TPTP Problem File: COM048_5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : COM048_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Quantifier elimination for Presburger arithmetic line 94
% 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_94 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 171 ( 47 unt; 55 typ; 0 def)
% Number of atoms : 252 ( 98 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 180 ( 44 ~; 17 |; 20 &)
% ( 36 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 77 ( 39 >; 38 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-7 aty)
% Number of functors : 45 ( 45 usr; 8 con; 0-6 aty)
% Number of variables : 514 ( 455 !; 11 ?; 514 :)
% ( 48 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:17:11
%------------------------------------------------------------------------------
%----Should-be-implicit typings (6)
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_Logic_Ofm,type,
fm: $tType > $tType ).
tff(ty_tc_PresArith_Oatom,type,
atom: $tType ).
tff(ty_tc_fun,type,
fun: ( $tType * $tType ) > $tType ).
%----Explicit typings (49)
tff(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : $o ).
tff(sy_c_COMBB,type,
combb:
!>[B: $tType,C: $tType,A: $tType] : ( ( fun(B,C) * fun(A,B) ) > fun(A,C) ) ).
tff(sy_c_COMBC,type,
combc:
!>[A: $tType,B: $tType,C: $tType] : ( ( fun(A,fun(B,C)) * B ) > fun(A,C) ) ).
tff(sy_c_COMBS,type,
combs:
!>[A: $tType,B: $tType,C: $tType] : ( ( fun(A,fun(B,C)) * fun(A,B) ) > fun(A,C) ) ).
tff(sy_c_GCD_OGcd__class_OLcm,type,
gcd_Lcm:
!>[A: $tType] : ( fun(A,bool) > A ) ).
tff(sy_c_GCD_Ogcd__class_Olcm,type,
gcd_lcm:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_List_Odistinct,type,
distinct:
!>[A: $tType] : ( list(A) > $o ) ).
tff(sy_c_List_Oinsert,type,
insert1:
!>[A: $tType] : ( ( A * list(A) ) > list(A) ) ).
tff(sy_c_List_Olist_OCons,type,
cons:
!>[A: $tType] : ( ( A * 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_Olist__rec,type,
list_rec:
!>[T: $tType,A: $tType] : ( ( T * fun(A,fun(list(A),fun(T,T))) * list(A) ) > T ) ).
tff(sy_c_List_Olist__ex1,type,
list_ex1:
!>[A: $tType] : ( ( fun(A,bool) * list(A) ) > $o ) ).
tff(sy_c_List_Oremdups,type,
remdups:
!>[A: $tType] : ( list(A) > list(A) ) ).
tff(sy_c_List_Oset,type,
set:
!>[A: $tType] : ( list(A) > fun(A,bool) ) ).
tff(sy_c_List_Osplice,type,
splice:
!>[A: $tType] : ( ( list(A) * list(A) ) > list(A) ) ).
tff(sy_c_Logic_OATOM,type,
atom1:
!>[A: $tType,B: $tType] : ( ( fun(A,fm(A)) * fun(A,bool) * fun(A,fun(list(B),bool)) * fun(A,bool) * fun(A,A) ) > $o ) ).
tff(sy_c_Logic_OATOM_Onormal,type,
normal:
!>[A: $tType] : ( ( fun(A,bool) * fm(A) ) > $o ) ).
tff(sy_c_Logic_Oamap__fm,type,
amap_fm:
!>[A: $tType,B: $tType] : ( ( fun(A,fm(B)) * fm(A) ) > fm(B) ) ).
tff(sy_c_Logic_Oand,type,
c_Logic_Oand:
!>[A: $tType] : ( ( fm(A) * fm(A) ) > fm(A) ) ).
tff(sy_c_Logic_Ofm_OAnd,type,
c_Logic_Ofm_OAnd:
!>[A: $tType] : ( ( fm(A) * fm(A) ) > fm(A) ) ).
tff(sy_c_Logic_Ofm_OExQ,type,
exQ:
!>[A: $tType] : ( fm(A) > fm(A) ) ).
tff(sy_c_Logic_Ofm_OOr,type,
c_Logic_Ofm_OOr:
!>[A: $tType] : ( ( fm(A) * fm(A) ) > fm(A) ) ).
tff(sy_c_Logic_Ointerpret,type,
interpret:
!>[A: $tType,B: $tType] : ( ( fun(A,fun(list(B),bool)) * fm(A) * list(B) ) > $o ) ).
tff(sy_c_Logic_Olist__conj,type,
list_conj:
!>[A: $tType] : ( list(fm(A)) > fm(A) ) ).
tff(sy_c_Logic_Olist__disj,type,
list_disj:
!>[A: $tType] : ( list(fm(A)) > fm(A) ) ).
tff(sy_c_Logic_Oor,type,
c_Logic_Oor:
!>[A: $tType] : ( ( fm(A) * fm(A) ) > fm(A) ) ).
tff(sy_c_PresArith_OI_092_060_094isub_062Z,type,
i_Z: fun(atom,fun(list(int),bool)) ).
tff(sy_c_PresArith_Oasubst,type,
asubst: ( int * list(int) * atom ) > atom ).
tff(sy_c_PresArith_Odivisor,type,
divisor: atom > int ).
tff(sy_c_PresArith_Ozlcms,type,
zlcms: list(int) > int ).
tff(sy_c_QE_OATOM_Olift__dnf__qe,type,
lift_dnf_qe:
!>[A: $tType] : ( ( fun(A,fm(A)) * fun(A,bool) * fun(A,A) * fun(list(A),fm(A)) * fm(A) ) > fm(A) ) ).
tff(sy_c_QE_OATOM_Olift__nnf__qe,type,
lift_nnf_qe:
!>[A: $tType] : ( ( fun(A,fm(A)) * fun(fm(A),fm(A)) * fm(A) ) > fm(A) ) ).
tff(sy_c_QE_OATOM_Oqelim,type,
qelim:
!>[A: $tType] : ( ( fun(A,bool) * fun(A,A) * fun(list(A),fm(A)) * list(A) ) > fm(A) ) ).
tff(sy_c_QEpres__Mirabelle__iocckttzyp_Oqe__pres_092_060_094isub_0621,type,
qEpres896714165pres_1: list(atom) > fm(atom) ).
tff(sy_c_Set_OCollect,type,
collect:
!>[A: $tType] : ( fun(A,bool) > fun(A,bool) ) ).
tff(sy_c_Set_Oinsert,type,
insert:
!>[A: $tType] : ( ( A * fun(A,bool) ) > fun(A,bool) ) ).
tff(sy_c_aa,type,
aa:
!>[A: $tType,B: $tType] : ( ( fun(A,B) * A ) > B ) ).
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_fdisj,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(sy_c_fequal,type,
fequal:
!>[A: $tType] : fun(A,fun(A,bool)) ).
tff(sy_c_fimplies,type,
fimplies: fun(bool,fun(bool,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_xs,type,
xs: list(int) ).
%----Relevant facts (99)
tff(fact_0_list_Oinject,axiom,
! [A: $tType,List3: list(A),A6: A,List2: list(A),A4: A] :
( ( cons(A,A4,List2) = cons(A,A6,List3) )
<=> ( ( A4 = A6 )
& ( List2 = List3 ) ) ) ).
tff(fact_1_set__ConsD,axiom,
! [A: $tType,Xsa: list(A),X2: A,Y2: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Y2),set(A,cons(A,X2,Xsa))))
=> ( ( Y2 = X2 )
| pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Y2),set(A,Xsa))) ) ) ).
tff(fact_2_norm,axiom,
! [X4: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),X4),set(atom,as)))
=> ( divisor(X4) != zero_zero(int) ) ) ).
tff(fact_3_not__Cons__self,axiom,
! [A: $tType,X1: A,Xs: list(A)] : Xs != cons(A,X1,Xs) ).
tff(fact_4_not__Cons__self2,axiom,
! [A: $tType,Xs: list(A),X1: A] : cons(A,X1,Xs) != Xs ).
tff(fact_5_List_Oinsert__def,axiom,
! [A: $tType,Xsa: list(A),X2: A] :
( ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
=> ( insert1(A,X2,Xsa) = Xsa ) )
& ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
=> ( insert1(A,X2,Xsa) = cons(A,X2,Xsa) ) ) ) ).
tff(fact_6_not__in__set__insert,axiom,
! [A: $tType,Xsa: list(A),X2: A] :
( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
=> ( insert1(A,X2,Xsa) = cons(A,X2,Xsa) ) ) ).
tff(fact_7_interpret_Osimps_I7_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Phi: fm(A),H: fun(A,fun(list(B),bool))] :
( interpret(A,B,H,exQ(A,Phi),Xsa)
<=> ? [X: B] : interpret(A,B,H,Phi,cons(B,X,Xsa)) ) ).
tff(fact_8_remdups_Osimps_I2_J,axiom,
! [A: $tType,Xsa: list(A),X2: A] :
( ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
=> ( remdups(A,cons(A,X2,Xsa)) = remdups(A,Xsa) ) )
& ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
=> ( remdups(A,cons(A,X2,Xsa)) = cons(A,X2,remdups(A,Xsa)) ) ) ) ).
tff(fact_9_list_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,List2: list(B),A4: B,F2: fun(B,fun(list(B),A)),F1: A] : list_case(A,B,F1,F2,cons(B,A4,List2)) = aa(list(B),A,aa(B,fun(list(B),A),F2,A4),List2) ).
tff(fact_10_List_Oset_Osimps_I2_J,axiom,
! [A: $tType,Xsa: list(A),X2: A] : set(A,cons(A,X2,Xsa)) = insert(A,X2,set(A,Xsa)) ).
tff(fact_11_distinct_Osimps_I2_J,axiom,
! [A: $tType,Xsa: list(A),X2: A] :
( distinct(A,cons(A,X2,Xsa))
<=> ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
& distinct(A,Xsa) ) ) ).
tff(fact_12_fm_Osimps_I5_J,axiom,
! [A: $tType,Fm4: fm(A),Fm3: fm(A)] :
( ( exQ(A,Fm3) = exQ(A,Fm4) )
<=> ( Fm3 = Fm4 ) ) ).
tff(fact_13_set__remdups,axiom,
! [A: $tType,Xsa: list(A)] : set(A,remdups(A,Xsa)) = set(A,Xsa) ).
tff(fact_14_distinct__remdups,axiom,
! [A: $tType,Xs: list(A)] : distinct(A,remdups(A,Xs)) ).
tff(fact_15_remdups__id__iff__distinct,axiom,
! [A: $tType,Xsa: list(A)] :
( ( remdups(A,Xsa) = Xsa )
<=> distinct(A,Xsa) ) ).
tff(fact_16_List_Oset__insert,axiom,
! [A: $tType,Xsa: list(A),X2: A] : set(A,insert1(A,X2,Xsa)) = insert(A,X2,set(A,Xsa)) ).
tff(fact_17_remdups__remdups,axiom,
! [A: $tType,Xs: list(A)] : remdups(A,remdups(A,Xs)) = remdups(A,Xs) ).
tff(fact_18_insert__remdups,axiom,
! [A: $tType,Xs: list(A),X1: A] : insert1(A,X1,remdups(A,Xs)) = remdups(A,insert1(A,X1,Xs)) ).
tff(fact_19_distinct__insert,axiom,
! [A: $tType,X1: A,Xs: list(A)] :
( distinct(A,Xs)
=> distinct(A,insert1(A,X1,Xs)) ) ).
tff(fact_20_distinct__remdups__id,axiom,
! [A: $tType,Xs: list(A)] :
( distinct(A,Xs)
=> ( remdups(A,Xs) = Xs ) ) ).
tff(fact_21_distinct__length__2__or__more,axiom,
! [A: $tType,Xsa: list(A),B4: A,A4: A] :
( distinct(A,cons(A,A4,cons(A,B4,Xsa)))
<=> ( ( A4 != B4 )
& distinct(A,cons(A,A4,Xsa))
& distinct(A,cons(A,B4,Xsa)) ) ) ).
tff(fact_22_in__set__insert,axiom,
! [A: $tType,Xsa: list(A),X2: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),set(A,Xsa)))
=> ( insert1(A,X2,Xsa) = Xsa ) ) ).
tff(fact_23_insert__absorb2,axiom,
! [A: $tType,A2: fun(A,bool),X2: A] : insert(A,X2,insert(A,X2,A2)) = insert(A,X2,A2) ).
tff(fact_24_insert__iff,axiom,
! [A: $tType,A2: fun(A,bool),B4: A,A4: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),insert(A,B4,A2)))
<=> ( ( A4 = B4 )
| pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),A2)) ) ) ).
tff(fact_25_insertE,axiom,
! [A: $tType,A2: fun(A,bool),B4: A,A4: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),insert(A,B4,A2)))
=> ( ( A4 != B4 )
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),A2)) ) ) ).
tff(fact_26_insertCI,axiom,
! [A: $tType,B4: A,B3: fun(A,bool),A4: A] :
( ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),B3))
=> ( A4 = B4 ) )
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),insert(A,B4,B3))) ) ).
tff(fact_27_splice_Osimps_I3_J,axiom,
! [A: $tType,Ys1: list(A),Y: A,Xs: list(A),X1: A] : splice(A,cons(A,X1,Xs),cons(A,Y,Ys1)) = cons(A,X1,cons(A,Y,splice(A,Xs,Ys1))) ).
tff(fact_28_Z_OI__list__conj,axiom,
! [Xsa: list(int),Fs: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,Fs),Xsa)
<=> ! [X: fm(atom)] :
( pp(aa(fun(fm(atom),bool),bool,aa(fm(atom),fun(fun(fm(atom),bool),bool),member(fm(atom)),X),set(fm(atom),Fs)))
=> interpret(atom,int,i_Z,X,Xsa) ) ) ).
tff(fact_29_list_Orecs_I2_J,axiom,
! [A: $tType,B: $tType,List2: list(B),A4: B,F2: fun(B,fun(list(B),fun(A,A))),F1: A] : list_rec(A,B,F1,F2,cons(B,A4,List2)) = aa(A,A,aa(list(B),fun(A,A),aa(B,fun(list(B),fun(A,A)),F2,A4),List2),list_rec(A,B,F1,F2,List2)) ).
tff(fact_30_insertI1,axiom,
! [A: $tType,B3: fun(A,bool),A4: A] : pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),insert(A,A4,B3))) ).
tff(fact_31_zero__reorient,axiom,
! [A: $tType] :
( zero(A)
=> ! [X2: A] :
( ( zero_zero(A) = X2 )
<=> ( X2 = zero_zero(A) ) ) ) ).
tff(fact_32_insert__absorb,axiom,
! [A: $tType,A2: fun(A,bool),A4: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),A2))
=> ( insert(A,A4,A2) = A2 ) ) ).
tff(fact_33_insertI2,axiom,
! [A: $tType,B4: A,B3: fun(A,bool),A4: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),B3))
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),insert(A,B4,B3))) ) ).
tff(fact_34_insert__eq__iff,axiom,
! [A: $tType,B3: fun(A,bool),B4: A,A2: fun(A,bool),A4: A] :
( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),A2))
=> ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),B4),B3))
=> ( ( insert(A,A4,A2) = insert(A,B4,B3) )
<=> ( ( ( A4 = B4 )
=> ( A2 = B3 ) )
& ( ( A4 != B4 )
=> ? [C2: fun(A,bool)] :
( ( A2 = insert(A,B4,C2) )
& ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),B4),C2))
& ( B3 = insert(A,A4,C2) )
& ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),C2)) ) ) ) ) ) ) ).
tff(fact_35_insert__ident,axiom,
! [A: $tType,B3: fun(A,bool),A2: fun(A,bool),X2: A] :
( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),A2))
=> ( ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),B3))
=> ( ( insert(A,X2,A2) = insert(A,X2,B3) )
<=> ( A2 = B3 ) ) ) ) ).
tff(fact_36_insert__code,axiom,
! [A: $tType,X2: A,A2: fun(A,bool),Y2: A] :
( pp(aa(A,bool,insert(A,Y2,A2),X2))
<=> ( ( Y2 = X2 )
| pp(aa(A,bool,A2,X2)) ) ) ).
tff(fact_37_insert__commute,axiom,
! [A: $tType,A2: fun(A,bool),Y2: A,X2: A] : insert(A,X2,insert(A,Y2,A2)) = insert(A,Y2,insert(A,X2,A2)) ).
tff(fact_38_insert__Collect,axiom,
! [A: $tType,P1: fun(A,bool),A4: A] : insert(A,A4,collect(A,P1)) = collect(A,combs(A,bool,bool,combb(bool,fun(bool,bool),A,fimplies,combb(bool,bool,A,fNot,combc(A,A,bool,fequal(A),A4))),P1)) ).
tff(fact_39_insert__compr,axiom,
! [A: $tType,B3: fun(A,bool),A4: A] : insert(A,A4,B3) = collect(A,combs(A,bool,bool,combb(bool,fun(bool,bool),A,fdisj,combc(A,A,bool,fequal(A),A4)),combc(A,fun(A,bool),bool,member(A),B3))) ).
tff(fact_40_Z_OI__list__disj,axiom,
! [Xsa: list(int),Fs: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,Fs),Xsa)
<=> ? [X: fm(atom)] :
( pp(aa(fun(fm(atom),bool),bool,aa(fm(atom),fun(fun(fm(atom),bool),bool),member(fm(atom)),X),set(fm(atom),Fs)))
& interpret(atom,int,i_Z,X,Xsa) ) ) ).
tff(fact_41_Set_Oset__insert,axiom,
! [A: $tType,A2: fun(A,bool),X2: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),A2))
=> ~ ! [B2: fun(A,bool)] :
( ( A2 = insert(A,X2,B2) )
=> pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),B2)) ) ) ).
tff(fact_42_mk__disjoint__insert,axiom,
! [A: $tType,A2: fun(A,bool),A4: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),A2))
=> ? [B2: fun(A,bool)] :
( ( A2 = insert(A,A4,B2) )
& ~ pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),A4),B2)) ) ) ).
tff(fact_43_ATOM_OI__list__conj,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Fs: list(fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( interpret(A,B,I_a,list_conj(A,Fs),Xsa)
<=> ! [X: fm(A)] :
( pp(aa(fun(fm(A),bool),bool,aa(fm(A),fun(fun(fm(A),bool),bool),member(fm(A)),X),set(fm(A),Fs)))
=> interpret(A,B,I_a,X,Xsa) ) ) ) ).
tff(fact_44_divisor__asubst,axiom,
! [A1: atom,Ks: list(int),I: int] : divisor(asubst(I,Ks,A1)) = divisor(A1) ).
tff(fact_45_zlcms0__iff,axiom,
! [Is1: list(int)] :
( ( zlcms(Is1) = zero_zero(int) )
<=> pp(aa(fun(int,bool),bool,aa(int,fun(fun(int,bool),bool),member(int),zero_zero(int)),set(int,Is1))) ) ).
tff(fact_46_ATOM_Oanormal__decr,axiom,
! [B: $tType,A: $tType,A4: A,Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( ~ pp(aa(A,bool,Depends_0,A4))
=> ( pp(aa(A,bool,Anormal,A4))
=> pp(aa(A,bool,Anormal,aa(A,A,Decr,A4))) ) ) ) ).
tff(fact_47_ATOM_Onot__dep__decr,axiom,
! [A: $tType,B: $tType,Xsa: list(B),X2: B,A4: A,Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( ~ pp(aa(A,bool,Depends_0,A4))
=> ( pp(aa(list(B),bool,aa(A,fun(list(B),bool),I_a,A4),cons(B,X2,Xsa)))
<=> pp(aa(list(B),bool,aa(A,fun(list(B),bool),I_a,aa(A,A,Decr,A4)),Xsa)) ) ) ) ).
tff(fact_48_ATOM_OI_092_060_094isub_062a__aneg,axiom,
! [A: $tType,B: $tType,Xsa: list(B),A4: A,Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( interpret(A,B,I_a,aa(A,fm(A),Aneg,A4),Xsa)
<=> ~ pp(aa(list(B),bool,aa(A,fun(list(B),bool),I_a,A4),Xsa)) ) ) ).
tff(fact_49_ATOM_OI__list__disj,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Fs: list(fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( interpret(A,B,I_a,list_disj(A,Fs),Xsa)
<=> ? [X: fm(A)] :
( pp(aa(fun(fm(A),bool),bool,aa(fm(A),fun(fun(fm(A),bool),bool),member(fm(A)),X),set(fm(A),Fs)))
& interpret(A,B,I_a,X,Xsa) ) ) ) ).
tff(fact_50_zlcms_Osimps_I2_J,axiom,
! [Is: list(int),I: int] : zlcms(cons(int,I,Is)) = gcd_lcm(int,I,zlcms(Is)) ).
tff(fact_51_ATOM_OI__qelim,axiom,
! [A: $tType,B: $tType,Asa: list(A),Qe: fun(list(A),fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( ! [As: list(A)] :
( ! [X4: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X4),set(A,As)))
=> pp(aa(A,bool,Depends_0,X4)) )
=> ! [Xs2: list(B)] :
( interpret(A,B,I_a,aa(list(A),fm(A),Qe,As),Xs2)
<=> ? [X: B] :
! [Xa: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,As)))
=> pp(aa(list(B),bool,aa(A,fun(list(B),bool),I_a,Xa),cons(B,X,Xs2))) ) ) )
=> ! [Xs1: list(B)] :
( interpret(A,B,I_a,qelim(A,Depends_0,Decr,Qe,Asa),Xs1)
<=> ? [X: B] :
! [Xa: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Xa),set(A,Asa)))
=> pp(aa(list(B),bool,aa(A,fun(list(B),bool),I_a,Xa),cons(B,X,Xs1))) ) ) ) ) ).
tff(fact_52_ATOM_Onormal__list__disj,axiom,
! [B: $tType,A: $tType,Fs: list(fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( ! [X3: fm(A)] :
( pp(aa(fun(fm(A),bool),bool,aa(fm(A),fun(fun(fm(A),bool),bool),member(fm(A)),X3),set(fm(A),Fs)))
=> normal(A,Anormal,X3) )
=> normal(A,Anormal,list_disj(A,Fs)) ) ) ).
tff(fact_53_insert__Nil,axiom,
! [A: $tType,X1: A] : insert1(A,X1,nil(A)) = cons(A,X1,nil(A)) ).
tff(fact_54_distinct_Osimps_I1_J,axiom,
! [A: $tType] : distinct(A,nil(A)) ).
tff(fact_55_remdups__eq__nil__iff,axiom,
! [A: $tType,X2: list(A)] :
( ( remdups(A,X2) = nil(A) )
<=> ( X2 = nil(A) ) ) ).
tff(fact_56_remdups__eq__nil__right__iff,axiom,
! [A: $tType,X2: list(A)] :
( ( nil(A) = remdups(A,X2) )
<=> ( X2 = nil(A) ) ) ).
tff(fact_57_remdups_Osimps_I1_J,axiom,
! [A: $tType] : remdups(A,nil(A)) = nil(A) ).
tff(fact_58_list_Osimps_I3_J,axiom,
! [A: $tType,List1: list(A),A5: A] : cons(A,A5,List1) != nil(A) ).
tff(fact_59_list_Osimps_I2_J,axiom,
! [A: $tType,List1: list(A),A5: A] : nil(A) != cons(A,A5,List1) ).
tff(fact_60_ATOM_Onormal__aneg,axiom,
! [B: $tType,A: $tType,A4: A,Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( pp(aa(A,bool,Anormal,A4))
=> normal(A,Anormal,aa(A,fm(A),Aneg,A4)) ) ) ).
tff(fact_61_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_62_splice_Osimps_I1_J,axiom,
! [A: $tType,Ys1: list(A)] : splice(A,nil(A),Ys1) = Ys1 ).
tff(fact_63_splice__Nil2,axiom,
! [A: $tType,Xs: list(A)] : splice(A,Xs,nil(A)) = Xs ).
tff(fact_64_list_Orecs_I1_J,axiom,
! [B: $tType,A: $tType,F2: fun(B,fun(list(B),fun(A,A))),F1: A] : list_rec(A,B,F1,F2,nil(B)) = F1 ).
tff(fact_65_distinct__singleton,axiom,
! [A: $tType,X1: A] : distinct(A,cons(A,X1,nil(A))) ).
tff(fact_66_ATOM_Onormal__simps_I7_J,axiom,
! [B: $tType,A: $tType,Phi: fm(A),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( normal(A,Anormal,exQ(A,Phi))
<=> normal(A,Anormal,Phi) ) ) ).
tff(fact_67_splice_Osimps_I2_J,axiom,
! [A: $tType,Va: list(A),V: A] : splice(A,cons(A,V,Va),nil(A)) = cons(A,V,Va) ).
tff(fact_68_lcm__0__left__int,axiom,
! [N2: int] : gcd_lcm(int,zero_zero(int),N2) = zero_zero(int) ).
tff(fact_69_lcm__0__int,axiom,
! [M1: int] : gcd_lcm(int,M1,zero_zero(int)) = zero_zero(int) ).
tff(fact_70_lcm__0__iff__int,axiom,
! [N: int,M: int] :
( ( gcd_lcm(int,M,N) = zero_zero(int) )
<=> ( ( M = zero_zero(int) )
| ( N = zero_zero(int) ) ) ) ).
tff(fact_71_list_Oexhaust,axiom,
! [A: $tType,Y: list(A)] :
( ( Y != nil(A) )
=> ~ ! [A3: A,List: list(A)] : Y != cons(A,A3,List) ) ).
tff(fact_72_lcm__commute__int,axiom,
! [B1: int,A1: int] : gcd_lcm(int,A1,B1) = gcd_lcm(int,B1,A1) ).
tff(fact_73_lcm__int_Oleft__commute,axiom,
! [C1: int,A1: int,B1: int] : gcd_lcm(int,B1,gcd_lcm(int,A1,C1)) = gcd_lcm(int,A1,gcd_lcm(int,B1,C1)) ).
tff(fact_74_ext,axiom,
! [B: $tType,A: $tType,G: fun(A,B),F: fun(A,B)] :
( ! [X3: A] : aa(A,B,F,X3) = aa(A,B,G,X3)
=> ( F = G ) ) ).
tff(fact_75_mem__def,axiom,
! [A: $tType,A2: fun(A,bool),X2: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X2),A2))
<=> pp(aa(A,bool,A2,X2)) ) ).
tff(fact_76_Collect__def,axiom,
! [A: $tType,P1: fun(A,bool)] : collect(A,P1) = P1 ).
tff(fact_77_lcm__assoc__int,axiom,
! [C1: int,B1: int,A1: int] : gcd_lcm(int,gcd_lcm(int,A1,B1),C1) = gcd_lcm(int,A1,gcd_lcm(int,B1,C1)) ).
tff(fact_78_neq__Nil__conv,axiom,
! [A: $tType,Xsa: list(A)] :
( ( Xsa != nil(A) )
<=> ? [Y1: A,Ys: list(A)] : Xsa = cons(A,Y1,Ys) ) ).
tff(fact_79_ATOM_Onormal__or,axiom,
! [B: $tType,A: $tType,Phi_2: fm(A),Phi_1: fm(A),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( normal(A,Anormal,Phi_1)
=> ( normal(A,Anormal,Phi_2)
=> normal(A,Anormal,c_Logic_Oor(A,Phi_1,Phi_2)) ) ) ) ).
tff(fact_80_ATOM_Onormal__and,axiom,
! [B: $tType,A: $tType,Phi_2: fm(A),Phi_1: fm(A),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( normal(A,Anormal,Phi_1)
=> ( normal(A,Anormal,Phi_2)
=> normal(A,Anormal,c_Logic_Oand(A,Phi_1,Phi_2)) ) ) ) ).
tff(fact_81_list__ex1__simps_I1_J,axiom,
! [A: $tType,P1: fun(A,bool)] : ~ list_ex1(A,P1,nil(A)) ).
tff(fact_82_list__ex1__iff,axiom,
! [A: $tType,Xsa: list(A),P1: fun(A,bool)] :
( list_ex1(A,P1,Xsa)
<=> ? [X: A] :
( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),X),set(A,Xsa)))
& pp(aa(A,bool,P1,X))
& ! [Y1: A] :
( ( pp(aa(fun(A,bool),bool,aa(A,fun(fun(A,bool),bool),member(A),Y1),set(A,Xsa)))
& pp(aa(A,bool,P1,Y1)) )
=> ( Y1 = X ) ) ) ) ).
tff(fact_83_Lcm__insert__int,axiom,
! [N1: fun(int,bool),N: int] : gcd_Lcm(int,insert(int,N,N1)) = gcd_lcm(int,N,gcd_Lcm(int,N1)) ).
tff(fact_84_ATOM_OI__and,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Phi_2: fm(A),Phi_1: fm(A),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( interpret(A,B,I_a,c_Logic_Oand(A,Phi_1,Phi_2),Xsa)
<=> interpret(A,B,I_a,c_Logic_Ofm_OAnd(A,Phi_1,Phi_2),Xsa) ) ) ).
tff(fact_85_fm_Osimps_I2_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A),Fm2: fm(A),Fm1: fm(A)] :
( ( c_Logic_Ofm_OAnd(A,Fm1,Fm2) = c_Logic_Ofm_OAnd(A,Fm11,Fm21) )
<=> ( ( Fm1 = Fm11 )
& ( Fm2 = Fm21 ) ) ) ).
tff(fact_86_interpret_Osimps_I4_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Phi_2: fm(A),Phi_1: fm(A),H: fun(A,fun(list(B),bool))] :
( interpret(A,B,H,c_Logic_Ofm_OAnd(A,Phi_1,Phi_2),Xsa)
<=> ( interpret(A,B,H,Phi_1,Xsa)
& interpret(A,B,H,Phi_2,Xsa) ) ) ).
tff(fact_87_Z_OI__and,axiom,
! [Xsa: list(int),Phi_2: fm(atom),Phi_1: fm(atom)] :
( interpret(atom,int,i_Z,c_Logic_Oand(atom,Phi_1,Phi_2),Xsa)
<=> interpret(atom,int,i_Z,c_Logic_Ofm_OAnd(atom,Phi_1,Phi_2),Xsa) ) ).
tff(fact_88_fm_Osimps_I41_J,axiom,
! [A: $tType,Fm22: fm(A),Fm12: fm(A),Fm: fm(A)] : exQ(A,Fm) != c_Logic_Ofm_OAnd(A,Fm12,Fm22) ).
tff(fact_89_fm_Osimps_I40_J,axiom,
! [A: $tType,Fm: fm(A),Fm22: fm(A),Fm12: fm(A)] : c_Logic_Ofm_OAnd(A,Fm12,Fm22) != exQ(A,Fm) ).
tff(fact_90_ATOM_Onormal__simps_I4_J,axiom,
! [B: $tType,A: $tType,Phi_2: fm(A),Phi_1: fm(A),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( normal(A,Anormal,c_Logic_Ofm_OAnd(A,Phi_1,Phi_2))
<=> ( normal(A,Anormal,Phi_1)
& normal(A,Anormal,Phi_2) ) ) ) ).
tff(fact_91_amap__fm_Osimps_I4_J,axiom,
! [A: $tType,B: $tType,Phi_2: fm(B),Phi_1: fm(B),H: fun(B,fm(A))] : amap_fm(B,A,H,c_Logic_Ofm_OAnd(B,Phi_1,Phi_2)) = c_Logic_Oand(A,amap_fm(B,A,H,Phi_1),amap_fm(B,A,H,Phi_2)) ).
tff(fact_92_ATOM_Olift__dnf__qe_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Phi_2: fm(A),Phi_1: fm(A),Qe: fun(list(A),fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( lift_dnf_qe(A,Aneg,Depends_0,Decr,Qe,c_Logic_Ofm_OAnd(A,Phi_1,Phi_2)) = c_Logic_Oand(A,lift_dnf_qe(A,Aneg,Depends_0,Decr,Qe,Phi_1),lift_dnf_qe(A,Aneg,Depends_0,Decr,Qe,Phi_2)) ) ) ).
tff(fact_93_ATOM_Olift__nnf__qe_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,Phi_2: fm(A),Phi_1: fm(A),Qe: fun(fm(A),fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( lift_nnf_qe(A,Aneg,Qe,c_Logic_Ofm_OAnd(A,Phi_1,Phi_2)) = c_Logic_Oand(A,lift_nnf_qe(A,Aneg,Qe,Phi_1),lift_nnf_qe(A,Aneg,Qe,Phi_2)) ) ) ).
tff(fact_94_ATOM_Olift__dnf__qe_Osimps_I2_J,axiom,
! [B: $tType,A: $tType,Phi_2: fm(A),Phi_1: fm(A),Qe: fun(list(A),fm(A)),Decr: fun(A,A),Depends_0: fun(A,bool),I_a: fun(A,fun(list(B),bool)),Anormal: fun(A,bool),Aneg: fun(A,fm(A))] :
( atom1(A,B,Aneg,Anormal,I_a,Depends_0,Decr)
=> ( lift_dnf_qe(A,Aneg,Depends_0,Decr,Qe,c_Logic_Ofm_OOr(A,Phi_1,Phi_2)) = c_Logic_Oor(A,lift_dnf_qe(A,Aneg,Depends_0,Decr,Qe,Phi_1),lift_dnf_qe(A,Aneg,Depends_0,Decr,Qe,Phi_2)) ) ) ).
tff(fact_95_fm_Osimps_I3_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A),Fm2: fm(A),Fm1: fm(A)] :
( ( c_Logic_Ofm_OOr(A,Fm1,Fm2) = c_Logic_Ofm_OOr(A,Fm11,Fm21) )
<=> ( ( Fm1 = Fm11 )
& ( Fm2 = Fm21 ) ) ) ).
tff(fact_96_interpret_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Phi_2: fm(A),Phi_1: fm(A),H: fun(A,fun(list(B),bool))] :
( interpret(A,B,H,c_Logic_Ofm_OOr(A,Phi_1,Phi_2),Xsa)
<=> ( interpret(A,B,H,Phi_1,Xsa)
| interpret(A,B,H,Phi_2,Xsa) ) ) ).
tff(fact_97_Z_OI__or,axiom,
! [Xsa: list(int),Phi_2: fm(atom),Phi_1: fm(atom)] :
( interpret(atom,int,i_Z,c_Logic_Oor(atom,Phi_1,Phi_2),Xsa)
<=> interpret(atom,int,i_Z,c_Logic_Ofm_OOr(atom,Phi_1,Phi_2),Xsa) ) ).
tff(fact_98_amap__fm_Osimps_I5_J,axiom,
! [A: $tType,B: $tType,Phi_2: fm(B),Phi_1: fm(B),H: fun(B,fm(A))] : amap_fm(B,A,H,c_Logic_Ofm_OOr(B,Phi_1,Phi_2)) = c_Logic_Oor(A,amap_fm(B,A,H,Phi_1),amap_fm(B,A,H,Phi_2)) ).
%----Arities (1)
tff(arity_Int_Oint___Groups_Ozero,axiom,
zero(int) ).
%----Helper facts (15)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
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,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,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,combs(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),aa(A,B,Q,R)) ).
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,X1: A] :
( ~ pp(aa(A,bool,aa(A,fun(A,bool),fequal(A),X1),Y))
| ( X1 = Y ) ) ).
tff(help_fequal_2_1_T,axiom,
! [A: $tType,Y: A,X1: A] :
( ( X1 != Y )
| pp(aa(A,bool,aa(A,fun(A,bool),fequal(A),X1),Y)) ) ).
tff(help_fimplies_1_1_U,axiom,
! [Q: bool,P: bool] :
( pp(P)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,P),Q)) ) ).
tff(help_fimplies_2_1_U,axiom,
! [P: bool,Q: bool] :
( ~ pp(Q)
| pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,P),Q)) ) ).
tff(help_fimplies_3_1_U,axiom,
! [Q: bool,P: bool] :
( ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fimplies,P),Q))
| ~ pp(P)
| pp(Q) ) ).
%----Conjectures (1)
tff(conj_0,conjecture,
~ ( interpret(atom,int,i_Z,qEpres896714165pres_1(as),xs)
<=> ~ ? [X: int] :
! [Xa: atom] :
( pp(aa(fun(atom,bool),bool,aa(atom,fun(fun(atom,bool),bool),member(atom),Xa),set(atom,as)))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,Xa),cons(int,X,xs))) ) ) ).
%------------------------------------------------------------------------------