_125_mem__def,axiom,
! [X_2,A] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))
<=> hBOOL(hAPP_f745298353l_bool(A,X_2)) ) ).
fof(fact_126_Collect__def,axiom,
! [Pa] :
( is_fun917378774i_bool(Pa)
=> collec45183100e_indi(Pa) = Pa ) ).
fof(fact_127_mktop__Lin,axiom,
! [X_2,L] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,L),X_2)),arrow_1239002508le_Lin)) ) ).
fof(fact_128_mkbot__Lin,axiom,
! [X_2,L] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,L),X_2)),arrow_1239002508le_Lin)) ) ).
fof(fact_129_above__Lin,axiom,
! [L,X_2,Y_1] :
( ( is_Arr553848933le_alt(X_2)
& is_Arr553848933le_alt(Y_1) )
=> ( X_2 != Y_1
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,L),X_2),Y_1)),arrow_1239002508le_Lin)) ) ) ) ).
fof(fact_130_const__Lin__Prof,axiom,
! [L] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,L)),arrow_413697182e_Prof)) ) ).
fof(fact_131_in__above,axiom,
! [X_2,Y_1,L,Aa,Ba] :
( ( is_Arr553848933le_alt(X_2)
& is_Arr553848933le_alt(Y_1)
& is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(L),arrow_1239002508le_Lin))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,L),Aa),Ba)))
<=> ( X_2 != Y_1
& ( X_2 = Ba
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Y_1)),L)) )
& ( X_2 != Ba
=> ( ( Y_1 = Ba
=> ( X_2 = Aa
| hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Aa)),L)) ) )
& ( Y_1 != Ba
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(X_2,Y_1)),L)) ) ) ) ) ) ) ) ) ).
fof(fact_132_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_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof))
=> ! [A_1,B_1] :
( ( is_Arr553848933le_alt(A_1)
& is_Arr553848933le_alt(B_1) )
=> ( A_1 != B_1
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_A1374816149t_bool(X_1,I_1)))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(A_1,B_1)),hAPP_f695124765t_bool(Fa,X_1))) ) ) ) )
=> hBOOL(hAPP_A1466488369i_bool(hAPP_f355113919i_bool(arrow_2061665457ctator,Fa),I_1)) ) ) ).
fof(fact_133_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_2)),hAPP_P2127852789l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) ) ) ).
fof(fact_134_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_2)),hAPP_A1374816149t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) ) ) ).
fof(fact_135_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B)))
=> ( ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_2)),hAPP_b1024867081t_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
fof(fact_136_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_2)),hAPP_A1912483895l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) ) ) ).
fof(fact_137_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_2)),hAPP_b1719629739l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
fof(fact_138_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_2)),hAPP_A1964572607l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) ) ) ).
fof(fact_139_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_2)),hAPP_b990649139l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
fof(fact_140_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_2)),hAPP_b1965422783l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A)) ) ) ).
fof(fact_141_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_2)),hAPP_P907763049i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A)) ) ) ).
fof(fact_142_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_2)),hAPP_f749892423i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) ) ) ).
fof(fact_143_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_2)),hAPP_f313042899l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) ) ) ).
fof(fact_144_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_2)),hAPP_f355113919i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) ) ) ).
fof(fact_145_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_2)),hAPP_f497468491l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A)) ) ) ).
fof(fact_146_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B)))
=> ( ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_2)),hAPP_f352490559i_bool(B,X_2)))
=> ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) ) ) ).
fof(fact_147_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B)))
=> ( ~ hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_2)),hAPP_f417299659l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A)) ) ) ).
fof(fact_148_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_2)),hAPP_f861484971l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A)) ) ) ).
fof(fact_149_PiE,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B)))
=> ( ~ hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_2)),hAPP_A1944296755l_bool(B,X_2)))
=> ~ hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A)) ) ) ).
fof(fact_150_complete__Lin,axiom,
! [Aa,Ba] :
( ( is_Arr553848933le_alt(Aa)
& is_Arr553848933le_alt(Ba) )
=> ( Aa != Ba
=> ? [X_1] :
( is_fun282293932t_bool(X_1)
& hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_1),arrow_1239002508le_Lin))
& hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(Aa,Ba)),X_1)) ) ) ) ).
fof(fact_151_PiProf,axiom,
! [Na] : hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(cOMBC_437064334t_bool(cOMBC_481590946t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),Na)),lab),lba)),arrow_413697182e_Prof)) ).
fof(fact_152_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,B)))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_2)),hAPP_P2127852789l_bool(B,X_2))) ) ) ).
fof(fact_153_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,B)))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_2)),hAPP_P907763049i_bool(B,X_2))) ) ) ).
fof(fact_154_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,B)))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_2)),hAPP_f749892423i_bool(B,X_2))) ) ) ).
fof(fact_155_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,B)))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_2)),hAPP_f313042899l_bool(B,X_2))) ) ) ).
fof(fact_156_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,B)))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_2)),hAPP_f355113919i_bool(B,X_2))) ) ) ).
fof(fact_157_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,B)))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_2)),hAPP_f497468491l_bool(B,X_2))) ) ) ).
fof(fact_158_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,B)))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_2)),hAPP_f352490559i_bool(B,X_2))) ) ) ).
fof(fact_159_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,B)))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_2)),hAPP_f417299659l_bool(B,X_2))) ) ) ).
fof(fact_160_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,B)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_2)),hAPP_A1374816149t_bool(B,X_2))) ) ) ).
fof(fact_161_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_2)),hAPP_b1024867081t_bool(B,X_2))) ) ) ).
fof(fact_162_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,B)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_2)),hAPP_A1912483895l_bool(B,X_2))) ) ) ).
fof(fact_163_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_2)),hAPP_b1719629739l_bool(B,X_2))) ) ) ).
fof(fact_164_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,B)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_2)),hAPP_A1964572607l_bool(B,X_2))) ) ) ).
fof(fact_165_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_2)),hAPP_b990649139l_bool(B,X_2))) ) ) ).
fof(fact_166_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,B)))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_2)),hAPP_b1965422783l_bool(B,X_2))) ) ) ).
fof(fact_167_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,B)))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_2)),hAPP_f861484971l_bool(B,X_2))) ) ) ).
fof(fact_168_Pi__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,B)))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_2)),hAPP_A1944296755l_bool(B,X_2))) ) ) ).
fof(fact_169_Prof__def,axiom,
arrow_413697182e_Prof = pi_Arr688267935t_bool(top_to1256827021i_bool,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,arrow_1239002508le_Lin)) ).
fof(fact_170_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(F),pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,B))))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_P2075002375t_bool(F,X_2)),B)) ) ) ).
fof(fact_171_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f460310451l_bool(member765089840e_indi(F),pi_Pro437273841e_indi(A,hAPP_f1970593179i_bool(cOMBK_100791596le_alt,B))))
=> ( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_P2024088443e_indi(F,X_2)),B)) ) ) ).
fof(fact_172_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f234874197l_bool(member1105181906e_indi(F),pi_fun1736243859e_indi(A,hAPP_f681113465i_bool(cOMBK_454107598t_bool,B))))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1818473245e_indi(F,X_2)),B)) ) ) ).
fof(fact_173_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f500145249l_bool(member1661336414l_bool(F),pi_fun1494794527l_bool(A,hAPP_f219827985l_bool(cOMBK_886533338t_bool,B))))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f1636546729l_bool(F,X_2)),B)) ) ) ).
fof(fact_174_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1766869725l_bool(member1122398042e_indi(F),pi_fun2075749915e_indi(A,hAPP_f1677452273i_bool(cOMBK_1372975190t_bool,B))))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f618619045e_indi(F,X_2)),B)) ) ) ).
fof(fact_175_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1279200745l_bool(member387398118l_bool(F),pi_fun525942951l_bool(A,hAPP_f1235573641l_bool(cOMBK_1072228194t_bool,B))))
=> ( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f785543729l_bool(F,X_2)),B)) ) ) ).
fof(fact_176_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f592909149l_bool(member329987264e_indi(F),pi_fun972956463e_indi(A,hAPP_f1903519657i_bool(cOMBK_2076140708t_bool,B))))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))
=> hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(hAPP_f1659504677e_indi(F,X_2)),B)) ) ) ).
fof(fact_177_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f526292585l_bool(member1033316428l_bool(F),pi_fun1727820731l_bool(A,hAPP_f1667233577l_bool(cOMBK_1015076504t_bool,B))))
=> ( hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(X_2),A))
=> hBOOL(hAPP_f387058535l_bool(member_bool(hAPP_f745298353l_bool(F,X_2)),B)) ) ) ).
fof(fact_178_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f483434675l_bool(member859582768le_alt(F),pi_Arr149813489le_alt(A,hAPP_f1507266205t_bool(cOMBK_1152753196e_indi,B))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_A1736628091le_alt(F,X_2)),B)) ) ) ).
fof(fact_179_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1895985727l_bool(member42699324le_alt(F),pi_boo1877522301le_alt(A,hAPP_f1520552209t_bool(cOMBK_697786936l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(hAPP_b1817367815le_alt(F,X_2)),B)) ) ) ).
fof(fact_180_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f204273237l_bool(member1833291218t_bool(F),pi_Arr1511953043t_bool(A,hAPP_f813556705l_bool(cOMBK_116240846e_indi,B))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_A1594182429t_bool(F,X_2)),B)) ) ) ).
fof(fact_181_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1018082273l_bool(member1911067358t_bool(F),pi_boo691944735t_bool(A,hAPP_f371807573l_bool(cOMBK_697604314l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(hAPP_b833696937t_bool(F,X_2)),B)) ) ) ).
fof(fact_182_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1012384989l_bool(member1467476314t_bool(F),pi_Arr372473371t_bool(A,hAPP_f1697527281l_bool(cOMBK_1292462166e_indi,B))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_A1062826149t_bool(F,X_2)),B)) ) ) ).
fof(fact_183_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1271180905l_bool(member2081512038t_bool(F),pi_boo71521447t_bool(A,hAPP_f448497509l_bool(cOMBK_1268833122l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(hAPP_b331122225t_bool(F,X_2)),B)) ) ) ).
fof(fact_184_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f1550037191l_bool(member497701034t_bool(F),pi_boo2007389459t_bool(A,hAPP_f2135750719l_bool(cOMBK_971068024l_bool,B))))
=> ( hBOOL(hAPP_f387058535l_bool(member_bool(X_2),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_b1024867081t_bool(F,X_2)),B)) ) ) ).
fof(fact_185_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f213304539l_bool(member1622429502t_bool(F),pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,B))))
=> ( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_2),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_f695124765t_bool(F,X_2)),B)) ) ) ).
fof(fact_186_funcset__mem,axiom,
! [X_2,F,A,B] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(F),pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,B))))
=> ( hBOOL(hAPP_f919661787l_bool(member2074804542e_indi(X_2),A))
=> hBOOL(hAPP_f503012287l_bool(member1965683644t_bool(hAPP_A1374816149t_bool(F,X_2)),B)) ) ) ).
fof(fact_187_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP_A1466488369i_bool(hAPP_f355113919i_bool(arrow_2061665457ctator,Fa),I_1))
<=> ! [X_1] :
( hBOOL(hAPP_f453661011l_bool(member1277417654t_bool(X_1),arrow_413697182e_Prof))
=> hAPP_f695124765t_bool(Fa,X_1) = hAPP_A1374816149t_bool(X_1,I_1) ) ) ).
fof(fact_188_Pi__UNIV,axiom,
! [A] : pi_Pro2135156861t_bool(A,hAPP_f1724001331l_bool(cOMBK_2008994872le_alt,top_to1647826457l_bool)) = top_to2005687013l_bool ).
fof(fact_189_Pi__UNIV,axiom,
! [A] : pi_fun433100839t_bool(A,hAPP_f20355883l_bool(cOMBK_1088865252t_bool,top_to2005687013l_bool)) = top_to40512653l_bool ).
fof(fact_190_Pi__UNIV,axiom,
! [A] : pi_Arr688267935t_bool(A,hAPP_f1979025587l_bool(cOMBK_1158753900e_indi,top_to2005687013l_bool)) = top_to1194196741l_bool ).
fof(fact_191__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am,axiom,
( hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_f695124765t_bool(f,cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_78446834_mktop,p),e)),cOMBS_867867294t_bool(cOMBS_102864562t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(fequal_nat,h),n)),cOMBC_1778077589t_bool(cOMBC_493523632t_bool(cOMBB_69933763e_indi(arrow_812378712_above,p),c),e)),cOMBC_1778077589t_bool(cOMBB_1292070696e_indi(arrow_2077223396_mkbot,p),e))))))
<=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),hAPP_f695124765t_bool(f,cOMBC_437064334t_bool(cOMBC_481590946t_bool(cOMBB_963584201e_indi(if_fun1419651289t_bool,cOMBC_277798809t_bool(cOMBB_317992461e_indi(ord_less_nat,h),n)),lab),lba)))) ) ).
fof(fact_192__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am,axiom,
! [I] :
( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_78446834_mktop,hAPP_A1374816149t_bool(p,I)),e))) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n))
=> ( ( hAPP_A588601142di_nat(h,I) = n
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_A619995676t_bool(hAPP_A384644407t_bool(hAPP_f1336478923t_bool(arrow_812378712_above,hAPP_A1374816149t_bool(p,I)),c),e))) )
& ( hAPP_A588601142di_nat(h,I) != n
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(e,d)),hAPP_A619995676t_bool(hAPP_f1290184496t_bool(arrow_2077223396_mkbot,hAPP_A1374816149t_bool(p,I)),e))) ) ) ) )
<=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),lab)) )
& ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_A588601142di_nat(h,I)),n))
=> hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),lba)) ) ) ) ).
fof(fact_193__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_194__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),lba)) ).
fof(fact_195__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096,axiom,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(a,b)),lab)) ).
fof(fact_196__096_Ia_M_Ab_J_A_126_058_ALba_096,axiom,
~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(a,b)),lba)) ).
fof(fact_197__096_Ib_M_Aa_J_A_126_058_ALab_096,axiom,
~ hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(b,a)),lab)) ).
%----Helper facts (40)
fof(help_fTrue_1_1_U,axiom,
hBOOL(fTrue) ).
fof(help_fTrue_1_1_T,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
! [X,Y] :
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
| X = Y ) ).
fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
! [X,Y] :
( X != Y
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).
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_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000,axiom,
! [P,Q,R] : hAPP_A1466488369i_bool(cOMBC_277798809t_bool(P,Q),R) = hAPP_nat_bool(hAPP_A1922697556t_bool(P,R),Q) ).
fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
! [P,Q,R] : hAPP_A1922697556t_bool(cOMBB_317992461e_indi(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_A588601142di_nat(Q,R)) ).
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_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn,axiom,
! [X,Y] :
( is_fun282293932t_bool(X)
=> hAPP_f1673487381t_bool(hAPP_f159424297t_bool(hAPP_b1915039793t_bool(if_fun1419651289t_bool,fTrue),X),Y) = X ) ).
fof(help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn,axiom,
! [X,Y] :
( is_fun282293932t_bool(Y)
=> hAPP_f1673487381t_bool(hAPP_f159424297t_bool(hAPP_b1915039793t_bool(if_fun1419651289t_bool,fFalse),X),Y) = Y ) ).
fof(help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fjewxadn,axiom,
! [P] :
( is_bool(P)
=> ( P = fTrue
| P = fFalse ) ) ).
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] : 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] : 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_026,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___027,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_028,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_029,axiom,
! [P,Q] : 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_030,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___031,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_032,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_033,axiom,
! [P,Q,R] : hAPP_A702630576t_bool(cOMBC_493523632t_bool(P,Q),R) = hAPP_A384644407t_bool(hAPP_A460042315t_bool(P,R),Q) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_034,axiom,
! [P,Q,R] : hAPP_A1374816149t_bool(cOMBC_437064334t_bool(P,Q),R) = hAPP_f1673487381t_bool(hAPP_A1333445289t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000,axiom,
! [P,Q,R] : hAPP_A1374816149t_bool(cOMBS_867867294t_bool(P,Q),R) = hAPP_f1673487381t_bool(hAPP_A1333445289t_bool(P,R),hAPP_A1374816149t_bool(Q,R)) ).
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_035,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_036,axiom,
! [P,Q] : 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_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____fj,axiom,
! [P,Q,R] : hAPP_A702630576t_bool(cOMBB_1292070696e_indi(P,Q),R) = hAPP_f1290184496t_bool(P,hAPP_A1374816149t_bool(Q,R)) ).
fof(help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____fjewxadnqg___037,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_038,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_039,axiom,
! [P,Q,R] : hAPP_A460042315t_bool(cOMBB_69933763e_indi(P,Q),R) = hAPP_f1336478923t_bool(P,hAPP_A1374816149t_bool(Q,R)) ).
fof(help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_040,axiom,
! [P,Q,R] : hAPP_A1333445289t_bool(cOMBC_481590946t_bool(P,Q),R) = hAPP_f159424297t_bool(hAPP_A869356733t_bool(P,R),Q) ).
fof(help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____fjewxadnqg__Oindi_000_041,axiom,
! [P,Q,R] : hAPP_A1333445289t_bool(cOMBS_102864562t_bool(P,Q),R) = hAPP_f159424297t_bool(hAPP_A869356733t_bool(P,R),hAPP_A1374816149t_bool(Q,R)) ).
fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_,axiom,
! [P,Q,R] : hAPP_A869356733t_bool(cOMBB_963584201e_indi(P,Q),R) = hAPP_b1915039793t_bool(P,hAPP_A1466488369i_bool(Q,R)) ).
%----Conjectures (1)
fof(conj_0,conjecture,
hBOOL(hAPP_f745298353l_bool(member1056080916le_alt(produc171383831le_alt(c,d)),hAPP_f695124765t_bool(f,p))) ).
%------------------------------------------------------------------------------