TPTP Problem File: COM087_5.p
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%------------------------------------------------------------------------------
% File : COM087_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Quantifier elimination for Presburger arithmetic line 210
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Nip08] Nipkow (2008), Linear Quantifier Elimination
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : qe_210 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 180 ( 46 unt; 52 typ; 0 def)
% Number of atoms : 262 ( 88 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 186 ( 52 ~; 15 |; 20 &)
% ( 22 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 19 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 39 ( 23 >; 16 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-6 aty)
% Number of variables : 519 ( 461 !; 8 ?; 519 :)
% ( 50 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:22:21
%------------------------------------------------------------------------------
%----Should-be-implicit typings (7)
tff(ty_tc_HOL_Obool,type,
bool: $tType ).
tff(ty_tc_Int_Oint,type,
int: $tType ).
tff(ty_tc_List_Olist,type,
list: $tType > $tType ).
tff(ty_tc_Nat_Onat,type,
nat: $tType ).
tff(ty_tc_PresArith_Oatom,type,
atom: $tType ).
tff(ty_tc_fun,type,
fun: ( $tType * $tType ) > $tType ).
tff(ty_tc_prod,type,
product_prod: ( $tType * $tType ) > $tType ).
%----Explicit typings (45)
tff(sy_cl_Rings_Oring,type,
ring:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ominus,type,
cl_Groups_Ominus:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ogroup__add,type,
group_add:
!>[A: $tType] : $o ).
tff(sy_cl_Finite__Set_Ofinite,type,
finite_finite1:
!>[A: $tType] : $o ).
tff(sy_c_COMBB,type,
combb:
!>[B: $tType,C: $tType,A: $tType] : fun(fun(B,C),fun(fun(A,B),fun(A,C))) ).
tff(sy_c_COMBC,type,
combc:
!>[A: $tType,B: $tType,C: $tType] : fun(fun(A,fun(B,C)),fun(B,fun(A,C))) ).
tff(sy_c_COMBS,type,
combs:
!>[A: $tType,B: $tType,C: $tType] : fun(fun(A,fun(B,C)),fun(fun(A,B),fun(A,C))) ).
tff(sy_c_Finite__Set_Ofinite,type,
finite_finite:
!>[A: $tType] : ( fun(A,bool) > $o ) ).
tff(sy_c_Groups_Ominus__class_Ominus,type,
minus_minus:
!>[A: $tType] : fun(A,fun(A,A)) ).
tff(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_ListVector_Oiprod,type,
iprod:
!>[A: $tType] : fun(list(A),fun(list(A),A)) ).
tff(sy_c_ListVector_Ozipwith0,type,
zipwith0:
!>[A: $tType,B: $tType,C: $tType] : ( fun(A,fun(B,C)) > fun(list(A),fun(list(B),list(C))) ) ).
tff(sy_c_List_Oinsert,type,
insert:
!>[A: $tType] : ( ( A * list(A) ) > list(A) ) ).
tff(sy_c_List_Olist_OCons,type,
cons:
!>[A: $tType] : fun(A,fun(list(A),list(A))) ).
tff(sy_c_List_Olist_ONil,type,
nil:
!>[A: $tType] : list(A) ).
tff(sy_c_List_Olist_Olist__case,type,
list_case:
!>[T: $tType,A: $tType] : ( ( T * fun(A,fun(list(A),T)) * list(A) ) > T ) ).
tff(sy_c_List_Olist__all,type,
list_all:
!>[A: $tType] : ( ( fun(A,bool) * list(A) ) > $o ) ).
tff(sy_c_List_Olist__ex1,type,
list_ex1:
!>[A: $tType] : ( ( fun(A,bool) * list(A) ) > $o ) ).
tff(sy_c_List_Olistset,type,
listset:
!>[A: $tType] : ( list(fun(A,bool)) > fun(list(A),bool) ) ).
tff(sy_c_List_Oset,type,
set:
!>[A: $tType] : ( list(A) > fun(A,bool) ) ).
tff(sy_c_List_Oset__Cons,type,
set_Cons:
!>[A: $tType] : ( ( fun(A,bool) * fun(list(A),bool) ) > fun(list(A),bool) ) ).
tff(sy_c_List_Osplice,type,
splice:
!>[A: $tType] : ( ( list(A) * list(A) ) > list(A) ) ).
tff(sy_c_List_Osublist,type,
sublist:
!>[A: $tType] : ( ( list(A) * fun(nat,bool) ) > list(A) ) ).
tff(sy_c_PresArith_OI_092_060_094isub_062Z,type,
i_Z: ( atom * list(int) ) > $o ).
tff(sy_c_PresArith_Odivisor,type,
divisor: atom > int ).
tff(sy_c_PresArith_Olbounds,type,
lbounds: list(atom) > list(product_prod(int,list(int))) ).
tff(sy_c_Product__Type_OPair,type,
product_Pair:
!>[A: $tType,B: $tType] : fun(A,fun(B,product_prod(A,B))) ).
tff(sy_c_Product__Type_Ocurry,type,
product_curry:
!>[A: $tType,B: $tType,C: $tType] : ( ( fun(product_prod(A,B),C) * A * B ) > C ) ).
tff(sy_c_Product__Type_Ointernal__split,type,
produc1605651328_split:
!>[A: $tType,B: $tType,C: $tType] : ( ( fun(A,fun(B,C)) * product_prod(A,B) ) > C ) ).
tff(sy_c_Product__Type_Oprod_Oprod__rec,type,
product_prod_rec:
!>[A: $tType,B: $tType,T: $tType] : ( ( fun(A,fun(B,T)) * product_prod(A,B) ) > T ) ).
tff(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( fun(A,bool) > fun(A,bool) ) ).
tff(sy_c_aa,type,
aa:
!>[A: $tType,B: $tType] : ( ( fun(A,B) * A ) > B ) ).
tff(sy_c_fEx,type,
fEx:
!>[A: $tType] : fun(fun(A,bool),bool) ).
tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fNot,type,
fNot: fun(bool,bool) ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_fconj,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(sy_c_fdisj,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(sy_c_fequal,type,
fequal:
!>[A: $tType] : fun(A,fun(A,bool)) ).
tff(sy_c_member,type,
member:
!>[A: $tType] : fun(A,fun(fun(A,bool),bool)) ).
tff(sy_c_pp,type,
pp: bool > $o ).
tff(sy_v_as,type,
as: list(atom) ).
tff(sy_v_x____,type,
x: int ).
tff(sy_v_xs,type,
xs: list(int) ).
%----Relevant facts (99)
tff(fact_0__096lbounds_Aas_A_126_061_A_091_093_096,axiom,
lbounds(as) != nil(product_prod(int,list(int))) ).
tff(fact_1_finite__set,axiom,
! [A: $tType,Xsa: list(A)] : finite_finite(A,set(A,Xsa)) ).
tff(fact_2_finite__Collect__disjI,axiom,
! [A: $tType,Q1: fun(A,bool),P1: fun(A,bool)] :
( finite_finite(A,collect(A,aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),aa(fun(A,bool),fun(A,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fdisj),P1)),Q1)))
<=> ( finite_finite(A,collect(A,P1))
& finite_finite(A,collect(A,Q1)) ) ) ).
tff(fact_3_finite__Collect__conjI,axiom,
! [A: $tType,Q1: fun(A,bool),P1: fun(A,bool)] :
( ( finite_finite(A,collect(A,P1))
| finite_finite(A,collect(A,Q1)) )
=> finite_finite(A,collect(A,aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),aa(fun(A,bool),fun(A,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),P1)),Q1))) ) ).
tff(fact_4_finite__code,axiom,
! [A: $tType] :
( finite_finite1(A)
=> ! [A1: fun(A,bool)] : finite_finite(A,A1) ) ).
tff(fact_5_split__paired__All,axiom,
! [A: $tType,B: $tType,P1: fun(product_prod(A,B),bool)] :
( ! [X11: product_prod(A,B)] : pp(aa(product_prod(A,B),bool,P1,X11))
<=> ! [A7: A,B4: B] : pp(aa(product_prod(A,B),bool,P1,aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A7),B4))) ) ).
tff(fact_6_Pair__eq,axiom,
! [A: $tType,B: $tType,B7: B,A6: A,B1: B,A3: A] :
( ( aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A3),B1) = aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A6),B7) )
<=> ( ( A3 = A6 )
& ( B1 = B7 ) ) ) ).
tff(fact_7_finite__image__set,axiom,
! [B: $tType,A: $tType,F: fun(A,B),P1: fun(A,bool)] :
( finite_finite(A,collect(A,P1))
=> finite_finite(B,collect(B,aa(fun(B,fun(A,bool)),fun(B,bool),aa(fun(fun(A,bool),bool),fun(fun(B,fun(A,bool)),fun(B,bool)),combb(fun(A,bool),bool,B),fEx(A)),aa(fun(A,bool),fun(B,fun(A,bool)),aa(fun(B,fun(fun(A,bool),fun(A,bool))),fun(fun(A,bool),fun(B,fun(A,bool))),combc(B,fun(A,bool),fun(A,bool)),aa(fun(B,fun(A,fun(bool,bool))),fun(B,fun(fun(A,bool),fun(A,bool))),aa(fun(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool))),fun(fun(B,fun(A,fun(bool,bool))),fun(B,fun(fun(A,bool),fun(A,bool)))),combb(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),B),combs(A,bool,bool)),aa(fun(B,fun(A,bool)),fun(B,fun(A,fun(bool,bool))),aa(fun(fun(A,bool),fun(A,fun(bool,bool))),fun(fun(B,fun(A,bool)),fun(B,fun(A,fun(bool,bool)))),combb(fun(A,bool),fun(A,fun(bool,bool)),B),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj)),aa(fun(A,B),fun(B,fun(A,bool)),aa(fun(B,fun(fun(A,B),fun(A,bool))),fun(fun(A,B),fun(B,fun(A,bool))),combc(B,fun(A,B),fun(A,bool)),aa(fun(B,fun(B,bool)),fun(B,fun(fun(A,B),fun(A,bool))),aa(fun(fun(B,bool),fun(fun(A,B),fun(A,bool))),fun(fun(B,fun(B,bool)),fun(B,fun(fun(A,B),fun(A,bool)))),combb(fun(B,bool),fun(fun(A,B),fun(A,bool)),B),combb(B,bool,A)),fequal(B))),F)))),P1)))) ) ).
tff(fact_8_finite__Collect__bounded__ex,axiom,
! [B: $tType,A: $tType,Q1: fun(B,fun(A,bool)),P1: fun(A,bool)] :
( finite_finite(A,collect(A,P1))
=> ( finite_finite(B,collect(B,aa(fun(B,fun(A,bool)),fun(B,bool),aa(fun(fun(A,bool),bool),fun(fun(B,fun(A,bool)),fun(B,bool)),combb(fun(A,bool),bool,B),fEx(A)),aa(fun(B,fun(A,bool)),fun(B,fun(A,bool)),aa(fun(fun(A,bool),fun(A,bool)),fun(fun(B,fun(A,bool)),fun(B,fun(A,bool))),combb(fun(A,bool),fun(A,bool),B),aa(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),aa(fun(A,bool),fun(A,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),P1))),Q1))))
<=> ! [Y2: A] :
( pp(aa(A,bool,P1,Y2))
=> finite_finite(B,collect(B,aa(A,fun(B,bool),aa(fun(B,fun(A,bool)),fun(A,fun(B,bool)),combc(B,A,bool),Q1),Y2))) ) ) ) ).
tff(fact_9_iprod__left__diff__distrib,axiom,
! [A: $tType] :
( ring(A)
=> ! [Zs: list(A),Ys1: list(A),Xs1: list(A)] : aa(list(A),A,aa(list(A),fun(list(A),A),iprod(A),aa(list(A),list(A),aa(list(A),fun(list(A),list(A)),minus_minus(list(A)),Xs1),Ys1)),Zs) = aa(A,A,aa(A,fun(A,A),minus_minus(A),aa(list(A),A,aa(list(A),fun(list(A),A),iprod(A),Xs1),Zs)),aa(list(A),A,aa(list(A),fun(list(A),A),iprod(A),Ys1),Zs)) ) ).
tff(fact_10_pred__equals__eq2,axiom,
! [B: $tType,A: $tType,S: fun(product_prod(A,B),bool),R1: fun(product_prod(A,B),bool)] :
( ! [X3: A,Xa2: B] :
( pp(aa(fun(product_prod(A,B),bool),bool,aa(product_prod(A,B),fun(fun(product_prod(A,B),bool),bool),member(product_prod(A,B)),aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),X3),Xa2)),R1))
<=> pp(aa(fun(product_prod(A,B),bool),bool,aa(product_prod(A,B),fun(fun(product_prod(A,B),bool),bool),member(product_prod(A,B)),aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),X3),Xa2)),S)) )
<=> ( R1 = S ) ) ).
tff(fact_11_finite__list,axiom,
! [A: $tType,A1: fun(A,bool)] :
( finite_finite(A,A1)
=> ? [Xs: list(A)] : set(A,Xs) = A1 ) ).
tff(fact_12_fun__diff__def,axiom,
! [B: $tType,A: $tType] :
( cl_Groups_Ominus(B)
=> ! [B2: fun(A,B),A1: fun(A,B),X2: A] : aa(A,B,aa(fun(A,B),fun(A,B),aa(fun(A,B),fun(fun(A,B),fun(A,B)),minus_minus(fun(A,B)),A1),B2),X2) = aa(B,B,aa(B,fun(B,B),minus_minus(B),aa(A,B,A1,X2)),aa(A,B,B2,X2)) ) ).
tff(fact_13_finite__Diff,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool)] :
( finite_finite(A,A1)
=> finite_finite(A,aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2)) ) ).
tff(fact_14_list__diff__Nil2,axiom,
! [A: $tType] :
( group_add(A)
=> ! [Xs1: list(A)] : aa(list(A),list(A),aa(list(A),fun(list(A),list(A)),minus_minus(list(A)),Xs1),nil(A)) = Xs1 ) ).
tff(fact_15_finite__Diff2,axiom,
! [A: $tType,A1: fun(A,bool),B2: fun(A,bool)] :
( finite_finite(A,B2)
=> ( finite_finite(A,aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2))
<=> finite_finite(A,A1) ) ) ).
tff(fact_16_Pair__inject,axiom,
! [A: $tType,B: $tType,B6: B,A5: A,B5: B,A2: A] :
( ( aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A2),B5) = aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A5),B6) )
=> ~ ( ( A2 = A5 )
=> ( B5 != B6 ) ) ) ).
tff(fact_17_finite,axiom,
! [A: $tType] :
( finite_finite1(A)
=> ! [A1: fun(A,bool)] : finite_finite(A,A1) ) ).
tff(fact_18_minus__apply,axiom,
! [A: $tType,B: $tType] :
( cl_Groups_Ominus(A)
=> ! [Xa: B,B2: fun(B,A),A1: fun(B,A)] : aa(B,A,aa(fun(B,A),fun(B,A),aa(fun(B,A),fun(fun(B,A),fun(B,A)),minus_minus(fun(B,A)),A1),B2),Xa) = aa(A,A,aa(A,fun(A,A),minus_minus(A),aa(B,A,A1,Xa)),aa(B,A,B2,Xa)) ) ).
tff(fact_19_split__paired__Ex,axiom,
! [A: $tType,B: $tType,P1: fun(product_prod(A,B),bool)] :
( ? [X11: product_prod(A,B)] : pp(aa(product_prod(A,B),bool,P1,X11))
<=> ? [A7: A,B4: B] : pp(aa(product_prod(A,B),bool,P1,aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A7),B4))) ) ).
tff(fact_20_prod_Orecs,axiom,
! [B: $tType,A: $tType,C: $tType,B1: C,A3: B,F1: fun(B,fun(C,A))] : product_prod_rec(B,C,A,F1,aa(C,product_prod(B,C),aa(B,fun(C,product_prod(B,C)),product_Pair(B,C),A3),B1)) = aa(C,A,aa(B,fun(C,A),F1,A3),B1) ).
tff(fact_21_list_Osimps_I4_J,axiom,
! [B: $tType,A: $tType,F2: fun(B,fun(list(B),A)),F1: A] : list_case(A,B,F1,F2,nil(B)) = F1 ).
tff(fact_22_prod_Oexhaust,axiom,
! [A: $tType,B: $tType,Y: product_prod(A,B)] :
~ ! [A4: A,B3: B] : Y != aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A4),B3) ).
tff(fact_23_PairE,axiom,
! [A: $tType,B: $tType,P2: product_prod(A,B)] :
~ ! [X1: A,Y3: B] : P2 != aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),X1),Y3) ).
tff(fact_24_prod__cases3,axiom,
! [A: $tType,B: $tType,C: $tType,Y: product_prod(A,product_prod(B,C))] :
~ ! [A4: A,B3: B,C2: C] : Y != aa(product_prod(B,C),product_prod(A,product_prod(B,C)),aa(A,fun(product_prod(B,C),product_prod(A,product_prod(B,C))),product_Pair(A,product_prod(B,C)),A4),aa(C,product_prod(B,C),aa(B,fun(C,product_prod(B,C)),product_Pair(B,C),B3),C2)) ).
tff(fact_25_prod__induct3,axiom,
! [C: $tType,B: $tType,A: $tType,Xa: product_prod(A,product_prod(B,C)),P1: fun(product_prod(A,product_prod(B,C)),bool)] :
( ! [A4: A,B3: B,C2: C] : pp(aa(product_prod(A,product_prod(B,C)),bool,P1,aa(product_prod(B,C),product_prod(A,product_prod(B,C)),aa(A,fun(product_prod(B,C),product_prod(A,product_prod(B,C))),product_Pair(A,product_prod(B,C)),A4),aa(C,product_prod(B,C),aa(B,fun(C,product_prod(B,C)),product_Pair(B,C),B3),C2))))
=> pp(aa(product_prod(A,product_prod(B,C)),bool,P1,Xa)) ) ).
tff(fact_26_prod__cases4,axiom,
! [A: $tType,B: $tType,C: $tType,D1: $tType,Y: product_prod(A,product_prod(B,product_prod(C,D1)))] :
~ ! [A4: A,B3: B,C2: C,D2: D1] : Y != aa(product_prod(B,product_prod(C,D1)),product_prod(A,product_prod(B,product_prod(C,D1))),aa(A,fun(product_prod(B,product_prod(C,D1)),product_prod(A,product_prod(B,product_prod(C,D1)))),product_Pair(A,product_prod(B,product_prod(C,D1))),A4),aa(product_prod(C,D1),product_prod(B,product_prod(C,D1)),aa(B,fun(product_prod(C,D1),product_prod(B,product_prod(C,D1))),product_Pair(B,product_prod(C,D1)),B3),aa(D1,product_prod(C,D1),aa(C,fun(D1,product_prod(C,D1)),product_Pair(C,D1),C2),D2))) ).
tff(fact_27_prod__induct4,axiom,
! [D1: $tType,C: $tType,B: $tType,A: $tType,Xa: product_prod(A,product_prod(B,product_prod(C,D1))),P1: fun(product_prod(A,product_prod(B,product_prod(C,D1))),bool)] :
( ! [A4: A,B3: B,C2: C,D2: D1] : pp(aa(product_prod(A,product_prod(B,product_prod(C,D1))),bool,P1,aa(product_prod(B,product_prod(C,D1)),product_prod(A,product_prod(B,product_prod(C,D1))),aa(A,fun(product_prod(B,product_prod(C,D1)),product_prod(A,product_prod(B,product_prod(C,D1)))),product_Pair(A,product_prod(B,product_prod(C,D1))),A4),aa(product_prod(C,D1),product_prod(B,product_prod(C,D1)),aa(B,fun(product_prod(C,D1),product_prod(B,product_prod(C,D1))),product_Pair(B,product_prod(C,D1)),B3),aa(D1,product_prod(C,D1),aa(C,fun(D1,product_prod(C,D1)),product_Pair(C,D1),C2),D2)))))
=> pp(aa(product_prod(A,product_prod(B,product_prod(C,D1))),bool,P1,Xa)) ) ).
tff(fact_28_prod__induct6,axiom,
! [F3: $tType,E: $tType,D1: $tType,C: $tType,B: $tType,A: $tType,Xa: product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),P1: fun(product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),bool)] :
( ! [A4: A,B3: B,C2: C,D2: D1,E1: E,F4: F3] : pp(aa(product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),bool,P1,aa(product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),aa(A,fun(product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),A4),aa(product_prod(C,product_prod(D1,product_prod(E,F3))),product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),aa(B,fun(product_prod(C,product_prod(D1,product_prod(E,F3))),product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),product_Pair(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),B3),aa(product_prod(D1,product_prod(E,F3)),product_prod(C,product_prod(D1,product_prod(E,F3))),aa(C,fun(product_prod(D1,product_prod(E,F3)),product_prod(C,product_prod(D1,product_prod(E,F3)))),product_Pair(C,product_prod(D1,product_prod(E,F3))),C2),aa(product_prod(E,F3),product_prod(D1,product_prod(E,F3)),aa(D1,fun(product_prod(E,F3),product_prod(D1,product_prod(E,F3))),product_Pair(D1,product_prod(E,F3)),D2),aa(F3,product_prod(E,F3),aa(E,fun(F3,product_prod(E,F3)),product_Pair(E,F3),E1),F4)))))))
=> pp(aa(product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),bool,P1,Xa)) ) ).
tff(fact_29_prod__cases6,axiom,
! [A: $tType,B: $tType,C: $tType,D1: $tType,E: $tType,F3: $tType,Y: product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))))] :
~ ! [A4: A,B3: B,C2: C,D2: D1,E1: E,F4: F3] : Y != aa(product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),aa(A,fun(product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),A4),aa(product_prod(C,product_prod(D1,product_prod(E,F3))),product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),aa(B,fun(product_prod(C,product_prod(D1,product_prod(E,F3))),product_prod(B,product_prod(C,product_prod(D1,product_prod(E,F3))))),product_Pair(B,product_prod(C,product_prod(D1,product_prod(E,F3)))),B3),aa(product_prod(D1,product_prod(E,F3)),product_prod(C,product_prod(D1,product_prod(E,F3))),aa(C,fun(product_prod(D1,product_prod(E,F3)),product_prod(C,product_prod(D1,product_prod(E,F3)))),product_Pair(C,product_prod(D1,product_prod(E,F3))),C2),aa(product_prod(E,F3),product_prod(D1,product_prod(E,F3)),aa(D1,fun(product_prod(E,F3),product_prod(D1,product_prod(E,F3))),product_Pair(D1,product_prod(E,F3)),D2),aa(F3,product_prod(E,F3),aa(E,fun(F3,product_prod(E,F3)),product_Pair(E,F3),E1),F4))))) ).
tff(fact_30_prod__induct5,axiom,
! [E: $tType,D1: $tType,C: $tType,B: $tType,A: $tType,Xa: product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E)))),P1: fun(product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E)))),bool)] :
( ! [A4: A,B3: B,C2: C,D2: D1,E1: E] : pp(aa(product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E)))),bool,P1,aa(product_prod(B,product_prod(C,product_prod(D1,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E)))),aa(A,fun(product_prod(B,product_prod(C,product_prod(D1,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D1,E)))),A4),aa(product_prod(C,product_prod(D1,E)),product_prod(B,product_prod(C,product_prod(D1,E))),aa(B,fun(product_prod(C,product_prod(D1,E)),product_prod(B,product_prod(C,product_prod(D1,E)))),product_Pair(B,product_prod(C,product_prod(D1,E))),B3),aa(product_prod(D1,E),product_prod(C,product_prod(D1,E)),aa(C,fun(product_prod(D1,E),product_prod(C,product_prod(D1,E))),product_Pair(C,product_prod(D1,E)),C2),aa(E,product_prod(D1,E),aa(D1,fun(E,product_prod(D1,E)),product_Pair(D1,E),D2),E1))))))
=> pp(aa(product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E)))),bool,P1,Xa)) ) ).
tff(fact_31_prod__cases5,axiom,
! [A: $tType,B: $tType,C: $tType,D1: $tType,E: $tType,Y: product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E))))] :
~ ! [A4: A,B3: B,C2: C,D2: D1,E1: E] : Y != aa(product_prod(B,product_prod(C,product_prod(D1,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E)))),aa(A,fun(product_prod(B,product_prod(C,product_prod(D1,E))),product_prod(A,product_prod(B,product_prod(C,product_prod(D1,E))))),product_Pair(A,product_prod(B,product_prod(C,product_prod(D1,E)))),A4),aa(product_prod(C,product_prod(D1,E)),product_prod(B,product_prod(C,product_prod(D1,E))),aa(B,fun(product_prod(C,product_prod(D1,E)),product_prod(B,product_prod(C,product_prod(D1,E)))),product_Pair(B,product_prod(C,product_prod(D1,E))),B3),aa(product_prod(D1,E),product_prod(C,product_prod(D1,E)),aa(C,fun(product_prod(D1,E),product_prod(C,product_prod(D1,E))),product_Pair(C,product_prod(D1,E)),C2),aa(E,product_prod(D1,E),aa(D1,fun(E,product_prod(D1,E)),product_Pair(D1,E),D2),E1)))) ).
tff(fact_32_Diff__iff,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool),C1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2)))
<=> ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),A1))
& ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),B2)) ) ) ).
tff(fact_33_Diff__idemp,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool)] : aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2)),B2) = aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2) ).
tff(fact_34_DiffE,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool),C1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2)))
=> ~ ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),A1))
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),B2)) ) ) ).
tff(fact_35_DiffI,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool),C1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),A1))
=> ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),B2))
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2))) ) ) ).
tff(fact_36_DiffD2,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool),C1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2)))
=> ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),B2)) ) ).
tff(fact_37_DiffD1,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool),C1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2)))
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),C1),A1)) ) ).
tff(fact_38_set__diff__eq,axiom,
! [A: $tType,B2: fun(A,bool),A1: fun(A,bool)] : aa(fun(A,bool),fun(A,bool),aa(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),A1),B2) = collect(A,aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),aa(fun(A,bool),fun(A,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),A1))),aa(fun(A,bool),fun(A,bool),aa(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),combb(bool,bool,A),fNot),aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),B2)))) ).
tff(fact_39_internal__split__conv,axiom,
! [B: $tType,A: $tType,C: $tType,B1: C,A3: B,C1: fun(B,fun(C,A))] : produc1605651328_split(B,C,A,C1,aa(C,product_prod(B,C),aa(B,fun(C,product_prod(B,C)),product_Pair(B,C),A3),B1)) = aa(C,A,aa(B,fun(C,A),C1,A3),B1) ).
tff(fact_40_x,axiom,
! [X2: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X2),set(atom,as)))
=> i_Z(X2,aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),x),xs)) ) ).
tff(fact_41_curry__conv,axiom,
! [A: $tType,B: $tType,C: $tType,B1: C,A3: B,F: fun(product_prod(B,C),A)] : product_curry(B,C,A,F,A3,B1) = aa(product_prod(B,C),A,F,aa(C,product_prod(B,C),aa(B,fun(C,product_prod(B,C)),product_Pair(B,C),A3),B1)) ).
tff(fact_42_list__diff__def,axiom,
! [A: $tType] :
( ( cl_Groups_Ominus(A)
& zero(A) )
=> ( minus_minus(list(A)) = zipwith0(A,A,A,minus_minus(A)) ) ) ).
tff(fact_43__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096,axiom,
? [X1: int] :
! [Xa1: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),Xa1),set(atom,as)))
=> i_Z(Xa1,aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X1),xs)) ) ).
tff(fact_44_list__ex1__simps_I1_J,axiom,
! [A: $tType,P1: fun(A,bool)] : ~ list_ex1(A,P1,nil(A)) ).
tff(fact_45_curryI,axiom,
! [A: $tType,B: $tType,B1: B,A3: A,F: fun(product_prod(A,B),bool)] :
( pp(aa(product_prod(A,B),bool,F,aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A3),B1)))
=> pp(product_curry(A,B,bool,F,A3,B1)) ) ).
tff(fact_46_list_Oinject,axiom,
! [A: $tType,List3: list(A),A6: A,List1: list(A),A3: A] :
( ( aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),A3),List1) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),A6),List3) )
<=> ( ( A3 = A6 )
& ( List1 = List3 ) ) ) ).
tff(fact_47_zipwith0_Osimps_I2_J,axiom,
! [B: $tType,A: $tType,C: $tType] :
( ( zero(C)
& zero(B) )
=> ! [Ys: list(C),Y1: C,Xsa: list(B),Xa: B,F: fun(B,fun(C,A))] : aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),aa(list(B),list(B),aa(B,fun(list(B),list(B)),cons(B),Xa),Xsa)),aa(list(C),list(C),aa(C,fun(list(C),list(C)),cons(C),Y1),Ys)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),aa(C,A,aa(B,fun(C,A),F,Xa),Y1)),aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),Xsa),Ys)) ) ).
tff(fact_48_zipwith0_Osimps_I1_J,axiom,
! [C: $tType,B: $tType,A: $tType] :
( ( zero(B)
& zero(C) )
=> ! [F: fun(B,fun(C,A))] : aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),nil(B)),nil(C)) = nil(A) ) ).
tff(fact_49_list__diff__Cons__Cons,axiom,
! [A: $tType] :
( ( cl_Groups_Ominus(A)
& zero(A) )
=> ! [Ys1: list(A),Y: A,Xs1: list(A),X: A] : aa(list(A),list(A),aa(list(A),fun(list(A),list(A)),minus_minus(list(A)),aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X),Xs1)),aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Y),Ys1)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),aa(A,A,aa(A,fun(A,A),minus_minus(A),X),Y)),aa(list(A),list(A),aa(list(A),fun(list(A),list(A)),minus_minus(list(A)),Xs1),Ys1)) ) ).
tff(fact_50__096_B_Bthesis_O_A_I_B_Bx_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X1: int] :
~ ! [Xa1: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),Xa1),set(atom,as)))
=> i_Z(Xa1,aa(list(int),list(int),aa(int,fun(list(int),list(int)),cons(int),X1),xs)) ) ).
tff(fact_51_not__Cons__self,axiom,
! [A: $tType,X: A,Xs1: list(A)] : Xs1 != aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X),Xs1) ).
tff(fact_52_not__Cons__self2,axiom,
! [A: $tType,Xs1: list(A),X: A] : aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X),Xs1) != Xs1 ).
tff(fact_53_set__ConsD,axiom,
! [A: $tType,Xsa: list(A),Xa: A,Y1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Y1),set(A,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),Xsa))))
=> ( ( Y1 = Xa )
| pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Y1),set(A,Xsa))) ) ) ).
tff(fact_54_list_Osimps_I3_J,axiom,
! [A: $tType,List2: list(A),A5: A] : aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),A5),List2) != nil(A) ).
tff(fact_55_list_Osimps_I2_J,axiom,
! [A: $tType,List2: list(A),A5: A] : nil(A) != aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),A5),List2) ).
tff(fact_56_list_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,List1: list(B),A3: B,F2: fun(B,fun(list(B),A)),F1: A] : list_case(A,B,F1,F2,aa(list(B),list(B),aa(B,fun(list(B),list(B)),cons(B),A3),List1)) = aa(list(B),A,aa(B,fun(list(B),A),F2,A3),List1) ).
tff(fact_57_curryD,axiom,
! [A: $tType,B: $tType,B1: B,A3: A,F: fun(product_prod(A,B),bool)] :
( pp(product_curry(A,B,bool,F,A3,B1))
=> pp(aa(product_prod(A,B),bool,F,aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A3),B1))) ) ).
tff(fact_58_curryE,axiom,
! [A: $tType,B: $tType,B1: B,A3: A,F: fun(product_prod(A,B),bool)] :
( pp(product_curry(A,B,bool,F,A3,B1))
=> pp(aa(product_prod(A,B),bool,F,aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),A3),B1))) ) ).
tff(fact_59_list__ex1__iff,axiom,
! [A: $tType,Xsa: list(A),P1: fun(A,bool)] :
( list_ex1(A,P1,Xsa)
<=> ? [X3: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X3),set(A,Xsa)))
& pp(aa(A,bool,P1,X3))
& ! [Y2: A] :
( ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Y2),set(A,Xsa)))
& pp(aa(A,bool,P1,Y2)) )
=> ( Y2 = X3 ) ) ) ) ).
tff(fact_60_curry__def,axiom,
! [C: $tType,A: $tType,B: $tType,X2: fun(product_prod(A,B),C),Xa1: A,Xb: B] : product_curry(A,B,C,X2,Xa1,Xb) = aa(product_prod(A,B),C,X2,aa(B,product_prod(A,B),aa(A,fun(B,product_prod(A,B)),product_Pair(A,B),Xa1),Xb)) ).
tff(fact_61_set__Cons__def,axiom,
! [A: $tType,XS: fun(list(A),bool),A1: fun(A,bool)] : set_Cons(A,A1,XS) = collect(list(A),aa(fun(list(A),fun(A,bool)),fun(list(A),bool),aa(fun(fun(A,bool),bool),fun(fun(list(A),fun(A,bool)),fun(list(A),bool)),combb(fun(A,bool),bool,list(A)),fEx(A)),aa(fun(list(A),fun(A,fun(list(A),bool))),fun(list(A),fun(A,bool)),aa(fun(fun(A,fun(list(A),bool)),fun(A,bool)),fun(fun(list(A),fun(A,fun(list(A),bool))),fun(list(A),fun(A,bool))),combb(fun(A,fun(list(A),bool)),fun(A,bool),list(A)),aa(fun(fun(list(A),bool),bool),fun(fun(A,fun(list(A),bool)),fun(A,bool)),combb(fun(list(A),bool),bool,A),fEx(list(A)))),aa(fun(A,fun(list(A),bool)),fun(list(A),fun(A,fun(list(A),bool))),aa(fun(list(A),fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),bool)))),fun(fun(A,fun(list(A),bool)),fun(list(A),fun(A,fun(list(A),bool)))),combc(list(A),fun(A,fun(list(A),bool)),fun(A,fun(list(A),bool))),aa(fun(list(A),fun(A,fun(fun(list(A),bool),fun(list(A),bool)))),fun(list(A),fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),bool)))),aa(fun(fun(A,fun(fun(list(A),bool),fun(list(A),bool))),fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),bool)))),fun(fun(list(A),fun(A,fun(fun(list(A),bool),fun(list(A),bool)))),fun(list(A),fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),bool))))),combb(fun(A,fun(fun(list(A),bool),fun(list(A),bool))),fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),bool))),list(A)),combs(A,fun(list(A),bool),fun(list(A),bool))),aa(fun(list(A),fun(A,fun(list(A),fun(bool,bool)))),fun(list(A),fun(A,fun(fun(list(A),bool),fun(list(A),bool)))),aa(fun(fun(A,fun(list(A),fun(bool,bool))),fun(A,fun(fun(list(A),bool),fun(list(A),bool)))),fun(fun(list(A),fun(A,fun(list(A),fun(bool,bool)))),fun(list(A),fun(A,fun(fun(list(A),bool),fun(list(A),bool))))),combb(fun(A,fun(list(A),fun(bool,bool))),fun(A,fun(fun(list(A),bool),fun(list(A),bool))),list(A)),aa(fun(fun(list(A),fun(bool,bool)),fun(fun(list(A),bool),fun(list(A),bool))),fun(fun(A,fun(list(A),fun(bool,bool))),fun(A,fun(fun(list(A),bool),fun(list(A),bool)))),combb(fun(list(A),fun(bool,bool)),fun(fun(list(A),bool),fun(list(A),bool)),A),combs(list(A),bool,bool))),aa(fun(list(A),fun(A,fun(list(A),bool))),fun(list(A),fun(A,fun(list(A),fun(bool,bool)))),aa(fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),fun(bool,bool)))),fun(fun(list(A),fun(A,fun(list(A),bool))),fun(list(A),fun(A,fun(list(A),fun(bool,bool))))),combb(fun(A,fun(list(A),bool)),fun(A,fun(list(A),fun(bool,bool))),list(A)),aa(fun(fun(list(A),bool),fun(list(A),fun(bool,bool))),fun(fun(A,fun(list(A),bool)),fun(A,fun(list(A),fun(bool,bool)))),combb(fun(list(A),bool),fun(list(A),fun(bool,bool)),A),aa(fun(bool,fun(bool,bool)),fun(fun(list(A),bool),fun(list(A),fun(bool,bool))),combb(bool,fun(bool,bool),list(A)),fconj))),aa(fun(A,fun(list(A),list(A))),fun(list(A),fun(A,fun(list(A),bool))),aa(fun(list(A),fun(fun(A,fun(list(A),list(A))),fun(A,fun(list(A),bool)))),fun(fun(A,fun(list(A),list(A))),fun(list(A),fun(A,fun(list(A),bool)))),combc(list(A),fun(A,fun(list(A),list(A))),fun(A,fun(list(A),bool))),aa(fun(list(A),fun(fun(list(A),list(A)),fun(list(A),bool))),fun(list(A),fun(fun(A,fun(list(A),list(A))),fun(A,fun(list(A),bool)))),aa(fun(fun(fun(list(A),list(A)),fun(list(A),bool)),fun(fun(A,fun(list(A),list(A))),fun(A,fun(list(A),bool)))),fun(fun(list(A),fun(fun(list(A),list(A)),fun(list(A),bool))),fun(list(A),fun(fun(A,fun(list(A),list(A))),fun(A,fun(list(A),bool))))),combb(fun(fun(list(A),list(A)),fun(list(A),bool)),fun(fun(A,fun(list(A),list(A))),fun(A,fun(list(A),bool))),list(A)),combb(fun(list(A),list(A)),fun(list(A),bool),A)),aa(fun(list(A),fun(list(A),bool)),fun(list(A),fun(fun(list(A),list(A)),fun(list(A),bool))),aa(fun(fun(list(A),bool),fun(fun(list(A),list(A)),fun(list(A),bool))),fun(fun(list(A),fun(list(A),bool)),fun(list(A),fun(fun(list(A),list(A)),fun(list(A),bool)))),combb(fun(list(A),bool),fun(fun(list(A),list(A)),fun(list(A),bool)),list(A)),combb(list(A),bool,list(A))),fequal(list(A))))),cons(A)))))),aa(fun(list(A),bool),fun(A,fun(list(A),bool)),aa(fun(A,fun(fun(list(A),bool),fun(list(A),bool))),fun(fun(list(A),bool),fun(A,fun(list(A),bool))),combc(A,fun(list(A),bool),fun(list(A),bool)),aa(fun(A,fun(bool,bool)),fun(A,fun(fun(list(A),bool),fun(list(A),bool))),aa(fun(fun(bool,bool),fun(fun(list(A),bool),fun(list(A),bool))),fun(fun(A,fun(bool,bool)),fun(A,fun(fun(list(A),bool),fun(list(A),bool)))),combb(fun(bool,bool),fun(fun(list(A),bool),fun(list(A),bool)),A),combb(bool,bool,list(A))),aa(fun(A,bool),fun(A,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fconj),aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(fun(A,bool),bool)),fun(fun(A,bool),fun(A,bool)),combc(A,fun(A,bool),bool),member(A)),A1)))),aa(fun(list(A),bool),fun(list(A),bool),aa(fun(list(A),fun(fun(list(A),bool),bool)),fun(fun(list(A),bool),fun(list(A),bool)),combc(list(A),fun(list(A),bool),bool),member(list(A))),XS)))))) ).
tff(fact_62_neq__Nil__conv,axiom,
! [A: $tType,Xsa: list(A)] :
( ( Xsa != nil(A) )
<=> ? [Y2: A,Ys2: list(A)] : Xsa = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Y2),Ys2) ) ).
tff(fact_63_list_Oexhaust,axiom,
! [A: $tType,Y: list(A)] :
( ( Y != nil(A) )
=> ~ ! [A4: A,List: list(A)] : Y != aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),A4),List) ) ).
tff(fact_64_insert__Nil,axiom,
! [A: $tType,X: A] : insert(A,X,nil(A)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X),nil(A)) ).
tff(fact_65_in__set__insert,axiom,
! [A: $tType,Xsa: list(A),Xa: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Xsa)))
=> ( insert(A,Xa,Xsa) = Xsa ) ) ).
tff(fact_66_not__in__set__insert,axiom,
! [A: $tType,Xsa: list(A),Xa: A] :
( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Xsa)))
=> ( insert(A,Xa,Xsa) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),Xsa) ) ) ).
tff(fact_67_List_Oinsert__def,axiom,
! [A: $tType,Xsa: list(A),Xa: A] :
( ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Xsa)))
=> ( insert(A,Xa,Xsa) = Xsa ) )
& ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Xsa)))
=> ( insert(A,Xa,Xsa) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),Xsa) ) ) ) ).
tff(fact_68_listset_Osimps_I2_J,axiom,
! [A: $tType,As: list(fun(A,bool)),A1: fun(A,bool)] : listset(A,aa(list(fun(A,bool)),list(fun(A,bool)),aa(fun(A,bool),fun(list(fun(A,bool)),list(fun(A,bool))),cons(fun(A,bool)),A1),As)) = set_Cons(A,A1,listset(A,As)) ).
tff(fact_69_list__ex1__simps_I2_J,axiom,
! [A: $tType,Xsa: list(A),Xa: A,P1: fun(A,bool)] :
( list_ex1(A,P1,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),Xsa))
<=> ( ( pp(aa(A,bool,P1,Xa))
=> list_all(A,aa(fun(A,bool),fun(A,bool),aa(fun(A,fun(bool,bool)),fun(fun(A,bool),fun(A,bool)),combs(A,bool,bool),aa(fun(A,bool),fun(A,fun(bool,bool)),aa(fun(bool,fun(bool,bool)),fun(fun(A,bool),fun(A,fun(bool,bool))),combb(bool,fun(bool,bool),A),fdisj),aa(fun(A,bool),fun(A,bool),aa(fun(bool,bool),fun(fun(A,bool),fun(A,bool)),combb(bool,bool,A),fNot),P1))),aa(A,fun(A,bool),fequal(A),Xa)),Xsa) )
& ( ~ pp(aa(A,bool,P1,Xa))
=> list_ex1(A,P1,Xsa) ) ) ) ).
tff(fact_70_splice_Osimps_I2_J,axiom,
! [A: $tType,Va: list(A),V: A] : splice(A,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),V),Va),nil(A)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),V),Va) ).
tff(fact_71_list__all__simps_I1_J,axiom,
! [A: $tType,Xsa: list(A),Xa: A,P1: fun(A,bool)] :
( list_all(A,P1,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),Xsa))
<=> ( pp(aa(A,bool,P1,Xa))
& list_all(A,P1,Xsa) ) ) ).
tff(fact_72_list__all__simps_I2_J,axiom,
! [A: $tType,P1: fun(A,bool)] : list_all(A,P1,nil(A)) ).
tff(fact_73_splice_Osimps_I3_J,axiom,
! [A: $tType,Ys1: list(A),Y: A,Xs1: list(A),X: A] : splice(A,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X),Xs1),aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Y),Ys1)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X),aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Y),splice(A,Xs1,Ys1))) ).
tff(fact_74_list__all__iff,axiom,
! [A: $tType,Xsa: list(A),P1: fun(A,bool)] :
( list_all(A,P1,Xsa)
<=> ! [X3: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X3),set(A,Xsa)))
=> pp(aa(A,bool,P1,X3)) ) ) ).
tff(fact_75_ext,axiom,
! [B: $tType,A: $tType,G: fun(A,B),F: fun(A,B)] :
( ! [X1: A] : aa(A,B,F,X1) = aa(A,B,G,X1)
=> ( F = G ) ) ).
tff(fact_76_mem__def,axiom,
! [A: $tType,A1: fun(A,bool),Xa: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),A1))
<=> pp(aa(A,bool,A1,Xa)) ) ).
tff(fact_77_Collect__def,axiom,
! [A: $tType,P1: fun(A,bool)] : collect(A,P1) = P1 ).
tff(fact_78_splice__Nil2,axiom,
! [A: $tType,Xs1: list(A)] : splice(A,Xs1,nil(A)) = Xs1 ).
tff(fact_79_splice_Osimps_I1_J,axiom,
! [A: $tType,Ys1: list(A)] : splice(A,nil(A),Ys1) = Ys1 ).
tff(fact_80_list__all__cong,axiom,
! [A: $tType,G: fun(A,bool),F: fun(A,bool),Ys: list(A),Xsa: list(A)] :
( ( Xsa = Ys )
=> ( ! [X1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X1),set(A,Ys)))
=> ( pp(aa(A,bool,F,X1))
<=> pp(aa(A,bool,G,X1)) ) )
=> ( list_all(A,F,Xsa)
<=> list_all(A,G,Ys) ) ) ) ).
tff(fact_81_norm,axiom,
! [X2: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X2),set(atom,as)))
=> ( divisor(X2) != zero_zero(int) ) ) ).
tff(fact_82_zipwith0_Osimps_I3_J,axiom,
! [B: $tType,A: $tType,C: $tType] :
( ( zero(C)
& zero(B) )
=> ! [Xsa: list(B),Xa: B,F: fun(B,fun(C,A))] : aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),aa(list(B),list(B),aa(B,fun(list(B),list(B)),cons(B),Xa),Xsa)),nil(C)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),aa(C,A,aa(B,fun(C,A),F,Xa),zero_zero(C))),aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),Xsa),nil(C))) ) ).
tff(fact_83_iprod__Nil2,axiom,
! [A: $tType] :
( ring(A)
=> ! [Xs1: list(A)] : aa(list(A),A,aa(list(A),fun(list(A),A),iprod(A),Xs1),nil(A)) = zero_zero(A) ) ).
tff(fact_84_iprod__Nil,axiom,
! [A: $tType] :
( ring(A)
=> ! [Ys1: list(A)] : aa(list(A),A,aa(list(A),fun(list(A),A),iprod(A),nil(A)),Ys1) = zero_zero(A) ) ).
tff(fact_85_zipwith0_Osimps_I4_J,axiom,
! [B: $tType,A: $tType,C: $tType] :
( ( zero(C)
& zero(B) )
=> ! [Ys: list(C),Y1: C,F: fun(B,fun(C,A))] : aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),nil(B)),aa(list(C),list(C),aa(C,fun(list(C),list(C)),cons(C),Y1),Ys)) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),aa(C,A,aa(B,fun(C,A),F,zero_zero(B)),Y1)),aa(list(C),list(A),aa(list(B),fun(list(C),list(A)),zipwith0(B,C,A,F),nil(B)),Ys)) ) ).
tff(fact_86_diff__self,axiom,
! [A: $tType] :
( group_add(A)
=> ! [A2: A] : aa(A,A,aa(A,fun(A,A),minus_minus(A),A2),A2) = zero_zero(A) ) ).
tff(fact_87_iprod0__if__coeffs0,axiom,
! [A: $tType] :
( ring(A)
=> ! [Xsa: list(A),Cs: list(A)] :
( ! [X1: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X1),set(A,Cs)))
=> ( X1 = zero_zero(A) ) )
=> ( aa(list(A),A,aa(list(A),fun(list(A),A),iprod(A),Cs),Xsa) = zero_zero(A) ) ) ) ).
tff(fact_88_zero__reorient,axiom,
! [A: $tType] :
( zero(A)
=> ! [Xa: A] :
( ( zero_zero(A) = Xa )
<=> ( Xa = zero_zero(A) ) ) ) ).
tff(fact_89_diff__eq__diff__eq,axiom,
! [A: $tType] :
( group_add(A)
=> ! [D: A,C1: A,B1: A,A3: A] :
( ( aa(A,A,aa(A,fun(A,A),minus_minus(A),A3),B1) = aa(A,A,aa(A,fun(A,A),minus_minus(A),C1),D) )
=> ( ( A3 = B1 )
<=> ( C1 = D ) ) ) ) ).
tff(fact_90_right__minus__eq,axiom,
! [A: $tType] :
( group_add(A)
=> ! [B1: A,A3: A] :
( ( aa(A,A,aa(A,fun(A,A),minus_minus(A),A3),B1) = zero_zero(A) )
<=> ( A3 = B1 ) ) ) ).
tff(fact_91_eq__iff__diff__eq__0,axiom,
! [A: $tType] :
( group_add(A)
=> ! [B1: A,A3: A] :
( ( A3 = B1 )
<=> ( aa(A,A,aa(A,fun(A,A),minus_minus(A),A3),B1) = zero_zero(A) ) ) ) ).
tff(fact_92_diff__0__right,axiom,
! [A: $tType] :
( group_add(A)
=> ! [A2: A] : aa(A,A,aa(A,fun(A,A),minus_minus(A),A2),zero_zero(A)) = A2 ) ).
tff(fact_93_sublist__singleton,axiom,
! [A: $tType,Xa: A,A1: fun(nat,bool)] :
( ( pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A1))
=> ( sublist(A,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),nil(A)),A1) = aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),nil(A)) ) )
& ( ~ pp(aa(fun(nat,bool),bool,aa(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),A1))
=> ( sublist(A,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),Xa),nil(A)),A1) = nil(A) ) ) ) ).
tff(fact_94_list__nonempty__induct,axiom,
! [A: $tType,P1: fun(list(A),bool),Xsa: list(A)] :
( ( Xsa != nil(A) )
=> ( ! [X1: A] : pp(aa(list(A),bool,P1,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X1),nil(A))))
=> ( ! [X1: A,Xs: list(A)] :
( ( Xs != nil(A) )
=> ( pp(aa(list(A),bool,P1,Xs))
=> pp(aa(list(A),bool,P1,aa(list(A),list(A),aa(A,fun(list(A),list(A)),cons(A),X1),Xs))) ) )
=> pp(aa(list(A),bool,P1,Xsa)) ) ) ) ).
tff(fact_95_sublist__nil,axiom,
! [A: $tType,A1: fun(nat,bool)] : sublist(A,nil(A),A1) = nil(A) ).
tff(fact_96_notin__set__sublistI,axiom,
! [A: $tType,I: fun(nat,bool),Xsa: list(A),Xa: A] :
( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Xsa)))
=> ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,sublist(A,Xsa,I)))) ) ).
tff(fact_97_in__set__sublistD,axiom,
! [A: $tType,I: fun(nat,bool),Xsa: list(A),Xa: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,sublist(A,Xsa,I))))
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Xsa))) ) ).
tff(fact_98_diff__self__eq__0,axiom,
! [M: nat] : aa(nat,nat,aa(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat) ).
%----Arities (12)
tff(arity_fun___Finite__Set_Ofinite,axiom,
! [T_1: $tType,T_2: $tType] :
( ( finite_finite1(T_2)
& finite_finite1(T_1) )
=> finite_finite1(fun(T_1,T_2)) ) ).
tff(arity_fun___Groups_Ominus,axiom,
! [T_1: $tType,T_2: $tType] :
( cl_Groups_Ominus(T_2)
=> cl_Groups_Ominus(fun(T_1,T_2)) ) ).
tff(arity_Int_Oint___Groups_Ogroup__add,axiom,
group_add(int) ).
tff(arity_Int_Oint___Groups_Ominus,axiom,
cl_Groups_Ominus(int) ).
tff(arity_Int_Oint___Groups_Ozero,axiom,
zero(int) ).
tff(arity_Int_Oint___Rings_Oring,axiom,
ring(int) ).
tff(arity_Nat_Onat___Groups_Ominus,axiom,
cl_Groups_Ominus(nat) ).
tff(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat) ).
tff(arity_HOL_Obool___Finite__Set_Ofinite,axiom,
finite_finite1(bool) ).
tff(arity_HOL_Obool___Groups_Ominus,axiom,
cl_Groups_Ominus(bool) ).
tff(arity_List_Olist___Groups_Ominus,axiom,
! [T_1: $tType] :
( ( zero(T_1)
& cl_Groups_Ominus(T_1) )
=> cl_Groups_Ominus(list(T_1)) ) ).
tff(arity_prod___Finite__Set_Ofinite,axiom,
! [T_1: $tType,T_2: $tType] :
( ( finite_finite1(T_2)
& finite_finite1(T_1) )
=> finite_finite1(product_prod(T_1,T_2)) ) ).
%----Helper facts (16)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
tff(help_fEx_1_1_U,axiom,
! [A: $tType,X: A,P: fun(A,bool)] :
( ~ pp(aa(A,bool,P,X))
| pp(aa(fun(A,bool),bool,fEx(A),P)) ) ).
tff(help_fNot_1_1_U,axiom,
! [P: bool] :
( ~ pp(aa(bool,bool,fNot,P))
| ~ pp(P) ) ).
tff(help_fNot_2_1_U,axiom,
! [P: bool] :
( pp(P)
| pp(aa(bool,bool,fNot,P)) ) ).
tff(help_COMBB_1_1_U,axiom,
! [C: $tType,B: $tType,A: $tType,R: A,Q: fun(A,B),P: fun(B,C)] : aa(A,C,aa(fun(A,B),fun(A,C),aa(fun(B,C),fun(fun(A,B),fun(A,C)),combb(B,C,A),P),Q),R) = aa(B,C,P,aa(A,B,Q,R)) ).
tff(help_COMBC_1_1_U,axiom,
! [A: $tType,C: $tType,B: $tType,R: A,Q: B,P: fun(A,fun(B,C))] : aa(A,C,aa(B,fun(A,C),aa(fun(A,fun(B,C)),fun(B,fun(A,C)),combc(A,B,C),P),Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q) ).
tff(help_COMBS_1_1_U,axiom,
! [C: $tType,B: $tType,A: $tType,R: A,Q: fun(A,B),P: fun(A,fun(B,C))] : aa(A,C,aa(fun(A,B),fun(A,C),aa(fun(A,fun(B,C)),fun(fun(A,B),fun(A,C)),combs(A,B,C),P),Q),R) = aa(B,C,aa(A,fun(B,C),P,R),aa(A,B,Q,R)) ).
tff(help_fconj_1_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(P)
| ~ pp(Q)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,P),Q)) ) ).
tff(help_fconj_2_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,P),Q))
| pp(P) ) ).
tff(help_fconj_3_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,P),Q))
| pp(Q) ) ).
tff(help_fdisj_1_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(P)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,P),Q)) ) ).
tff(help_fdisj_2_1_U,axiom,
! [P: bool,Q: bool] :
( ~ pp(Q)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,P),Q)) ) ).
tff(help_fdisj_3_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fdisj,P),Q))
| pp(P)
| pp(Q) ) ).
tff(help_fequal_1_1_T,axiom,
! [A: $tType,Y: A,X: A] :
( ~ pp(aa(A,bool,aa(A,fun(A,bool),fequal(A),X),Y))
| ( X = Y ) ) ).
tff(help_fequal_2_1_T,axiom,
! [A: $tType,Y: A,X: A] :
( ( X != Y )
| pp(aa(A,bool,aa(A,fun(A,bool),fequal(A),X),Y)) ) ).
%----Conjectures (1)
tff(conj_0,conjecture,
finite_finite(int,collect(int,aa(fun(int,fun(list(int),bool)),fun(int,bool),aa(fun(fun(list(int),bool),bool),fun(fun(int,fun(list(int),bool)),fun(int,bool)),combb(fun(list(int),bool),bool,int),fEx(list(int))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool)),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),bool))),combb(fun(list(int),fun(int,bool)),fun(list(int),bool),int),aa(fun(fun(int,bool),bool),fun(fun(list(int),fun(int,bool)),fun(list(int),bool)),combb(fun(int,bool),bool,list(int)),fEx(int))),aa(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,bool)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),aa(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),aa(fun(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(int,fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))))),combb(fun(list(int),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,bool))),int),combs(list(int),fun(int,bool),fun(int,bool))),aa(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool)))),aa(fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),fun(fun(int,fun(list(int),fun(int,fun(bool,bool)))),fun(int,fun(list(int),fun(fun(int,bool),fun(int,bool))))),combb(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool))),int),aa(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(bool,bool))),fun(list(int),fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),list(int)),combs(int,bool,bool))),aa(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool)))),aa(fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),fun(fun(int,fun(list(int),fun(int,bool))),fun(int,fun(list(int),fun(int,fun(bool,bool))))),combb(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool))),int),aa(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(list(int),fun(int,bool)),fun(list(int),fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),list(int)),aa(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj))),aa(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(list(int),fun(int,int)),fun(int,fun(list(int),fun(int,bool)))),combc(int,fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),aa(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),aa(fun(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool)))),fun(fun(int,fun(fun(int,int),fun(int,bool))),fun(int,fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))))),combb(fun(fun(int,int),fun(int,bool)),fun(fun(list(int),fun(int,int)),fun(list(int),fun(int,bool))),int),combb(fun(int,int),fun(int,bool),list(int))),aa(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool))),aa(fun(fun(int,bool),fun(fun(int,int),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(fun(int,int),fun(int,bool)))),combb(fun(int,bool),fun(fun(int,int),fun(int,bool)),int),combb(int,bool,int)),fequal(int)))),aa(fun(list(int),int),fun(list(int),fun(int,int)),aa(fun(int,fun(int,int)),fun(fun(list(int),int),fun(list(int),fun(int,int))),combb(int,fun(int,int),list(int)),aa(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int))),aa(list(int),fun(list(int),int),aa(fun(list(int),fun(list(int),int)),fun(list(int),fun(list(int),int)),combc(list(int),list(int),int),iprod(int)),xs))))))),aa(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool)),aa(fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(product_prod(int,list(int)),bool),fun(list(int),fun(int,bool))),combc(list(int),fun(product_prod(int,list(int)),bool),fun(int,bool)),aa(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),aa(fun(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool))),fun(fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(list(int),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)))),combb(fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(product_prod(int,list(int)),bool),fun(int,bool)),list(int)),combc(int,fun(product_prod(int,list(int)),bool),bool)),aa(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),aa(fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),fun(fun(list(int),fun(int,product_prod(int,list(int)))),fun(list(int),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)))),combb(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool)),list(int)),aa(fun(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool)),fun(fun(int,product_prod(int,list(int))),fun(int,fun(fun(product_prod(int,list(int)),bool),bool))),combb(product_prod(int,list(int)),fun(fun(product_prod(int,list(int)),bool),bool),int),member(product_prod(int,list(int))))),aa(fun(int,fun(list(int),product_prod(int,list(int)))),fun(list(int),fun(int,product_prod(int,list(int)))),combc(int,list(int),product_prod(int,list(int))),product_Pair(int,list(int)))))),set(product_prod(int,list(int)),lbounds(as)))))))) ).
%------------------------------------------------------------------------------