TPTP Problem File: SCT170+5.p
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%------------------------------------------------------------------------------
% File : SCT170+5 : 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_fofpt_l204 [Bla11]
% Status : Theorem
% Rating : 1.00 v5.3.0
% Syntax : Number of formulae : 154 ( 96 unt; 0 def)
% Number of atoms : 290 ( 139 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 196 ( 60 ~; 3 |; 13 &)
% ( 30 <=>; 90 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 25 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 48 ( 48 usr; 20 con; 0-4 aty)
% Number of variables : 477 ( 466 !; 11 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-08-09 14:05:37
% : Encoded with polymorphic tags.
%------------------------------------------------------------------------------
%----Explicit typings (44)
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OIIA_res,axiom,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_612047104le_IIA) = arrow_612047104le_IIA ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OLin_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_638930832le_Lin) = arrow_638930832le_Lin ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_OProf_res,axiom,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1834574746e_Prof) = arrow_1834574746e_Prof ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Oabove_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),arrow_1726925404_above) = arrow_1726925404_above ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Obelow_res,hypothesis,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),arrow_888040304_below) = arrow_888040304_below ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Odictator_res,axiom,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool)),arrow_1990387629ctator) = arrow_1990387629ctator ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omkbot_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_844286440_mkbot) = arrow_844286440_mkbot ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Omktop_res,axiom,
ti(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_992993526_mktop) = arrow_992993526_mktop ).
fof(tsy_c_Arrow__Order__Mirabelle__rvjphhsdgg_Ounanimity_res,axiom,
ti(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),arrow_1932713123nimity) = arrow_1932713123nimity ).
fof(tsy_c_COMBB_res,axiom,
! [X_b,X_c,X_a] : ti(fun(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c))),combb(X_b,X_c,X_a)) = combb(X_b,X_c,X_a) ).
fof(tsy_c_COMBC_res,axiom,
! [X_a,X_b,X_c] : ti(fun(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c))),combc(X_a,X_b,X_c)) = combc(X_a,X_b,X_c) ).
fof(tsy_c_COMBI_res,axiom,
! [X_a] : ti(fun(X_a,X_a),combi(X_a)) = combi(X_a) ).
fof(tsy_c_COMBK_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(X_b,X_a)),combk(X_a,X_b)) = combk(X_a,X_b) ).
fof(tsy_c_FunDef_Oin__rel_res,axiom,
! [X_a,X_b] : ti(fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),in_rel(X_a,X_b)) = in_rel(X_a,X_b) ).
fof(tsy_c_FuncSet_OPi_res,axiom,
! [X_a,X_b] : ti(fun(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool))),pi(X_a,X_b)) = pi(X_a,X_b) ).
fof(tsy_c_HOL_Oequal__class_Oequal_res,axiom,
! [X_a] : ti(fun(list(X_a),fun(list(X_a),bool)),equal_equal(list(X_a))) = equal_equal(list(X_a)) ).
fof(tsy_c_HOL_Oundefined_res,axiom,
! [X_a] : ti(X_a,undefined(X_a)) = undefined(X_a) ).
fof(tsy_c_List_Odistinct_res,axiom,
! [X_a] : ti(fun(list(X_a),bool),distinct(X_a)) = distinct(X_a) ).
fof(tsy_c_List_Oinsert_res,axiom,
! [X_a] : ti(fun(X_a,fun(list(X_a),list(X_a))),insert(X_a)) = insert(X_a) ).
fof(tsy_c_List_Olist_OCons_res,axiom,
! [X_a] : ti(fun(X_a,fun(list(X_a),list(X_a))),cons(X_a)) = cons(X_a) ).
fof(tsy_c_List_Olist_ONil_res,axiom,
! [X_a] : ti(list(X_a),nil(X_a)) = nil(X_a) ).
fof(tsy_c_List_Olist_Olist__case_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a))),list_case(X_a,X_b)) = list_case(X_a,X_b) ).
fof(tsy_c_List_Olist_Olist__rec_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a))),list_rec(X_a,X_b)) = list_rec(X_a,X_b) ).
fof(tsy_c_List_Onull_res,axiom,
! [X_a] : ti(fun(list(X_a),bool),null(X_a)) = null(X_a) ).
fof(tsy_c_List_Osplice_res,axiom,
! [X_a] : ti(fun(list(X_a),fun(list(X_a),list(X_a))),splice(X_a)) = splice(X_a) ).
fof(tsy_c_Orderings_Otop__class_Otop_res,axiom,
! [X_a] :
( top(X_a)
=> ti(X_a,top_top(X_a)) = top_top(X_a) ) ).
fof(tsy_c_Product__Type_OPair_res,axiom,
! [X_a,X_b] : ti(fun(X_a,fun(X_b,product_prod(X_a,X_b))),product_Pair(X_a,X_b)) = product_Pair(X_a,X_b) ).
fof(tsy_c_Product__Type_Ocurry_res,axiom,
! [X_a,X_b,X_c] : ti(fun(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c))),product_curry(X_a,X_b,X_c)) = product_curry(X_a,X_b,X_c) ).
fof(tsy_c_Product__Type_Ointernal__split_res,axiom,
! [X_b,X_c,X_a] : ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),produc1605651328_split(X_b,X_c,X_a)) = produc1605651328_split(X_b,X_c,X_a) ).
fof(tsy_c_Product__Type_Oprod_Oprod__rec_res,axiom,
! [X_b,X_c,X_a] : ti(fun(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a)),product_prod_rec(X_b,X_c,X_a)) = product_prod_rec(X_b,X_c,X_a) ).
fof(tsy_c_Set_OCollect_res,axiom,
! [X_a] : ti(fun(fun(X_a,bool),fun(X_a,bool)),collect(X_a)) = collect(X_a) ).
fof(tsy_c_fFalse_res,axiom,
ti(bool,fFalse) = fFalse ).
fof(tsy_c_fTrue_res,axiom,
ti(bool,fTrue) = fTrue ).
fof(tsy_c_hAPP_arg1,axiom,
! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hAPP_res,axiom,
! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [B_1_1] :
( hBOOL(ti(bool,B_1_1))
<=> hBOOL(B_1_1) ) ).
fof(tsy_c_member_res,axiom,
! [X_b] : ti(fun(X_b,fun(fun(X_b,bool),bool)),member(X_b)) = member(X_b) ).
fof(tsy_v_F_res,axiom,
ti(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),f) = f ).
fof(tsy_v_P_H_____res,axiom,
ti(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),p_1) = p_1 ).
fof(tsy_v_P_____res,hypothesis,
ti(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),p) = p ).
fof(tsy_v_a_____res,hypothesis,
ti(arrow_1212486748le_alt,a) = a ).
fof(tsy_v_b_____res,hypothesis,
ti(arrow_1212486748le_alt,b) = b ).
fof(tsy_v_c_____res,hypothesis,
ti(arrow_1212486748le_alt,c) = c ).
%----Relevant facts (100)
fof(fact_0__096P_A_058_AProf_096,axiom,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),p),arrow_1834574746e_Prof)) ).
fof(fact_1_assms_I3_J,axiom,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,f)) ).
fof(fact_2_u,axiom,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,f)) ).
fof(fact_3__096a_A_126_061_Ab_096,axiom,
a != b ).
fof(fact_4_dist,axiom,
hBOOL(hAPP(list(arrow_1212486748le_alt),bool,distinct(arrow_1212486748le_alt),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),a),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),b),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),c),nil(arrow_1212486748le_alt)))))) ).
fof(fact_5_iff,axiom,
! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),b),a)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),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] : ~ hBOOL(hAPP(list(arrow_1212486748le_alt),bool,distinct(arrow_1212486748le_alt),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),a),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),b),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),C),nil(arrow_1212486748le_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(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_888040304_below),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_888040304_below),p)),c)),b))),b)),a)),arrow_1834574746e_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(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_888040304_below),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_888040304_below),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_888040304_below),p)),c)),b))),b)),a))),a)),c)),arrow_1834574746e_Prof)) ).
fof(fact_9__096_I_Fp_O_Abelow_A_IP_Ap_J_Ac_Ab_J_A_058_AProf_096,axiom,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(arrow_1212486748le_alt,fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),combc(arrow_1384031255e_indi,arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)))),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))))),combb(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1384031255e_indi),arrow_888040304_below),p)),c)),b)),arrow_1834574746e_Prof)) ).
fof(fact_10_in__mkbot,axiom,
! [X_1,Y,L_1,Z] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L_1),Z)))
<=> ( ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Z)
& ( ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Z)
=> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) )
& ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Z)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)) ) ) ) ).
fof(fact_11_in__mktop,axiom,
! [X_1,Y,L_1,Z] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L_1),Z)))
<=> ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Z)
& ( ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Z)
=> ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y) )
& ( ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Z)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)) ) ) ) ).
fof(fact_12_in__below,axiom,
! [X_1,Y,L_1,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_888040304_below,L_1),Aa),Ba)))
<=> ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)
& ( ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Aa)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Ba)),L_1)) )
& ( ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Aa)
=> ( ( ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Aa)
=> ( ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Ba)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Y)),L_1)) ) )
& ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Aa)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)) ) ) ) ) ) ) ) ).
fof(fact_13_split__paired__All,axiom,
! [X_a,X_b,Pa] :
( ! [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
<=> ! [A_2,B] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B))) ) ).
fof(fact_14_Pair__eq,axiom,
! [X_b,X_a,Aa,Ba,A_4,B_3] :
( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_3)
<=> ( ti(X_a,Aa) = ti(X_a,A_4)
& ti(X_b,Ba) = ti(X_b,B_3) ) ) ).
fof(fact_15_Pair__inject,axiom,
! [X_b,X_a,A_5,B_2,A_3,B_4] :
( hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_5),B_2) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_3),B_4)
=> ~ ( ti(X_a,A_5) = ti(X_a,A_3)
=> ti(X_b,B_2) != ti(X_b,B_4) ) ) ).
fof(fact_16_in__rel__def,axiom,
! [X_b,X_a,R_1,X_1,Y] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_1),X_1),Y))
<=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y)),R_1)) ) ).
fof(fact_17_below__Lin,axiom,
! [L_1,X_1,Y] :
( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_888040304_below,L_1),X_1),Y)),arrow_638930832le_Lin)) ) ) ).
fof(fact_18__096P_H_A_058_AProf_096,axiom,
hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),p_1),arrow_1834574746e_Prof)) ).
fof(fact_19__C1_C,axiom,
! [P_a,Pa,A_4,B_3,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,A_4)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_a),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_a,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_a))) ) ) ) ) ) ) ) ) ).
fof(fact_20__C2_C,axiom,
! [P_a,Pa,A_4,B_3,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,A_4) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,B_3)
=> ( ti(arrow_1212486748le_alt,Ba) != ti(arrow_1212486748le_alt,A_4)
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Pa),arrow_1834574746e_Prof))
=> ( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),P_a),arrow_1834574746e_Prof))
=> ( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Pa,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),P_a,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,Pa)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_4),B_3)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),f,P_a))) ) ) ) ) ) ) ) ) ).
fof(fact_21_assms_I1_J,axiom,
hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),f),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin)))) ).
fof(fact_22_const__Lin__Prof,axiom,
! [L_1] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),combk(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),arrow_1384031255e_indi),L_1)),arrow_1834574746e_Prof)) ) ).
fof(fact_23_mkbot__Lin,axiom,
! [X_1,L_1] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_844286440_mkbot,L_1),X_1)),arrow_638930832le_Lin)) ) ).
fof(fact_24_mktop__Lin,axiom,
! [X_1,L_1] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_992993526_mktop,L_1),X_1)),arrow_638930832le_Lin)) ) ).
fof(fact_25_Lin__irrefl,axiom,
! [Aa,Ba,L_1] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),L_1))
=> ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Ba),Aa)),L_1)) ) ) ).
fof(fact_26_notin__Lin__iff,axiom,
! [X_1,Y,L_1] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)
=> ( ~ hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Y),X_1)),L_1)) ) ) ) ).
fof(fact_27_third__alt,axiom,
! [A_5,B_2] :
( ti(arrow_1212486748le_alt,A_5) != ti(arrow_1212486748le_alt,B_2)
=> ? [C] : hBOOL(hAPP(list(arrow_1212486748le_alt),bool,distinct(arrow_1212486748le_alt),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),A_5),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),B_2),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),C),nil(arrow_1212486748le_alt)))))) ) ).
fof(fact_28_IIA__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_612047104le_IIA,Fa))
<=> ! [X] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof))
=> ! [Xa] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Xa),arrow_1834574746e_Prof))
=> ! [A_2,B] :
( ! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Xa,I))) )
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,Xa))) ) ) ) ) ) ).
fof(fact_29_unanimity__def,axiom,
! [Fa] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool,arrow_1932713123nimity,Fa))
<=> ! [X] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof))
=> ! [A_2,B] :
( ! [I] : hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I)))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X))) ) ) ) ).
fof(fact_30_complete__Lin,axiom,
! [Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ? [X] :
( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),X),arrow_638930832le_Lin))
& hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Ba)),X)) ) ) ).
fof(fact_31_in__above,axiom,
! [X_1,Y,L_1,Aa,Ba] :
( ti(arrow_1212486748le_alt,Aa) != ti(arrow_1212486748le_alt,Ba)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L_1),Aa),Ba)))
<=> ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)
& ( ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),Aa),Y)),L_1)) )
& ( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Ba)
=> ( ( ti(arrow_1212486748le_alt,Y) = ti(arrow_1212486748le_alt,Ba)
=> ( ti(arrow_1212486748le_alt,X_1) = ti(arrow_1212486748le_alt,Aa)
| hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Aa)),L_1)) ) )
& ( ti(arrow_1212486748le_alt,Y) != ti(arrow_1212486748le_alt,Ba)
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),X_1),Y)),L_1)) ) ) ) ) ) ) ) ).
fof(fact_32_prod_Orecs,axiom,
! [X_b,X_c,X_a,F1,Aa,Ba] : hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,Aa),Ba) ).
fof(fact_33_distinct_Osimps_I1_J,axiom,
! [X_a] : hBOOL(hAPP(list(X_a),bool,distinct(X_a),nil(X_a))) ).
fof(fact_34_list_Osimps_I2_J,axiom,
! [X_a,A_3,List_2] : nil(X_a) != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2) ).
fof(fact_35_list_Oinject,axiom,
! [X_a,Aa,List,A_4,List_3] :
( hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Aa),List) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_4),List_3)
<=> ( ti(X_a,Aa) = ti(X_a,A_4)
& List = List_3 ) ) ).
fof(fact_36_not__Cons__self2,axiom,
! [X_a,X_2,Xs_1] : hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_1) != Xs_1 ).
fof(fact_37_not__Cons__self,axiom,
! [X_a,Xs_1,X_2] : Xs_1 != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_1) ).
fof(fact_38_above__Lin,axiom,
! [L_1,X_1,Y] :
( ti(arrow_1212486748le_alt,X_1) != ti(arrow_1212486748le_alt,Y)
=> ( hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L_1),arrow_638930832le_Lin))
=> hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_1726925404_above,L_1),X_1),Y)),arrow_638930832le_Lin)) ) ) ).
fof(fact_39_list_Osimps_I3_J,axiom,
! [X_a,A_3,List_2] : hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_3),List_2) != nil(X_a) ).
fof(fact_40_dictatorI,axiom,
! [I_1,Fa] :
( hBOOL(hAPP(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),Fa),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),arrow_1834574746e_Prof),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_638930832le_Lin))))
=> ( ! [X] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof))
=> ! [A_2,B] :
( ti(arrow_1212486748le_alt,A_2) != ti(arrow_1212486748le_alt,B)
=> ( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I_1)))
=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),A_2),B)),hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X))) ) ) )
=> hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1)) ) ) ).
fof(fact_41_PiE,axiom,
! [X_a,X_b,X_1,F,A_1,B_1] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1)))
=> ( ~ hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B_1,X_1)))
=> ~ hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1)) ) ) ).
fof(fact_42_list_Oexhaust,axiom,
! [X_a,Y_1] :
( Y_1 != nil(X_a)
=> ~ ! [A_2,List_1] : Y_1 != hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),A_2),List_1) ) ).
fof(fact_43_neq__Nil__conv,axiom,
! [X_a,Xs] :
( Xs != nil(X_a)
<=> ? [Y_2,Ys_1] : Xs = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_2),Ys_1) ) ).
fof(fact_44_alt3,axiom,
? [A_2,B,C] : hBOOL(hAPP(list(arrow_1212486748le_alt),bool,distinct(arrow_1212486748le_alt),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),A_2),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),B),hAPP(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(list(arrow_1212486748le_alt),list(arrow_1212486748le_alt)),cons(arrow_1212486748le_alt),C),nil(arrow_1212486748le_alt)))))) ).
fof(fact_45_Pi__mem,axiom,
! [X_a,X_b,X_1,F,A_1,B_1] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1)))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,fun(X_b,bool),B_1,X_1))) ) ) ).
fof(fact_46_funcset__mem,axiom,
! [X_a,X_b,X_1,F,A_1,B_1] :
( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B_1))))
=> ( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),B_1)) ) ) ).
fof(fact_47_funcset__id,axiom,
! [X_a,A_1] : hBOOL(hAPP(fun(fun(X_a,X_a),bool),bool,hAPP(fun(X_a,X_a),fun(fun(fun(X_a,X_a),bool),bool),member(fun(X_a,X_a)),combi(X_a)),hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_a,bool)),fun(fun(X_a,X_a),bool)),pi(X_a,X_a),A_1),hAPP(fun(X_a,bool),fun(X_a,fun(X_a,bool)),combk(fun(X_a,bool),X_a),A_1)))) ).
fof(fact_48_dictator__def,axiom,
! [Fa,I_1] :
( hBOOL(hAPP(arrow_1384031255e_indi,bool,hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(arrow_1384031255e_indi,bool),arrow_1990387629ctator,Fa),I_1))
<=> ! [X] :
( hBOOL(hAPP(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool,hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),bool),member(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),X),arrow_1834574746e_Prof))
=> hAPP(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),Fa,X) = hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),X,I_1) ) ) ).
fof(fact_49_Pi__I,axiom,
! [X_b,X_a,F,B_1,A_1] :
( ! [X] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X)),hAPP(X_a,fun(X_b,bool),B_1,X))) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))) ) ).
fof(fact_50_funcsetI,axiom,
! [X_b,X_a,F,B_1,A_1] :
( ! [X] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X)),B_1)) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),B_1)))) ) ).
fof(fact_51_linear__alt,axiom,
? [L] : hBOOL(hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),bool),member(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),L),arrow_638930832le_Lin)) ).
fof(fact_52_Pi__I_H,axiom,
! [X_b,X_a,F,B_1,A_1] :
( ! [X] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1))
=> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X)),hAPP(X_a,fun(X_b,bool),B_1,X))) )
=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))) ) ).
fof(fact_53_Pi__cong,axiom,
! [X_b,X_a,B_1,F,G,A_1] :
( ! [W] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),W),A_1))
=> hAPP(X_a,X_b,F,W) = hAPP(X_a,X_b,G,W) )
=> ( hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),F),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1)))
<=> hBOOL(hAPP(fun(fun(X_a,X_b),bool),bool,hAPP(fun(X_a,X_b),fun(fun(fun(X_a,X_b),bool),bool),member(fun(X_a,X_b)),G),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),B_1))) ) ) ).
fof(fact_54_splice_Osimps_I2_J,axiom,
! [X_a,V,Va] : hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Va)),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),V),Va) ).
fof(fact_55_list_Osimps_I4_J,axiom,
! [X_b,X_a,F1,F2] : hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),nil(X_b)) = ti(X_a,F1) ).
fof(fact_56_list_Osimps_I5_J,axiom,
! [X_b,X_a,F1,F2,Aa,List] : hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),X_a)),fun(list(X_b),X_a)),list_case(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List)) = hAPP(list(X_b),X_a,hAPP(X_b,fun(list(X_b),X_a),F2,Aa),List) ).
fof(fact_57_splice_Osimps_I3_J,axiom,
! [X_a,X_2,Xs_1,Y_1,Ys] : hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_1)),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),Ys)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),Y_1),hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs_1),Ys))) ).
fof(fact_58_splice_Osimps_I1_J,axiom,
! [X_a,Ys] : hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),nil(X_a)),Ys) = Ys ).
fof(fact_59_splice__Nil2,axiom,
! [X_a,Xs_1] : hAPP(list(X_a),list(X_a),hAPP(list(X_a),fun(list(X_a),list(X_a)),splice(X_a),Xs_1),nil(X_a)) = Xs_1 ).
fof(fact_60_pred__equals__eq2,axiom,
! [X_a,X_b,S,R_1] :
( ! [X,Xa] :
( hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Xa)),R_1))
<=> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Xa)),S)) )
<=> ti(fun(product_prod(X_a,X_b),bool),R_1) = ti(fun(product_prod(X_a,X_b),bool),S) ) ).
fof(fact_61_prod_Oexhaust,axiom,
! [X_a,X_b,Y_1] :
~ ! [A_2,B] : ti(product_prod(X_a,X_b),Y_1) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B) ).
fof(fact_62_PairE,axiom,
! [X_a,X_b,P_1] :
~ ! [X,Y_2] : ti(product_prod(X_a,X_b),P_1) != hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X),Y_2) ).
fof(fact_63_split__paired__Ex,axiom,
! [X_a,X_b,Pa] :
( ? [X1] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,X1))
<=> ? [A_2,B] : hBOOL(hAPP(product_prod(X_a,X_b),bool,Pa,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B))) ) ).
fof(fact_64_prod__induct6,axiom,
! [X_a,X_b,X_c,X_d,X_e,X_f,X_1,Pa] :
( ! [A_2,B,C,D,E,F_1] : hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1)))))))
=> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,Pa,X_1)) ) ).
fof(fact_65_prod__cases6,axiom,
! [X_a,X_b,X_c,X_d,X_e,X_f,Y_1] :
~ ! [A_2,B,C,D,E,F_1] : ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y_1) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_2),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_1))))) ).
fof(fact_66_prod__cases5,axiom,
! [X_a,X_b,X_c,X_d,X_e,Y_1] :
~ ! [A_2,B,C,D,E] : ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),Y_1) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E)))) ).
fof(fact_67_prod__induct5,axiom,
! [X_a,X_b,X_c,X_d,X_e,X_1,Pa] :
( ! [A_2,B,C,D,E] : hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_2),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D),E))))))
=> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,Pa,X_1)) ) ).
fof(fact_68_prod__cases4,axiom,
! [X_a,X_b,X_c,X_d,Y_1] :
~ ! [A_2,B,C,D] : ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y_1) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C),D))) ).
fof(fact_69_prod__induct4,axiom,
! [X_a,X_b,X_c,X_d,X_1,Pa] :
( ! [A_2,B,C,D] : hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_2),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C),D)))))
=> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,Pa,X_1)) ) ).
fof(fact_70_prod__induct3,axiom,
! [X_a,X_b,X_c,X_1,Pa] :
( ! [A_2,B,C] : hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B),C))))
=> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,Pa,X_1)) ) ).
fof(fact_71_prod__cases3,axiom,
! [X_a,X_b,X_c,Y_1] :
~ ! [A_2,B,C] : ti(product_prod(X_a,product_prod(X_b,X_c)),Y_1) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_2),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B),C)) ).
fof(fact_72_internal__split__conv,axiom,
! [X_b,X_c,X_a,Ca,Aa,Ba] : hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),produc1605651328_split(X_b,X_c,X_a),Ca),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),Ca,Aa),Ba) ).
fof(fact_73_insert__Nil,axiom,
! [X_a,X_2] : hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_2),nil(X_a)) = hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),nil(X_a)) ).
fof(fact_74_distinct__insert,axiom,
! [X_a,X_2,Xs_1] :
( hBOOL(hAPP(list(X_a),bool,distinct(X_a),Xs_1))
=> hBOOL(hAPP(list(X_a),bool,distinct(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),insert(X_a),X_2),Xs_1))) ) ).
fof(fact_75_ext,axiom,
! [X_a,X_b,F,G] :
( ! [X] : hAPP(X_a,X_b,F,X) = hAPP(X_a,X_b,G,X)
=> ti(fun(X_a,X_b),F) = ti(fun(X_a,X_b),G) ) ).
fof(fact_76_mem__def,axiom,
! [X_a,X_1,A_1] :
( hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_1))
<=> hBOOL(hAPP(X_a,bool,A_1,X_1)) ) ).
fof(fact_77_Collect__def,axiom,
! [X_a,Pa] : hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Pa) = ti(fun(X_a,bool),Pa) ).
fof(fact_78_list__nonempty__induct,axiom,
! [X_a,Pa,Xs] :
( Xs != nil(X_a)
=> ( ! [X] : hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),nil(X_a))))
=> ( ! [X,Xs_2] :
( Xs_2 != nil(X_a)
=> ( hBOOL(hAPP(list(X_a),bool,Pa,Xs_2))
=> hBOOL(hAPP(list(X_a),bool,Pa,hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X),Xs_2))) ) )
=> hBOOL(hAPP(list(X_a),bool,Pa,Xs)) ) ) ) ).
fof(fact_79_list_Orecs_I1_J,axiom,
! [X_b,X_a,F1,F2] : hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),nil(X_b)) = ti(X_a,F1) ).
fof(fact_80_list_Orecs_I2_J,axiom,
! [X_b,X_a,F1,F2,Aa,List] : hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),hAPP(list(X_b),list(X_b),hAPP(X_b,fun(list(X_b),list(X_b)),cons(X_b),Aa),List)) = hAPP(X_a,X_a,hAPP(list(X_b),fun(X_a,X_a),hAPP(X_b,fun(list(X_b),fun(X_a,X_a)),F2,Aa),List),hAPP(list(X_b),X_a,hAPP(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a),hAPP(X_a,fun(fun(X_b,fun(list(X_b),fun(X_a,X_a))),fun(list(X_b),X_a)),list_rec(X_a,X_b),F1),F2),List)) ).
fof(fact_81_curry__def,axiom,
! [X_b,X_c,X_a,X,Xa,Xb] : hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),hAPP(fun(product_prod(X_a,X_b),X_c),fun(X_a,fun(X_b,X_c)),product_curry(X_a,X_b,X_c),X),Xa),Xb) = hAPP(product_prod(X_a,X_b),X_c,X,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Xa),Xb)) ).
fof(fact_82_curryI,axiom,
! [X_a,X_b,F,Aa,Ba] :
( hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba)))
=> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba)) ) ).
fof(fact_83_curryE,axiom,
! [X_b,X_a,F,Aa,Ba] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))
=> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) ) ).
fof(fact_84_curryD,axiom,
! [X_b,X_a,F,Aa,Ba] :
( hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),product_curry(X_a,X_b,bool),F),Aa),Ba))
=> hBOOL(hAPP(product_prod(X_a,X_b),bool,F,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),Aa),Ba))) ) ).
fof(fact_85_curry__conv,axiom,
! [X_c,X_a,X_b,F,Aa,Ba] : hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),hAPP(fun(product_prod(X_b,X_c),X_a),fun(X_b,fun(X_c,X_a)),product_curry(X_b,X_c,X_a),F),Aa),Ba) = hAPP(product_prod(X_b,X_c),X_a,F,hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),Aa),Ba)) ).
fof(fact_86_eq__Nil__null,axiom,
! [X_a,Xs] :
( Xs = nil(X_a)
<=> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)) ) ).
fof(fact_87_List_Onull__def,axiom,
! [X_a,Xs] :
( hBOOL(hAPP(list(X_a),bool,null(X_a),Xs))
<=> Xs = nil(X_a) ) ).
fof(fact_88_null__rec_I1_J,axiom,
! [X_a,X_2,Xs_1] : ~ hBOOL(hAPP(list(X_a),bool,null(X_a),hAPP(list(X_a),list(X_a),hAPP(X_a,fun(list(X_a),list(X_a)),cons(X_a),X_2),Xs_1))) ).
fof(fact_89_null__rec_I2_J,axiom,
! [X_b] : hBOOL(hAPP(list(X_b),bool,null(X_b),nil(X_b))) ).
fof(fact_90_equal__Nil__null,axiom,
! [X_a,Xs] :
( hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),Xs),nil(X_a)))
<=> hBOOL(hAPP(list(X_a),bool,null(X_a),Xs)) ) ).
fof(fact_91_Prof__def,axiom,
arrow_1834574746e_Prof = hAPP(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool),hAPP(fun(arrow_1384031255e_indi,bool),fun(fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),fun(fun(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),bool)),pi(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),top_top(fun(arrow_1384031255e_indi,bool))),hAPP(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),fun(arrow_1384031255e_indi,fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),arrow_1384031255e_indi),arrow_638930832le_Lin)) ).
fof(fact_92_top1I,axiom,
! [X_a,X_1] : hBOOL(hAPP(X_a,bool,top_top(fun(X_a,bool)),X_1)) ).
fof(fact_93_Pi__UNIV,axiom,
! [X_a,X_b,A_1] : hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_a,fun(X_b,bool)),fun(fun(X_a,X_b),bool)),pi(X_a,X_b),A_1),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),combk(fun(X_b,bool),X_a),top_top(fun(X_b,bool)))) = top_top(fun(fun(X_a,X_b),bool)) ).
fof(fact_94_equal__list__def,axiom,
! [X_a,X_1,Y] :
( hBOOL(hAPP(list(X_a),bool,hAPP(list(X_a),fun(list(X_a),bool),equal_equal(list(X_a)),X_1),Y))
<=> X_1 = Y ) ).
fof(fact_95_iso__tuple__UNIV__I,axiom,
! [X_a,X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool)))) ).
fof(fact_96_UNIV__I,axiom,
! [X_a,X_1] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),top_top(fun(X_a,bool)))) ).
fof(fact_97_UNIV__def,axiom,
! [X_a] : top_top(fun(X_a,bool)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(bool,fun(X_a,bool),combk(bool,X_a),fTrue)) ).
fof(fact_98_top__apply,axiom,
! [X_b,X_a] :
( top(X_a)
=> ! [X_1] : hAPP(X_b,X_a,top_top(fun(X_b,X_a)),X_1) = top_top(X_a) ) ).
fof(fact_99_UNIV__eq__I,axiom,
! [X_a,A_1] :
( ! [X] : hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X),A_1))
=> top_top(fun(X_a,bool)) = ti(fun(X_a,bool),A_1) ) ).
%----Arities (2)
fof(arity_fun___Orderings_Otop,axiom,
! [T_2,T_1] :
( top(T_1)
=> top(fun(T_2,T_1)) ) ).
fof(arity_HOL_Obool___Orderings_Otop,axiom,
top(bool) ).
%----Helper facts (7)
fof(help_ti_idem,axiom,
! [T,A] : ti(T,ti(T,A)) = ti(T,A) ).
fof(help_COMBB_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),P),Q),R) = hAPP(X_b,X_c,P,hAPP(X_a,X_b,Q,R)) ).
fof(help_COMBC_1_1_U,axiom,
! [X_a,X_c,X_b,P,Q,R] : hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),P),Q),R) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q) ).
fof(help_COMBI_1_1_U,axiom,
! [X_a,P] : hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P) ).
fof(help_COMBK_1_1_U,axiom,
! [X_b,X_a,P,Q] : hAPP(X_b,X_a,hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),P),Q) = ti(X_a,P) ).
fof(help_fTrue_1_1_U,axiom,
hBOOL(fTrue) ).
fof(help_fTrue_1_1_T,axiom,
! [P] :
( ti(bool,P) = fTrue
| ti(bool,P) = fFalse ) ).
%----Conjectures (1)
fof(conj_0,conjecture,
! [I] :
( hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),b)),hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)))
<=> hBOOL(hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool,hAPP(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),fun(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),bool),member(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),hAPP(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt)),product_Pair(arrow_1212486748le_alt,arrow_1212486748le_alt),a),c)),hAPP(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),hAPP(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool)),hAPP(fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),fun(arrow_1212486748le_alt,fun(arrow_1212486748le_alt,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool))),arrow_888040304_below,hAPP(arrow_1384031255e_indi,fun(product_prod(arrow_1212486748le_alt,arrow_1212486748le_alt),bool),p,I)),c),b))) ) ).
%------------------------------------------------------------------------------