TPTP Problem File: COM082_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : COM082_5 : TPTP v9.0.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Quantifier elimination for Presburger arithmetic line 191
% 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_191 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 142 ( 77 unt; 39 typ; 0 def)
% Number of atoms : 138 ( 92 equ)
% Maximal formula atoms : 3 ( 0 avg)
% Number of connectives : 86 ( 51 ~; 2 |; 5 &)
% ( 20 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 39 ( 24 >; 15 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 0 prp; 1-5 aty)
% Number of functors : 32 ( 32 usr; 7 con; 0-5 aty)
% Number of variables : 310 ( 280 !; 3 ?; 310 :)
% ( 27 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:21:35
%------------------------------------------------------------------------------
%----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 (33)
tff(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : $o ).
tff(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_List_Ofoldr,type,
foldr:
!>[A: $tType,B: $tType] : ( ( fun(A,fun(B,B)) * list(A) * B ) > B ) ).
tff(sy_c_List_Olist_OCons,type,
cons:
!>[A: $tType] : ( ( A * list(A) ) > list(A) ) ).
tff(sy_c_List_Oset,type,
set:
!>[A: $tType] : ( list(A) > fun(A,bool) ) ).
tff(sy_c_Logic_OATOM_Onnf,type,
nnf:
!>[A: $tType] : ( ( fun(A,fm(A)) * fm(A) ) > fm(A) ) ).
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] : fun(fm(A),fun(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_OAtom,type,
atom1:
!>[A: $tType] : ( A > fm(A) ) ).
tff(sy_c_Logic_Ofm_OExQ,type,
exQ:
!>[A: $tType] : ( fm(A) > fm(A) ) ).
tff(sy_c_Logic_Ofm_OFalseF,type,
falseF:
!>[A: $tType] : fm(A) ).
tff(sy_c_Logic_Ofm_ONeg,type,
neg:
!>[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_Ofm_OTrueF,type,
trueF:
!>[A: $tType] : 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_Oneg,type,
neg1:
!>[A: $tType] : ( 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_Odivisor,type,
divisor: atom > int ).
tff(sy_c_PresArith_Oneg_092_060_094isub_062Z,type,
neg_Z: fun(atom,fm(atom)) ).
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_QEpres__Mirabelle__iocckttzyp_Oqe__pres_092_060_094isub_0621,type,
qEpres896714165pres_1: list(atom) > fm(atom) ).
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_fTrue,type,
fTrue: bool ).
tff(sy_c_member,type,
member:
!>[A: $tType] : ( ( A * fun(A,bool) ) > $o ) ).
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_x,axiom,
! [X3: atom] :
( member(atom,X3,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,X3),cons(int,x,xs))) ) ).
tff(fact_1__096EX_Ax_O_AALL_Aa_058set_Aas_O_AI_092_060_094isub_062Z_Aa_A_Ix_A_D_Axs_J_096,axiom,
? [X: int] :
! [Xa1: atom] :
( member(atom,Xa1,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,Xa1),cons(int,X,xs))) ) ).
tff(fact_2__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,
~ ! [X: int] :
~ ! [Xa1: atom] :
( member(atom,Xa1,set(atom,as))
=> pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,Xa1),cons(int,X,xs))) ) ).
tff(fact_3_Z_OI_092_060_094isub_062a__aneg,axiom,
! [Xsa: list(int),A4: atom] :
( interpret(atom,int,i_Z,aa(atom,fm(atom),neg_Z,A4),Xsa)
<=> ~ pp(aa(list(int),bool,aa(atom,fun(list(int),bool),i_Z,A4),Xsa)) ) ).
tff(fact_4_norm,axiom,
! [X3: atom] :
( member(atom,X3,set(atom,as))
=> ( divisor(X3) != zero_zero(int) ) ) ).
tff(fact_5_Z_OI__list__conj,axiom,
! [Xsa: list(int),Fs: list(fm(atom))] :
( interpret(atom,int,i_Z,list_conj(atom,Fs),Xsa)
<=> ! [X1: fm(atom)] :
( member(fm(atom),X1,set(fm(atom),Fs))
=> interpret(atom,int,i_Z,X1,Xsa) ) ) ).
tff(fact_6_Z_OI__and,axiom,
! [Xsa: list(int),Phi_2: fm(atom),Phi_1: fm(atom)] :
( interpret(atom,int,i_Z,aa(fm(atom),fm(atom),aa(fm(atom),fun(fm(atom),fm(atom)),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_7_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_8_Z_OI__neg,axiom,
! [Xsa: list(int),Phi: fm(atom)] :
( interpret(atom,int,i_Z,neg1(atom,Phi),Xsa)
<=> interpret(atom,int,i_Z,neg(atom,Phi),Xsa) ) ).
tff(fact_9_Z_OI__list__disj,axiom,
! [Xsa: list(int),Fs: list(fm(atom))] :
( interpret(atom,int,i_Z,list_disj(atom,Fs),Xsa)
<=> ? [X1: fm(atom)] :
( member(fm(atom),X1,set(fm(atom),Fs))
& interpret(atom,int,i_Z,X1,Xsa) ) ) ).
tff(fact_10_interpret_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),A4: A,H: fun(A,fun(list(B),bool))] :
( interpret(A,B,H,atom1(A,A4),Xsa)
<=> pp(aa(list(B),bool,aa(A,fun(list(B),bool),H,A4),Xsa)) ) ).
tff(fact_11_interpret_Osimps_I1_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),H: fun(A,fun(list(B),bool))] : interpret(A,B,H,trueF(A),Xsa) ).
tff(fact_12_fm_Osimps_I4_J,axiom,
! [A: $tType,Fm5: fm(A),Fm4: fm(A)] :
( ( neg(A,Fm4) = neg(A,Fm5) )
<=> ( Fm4 = Fm5 ) ) ).
tff(fact_13_fm_Osimps_I1_J,axiom,
! [A: $tType,A5: A,A4: A] :
( ( atom1(A,A4) = atom1(A,A5) )
<=> ( A4 = A5 ) ) ).
tff(fact_14_fm_Osimps_I3_J,axiom,
! [A: $tType,Fm23: fm(A),Fm13: fm(A),Fm22: fm(A),Fm12: fm(A)] :
( ( c_Logic_Ofm_OOr(A,Fm12,Fm22) = c_Logic_Ofm_OOr(A,Fm13,Fm23) )
<=> ( ( Fm12 = Fm13 )
& ( Fm22 = Fm23 ) ) ) ).
tff(fact_15_fm_Osimps_I2_J,axiom,
! [A: $tType,Fm23: fm(A),Fm13: fm(A),Fm22: fm(A),Fm12: fm(A)] :
( ( c_Logic_Ofm_OAnd(A,Fm12,Fm22) = c_Logic_Ofm_OAnd(A,Fm13,Fm23) )
<=> ( ( Fm12 = Fm13 )
& ( Fm22 = Fm23 ) ) ) ).
tff(fact_16_interpret_Osimps_I6_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),Phi: fm(A),H: fun(A,fun(list(B),bool))] :
( interpret(A,B,H,neg(A,Phi),Xsa)
<=> ~ interpret(A,B,H,Phi,Xsa) ) ).
tff(fact_17_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_18_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_19_fm_Osimps_I14_J,axiom,
! [A: $tType,Fm: fm(A)] : ( trueF(A) != neg(A,Fm) ) ).
tff(fact_20_fm_Osimps_I8_J,axiom,
! [A: $tType,A2: A] : ( trueF(A) != atom1(A,A2) ) ).
tff(fact_21_fm_Osimps_I12_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( trueF(A) != c_Logic_Ofm_OOr(A,Fm11,Fm21) ) ).
tff(fact_22_fm_Osimps_I10_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( trueF(A) != c_Logic_Ofm_OAnd(A,Fm11,Fm21) ) ).
tff(fact_23_fm_Osimps_I15_J,axiom,
! [A: $tType,Fm: fm(A)] : ( neg(A,Fm) != trueF(A) ) ).
tff(fact_24_fm_Osimps_I9_J,axiom,
! [A: $tType,A2: A] : ( atom1(A,A2) != trueF(A) ) ).
tff(fact_25_fm_Osimps_I33_J,axiom,
! [A: $tType,A1: A,Fm: fm(A)] : ( neg(A,Fm) != atom1(A,A1) ) ).
tff(fact_26_fm_Osimps_I32_J,axiom,
! [A: $tType,Fm: fm(A),A1: A] : ( atom1(A,A1) != neg(A,Fm) ) ).
tff(fact_27_fm_Osimps_I43_J,axiom,
! [A: $tType,Fm2: fm(A),Fm1: fm(A),Fm: fm(A)] : ( neg(A,Fm) != c_Logic_Ofm_OOr(A,Fm1,Fm2) ) ).
tff(fact_28_fm_Osimps_I39_J,axiom,
! [A: $tType,Fm2: fm(A),Fm1: fm(A),Fm: fm(A)] : ( neg(A,Fm) != c_Logic_Ofm_OAnd(A,Fm1,Fm2) ) ).
tff(fact_29_fm_Osimps_I30_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A),A1: A] : ( atom1(A,A1) != c_Logic_Ofm_OOr(A,Fm11,Fm21) ) ).
tff(fact_30_fm_Osimps_I28_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A),A1: A] : ( atom1(A,A1) != c_Logic_Ofm_OAnd(A,Fm11,Fm21) ) ).
tff(fact_31_fm_Osimps_I13_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OOr(A,Fm11,Fm21) != trueF(A) ) ).
tff(fact_32_fm_Osimps_I11_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OAnd(A,Fm11,Fm21) != trueF(A) ) ).
tff(fact_33_fm_Osimps_I42_J,axiom,
! [A: $tType,Fm: fm(A),Fm2: fm(A),Fm1: fm(A)] : ( c_Logic_Ofm_OOr(A,Fm1,Fm2) != neg(A,Fm) ) ).
tff(fact_34_fm_Osimps_I31_J,axiom,
! [A: $tType,A1: A,Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OOr(A,Fm11,Fm21) != atom1(A,A1) ) ).
tff(fact_35_fm_Osimps_I38_J,axiom,
! [A: $tType,Fm: fm(A),Fm2: fm(A),Fm1: fm(A)] : ( c_Logic_Ofm_OAnd(A,Fm1,Fm2) != neg(A,Fm) ) ).
tff(fact_36_fm_Osimps_I29_J,axiom,
! [A: $tType,A1: A,Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OAnd(A,Fm11,Fm21) != atom1(A,A1) ) ).
tff(fact_37_fm_Osimps_I37_J,axiom,
! [A: $tType,Fm2: fm(A),Fm1: fm(A),Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OOr(A,Fm11,Fm21) != c_Logic_Ofm_OAnd(A,Fm1,Fm2) ) ).
tff(fact_38_fm_Osimps_I36_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_OOr(A,Fm11,Fm21) ) ).
tff(fact_39_list_Oinject,axiom,
! [A: $tType,List1: list(A),A5: A,List: list(A),A4: A] :
( ( cons(A,A4,List) = cons(A,A5,List1) )
<=> ( ( A4 = A5 )
& ( List = List1 ) ) ) ).
tff(fact_40_set__ConsD,axiom,
! [A: $tType,Xsa: list(A),Xa: A,Y: A] :
( member(A,Y,set(A,cons(A,Xa,Xsa)))
=> ( ( Y = Xa )
| member(A,Y,set(A,Xsa)) ) ) ).
tff(fact_41_Z_Onnf_Osimps_I7_J,axiom,
! [Phi_2: fm(atom),Phi_1: fm(atom)] : ( nnf(atom,neg_Z,neg(atom,c_Logic_Ofm_OOr(atom,Phi_1,Phi_2))) = c_Logic_Ofm_OAnd(atom,nnf(atom,neg_Z,neg(atom,Phi_1)),nnf(atom,neg_Z,neg(atom,Phi_2))) ) ).
tff(fact_42_Z_Onnf_Osimps_I6_J,axiom,
! [Phi_2: fm(atom),Phi_1: fm(atom)] : ( nnf(atom,neg_Z,neg(atom,c_Logic_Ofm_OAnd(atom,Phi_1,Phi_2))) = c_Logic_Ofm_OOr(atom,nnf(atom,neg_Z,neg(atom,Phi_1)),nnf(atom,neg_Z,neg(atom,Phi_2))) ) ).
tff(fact_43_Z_Olift__nnf__qe_Osimps_I3_J,axiom,
! [Phi: fm(atom),Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,neg(atom,Phi)) = neg1(atom,lift_nnf_qe(atom,neg_Z,Qe,Phi)) ) ).
tff(fact_44_Z_Olift__nnf__qe_Osimps_I2_J,axiom,
! [Phi_2: fm(atom),Phi_1: fm(atom),Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,c_Logic_Ofm_OOr(atom,Phi_1,Phi_2)) = c_Logic_Oor(atom,lift_nnf_qe(atom,neg_Z,Qe,Phi_1),lift_nnf_qe(atom,neg_Z,Qe,Phi_2)) ) ).
tff(fact_45_Z_Olift__nnf__qe_Osimps_I1_J,axiom,
! [Phi_2: fm(atom),Phi_1: fm(atom),Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,c_Logic_Ofm_OAnd(atom,Phi_1,Phi_2)) = aa(fm(atom),fm(atom),aa(fm(atom),fun(fm(atom),fm(atom)),c_Logic_Oand(atom),lift_nnf_qe(atom,neg_Z,Qe,Phi_1)),lift_nnf_qe(atom,neg_Z,Qe,Phi_2)) ) ).
tff(fact_46_amap__fm_Osimps_I6_J,axiom,
! [A: $tType,B: $tType,Phi: fm(B),H: fun(B,fm(A))] : ( amap_fm(B,A,H,neg(B,Phi)) = neg1(A,amap_fm(B,A,H,Phi)) ) ).
tff(fact_47_Z_Onnf_Osimps_I11_J,axiom,
! [V: atom] : ( nnf(atom,neg_Z,atom1(atom,V)) = atom1(atom,V) ) ).
tff(fact_48_Z_Onnf_Osimps_I9_J,axiom,
nnf(atom,neg_Z,trueF(atom)) = trueF(atom) ).
tff(fact_49_Z_Olift__nnf__qe_Osimps_I7_J,axiom,
! [V: atom,Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,atom1(atom,V)) = atom1(atom,V) ) ).
tff(fact_50_Z_Olift__nnf__qe_Osimps_I5_J,axiom,
! [Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,trueF(atom)) = trueF(atom) ) ).
tff(fact_51_amap__fm_Osimps_I1_J,axiom,
! [B: $tType,A: $tType,H: fun(B,fm(A))] : ( amap_fm(B,A,H,trueF(B)) = trueF(A) ) ).
tff(fact_52_amap__fm_Osimps_I3_J,axiom,
! [A: $tType,B: $tType,A4: B,H: fun(B,fm(A))] : ( amap_fm(B,A,H,atom1(B,A4)) = aa(B,fm(A),H,A4) ) ).
tff(fact_53_Z_Onnf_Osimps_I5_J,axiom,
! [Phi: fm(atom)] : ( nnf(atom,neg_Z,neg(atom,neg(atom,Phi))) = nnf(atom,neg_Z,Phi) ) ).
tff(fact_54_Z_Onnf_Osimps_I8_J,axiom,
! [A4: atom] : ( nnf(atom,neg_Z,neg(atom,atom1(atom,A4))) = aa(atom,fm(atom),neg_Z,A4) ) ).
tff(fact_55_Z_Onnf_Osimps_I1_J,axiom,
! [Phi_2: fm(atom),Phi_1: fm(atom)] : ( nnf(atom,neg_Z,c_Logic_Ofm_OAnd(atom,Phi_1,Phi_2)) = c_Logic_Ofm_OAnd(atom,nnf(atom,neg_Z,Phi_1),nnf(atom,neg_Z,Phi_2)) ) ).
tff(fact_56_Z_Onnf_Osimps_I2_J,axiom,
! [Phi_2: fm(atom),Phi_1: fm(atom)] : ( nnf(atom,neg_Z,c_Logic_Ofm_OOr(atom,Phi_1,Phi_2)) = c_Logic_Ofm_OOr(atom,nnf(atom,neg_Z,Phi_1),nnf(atom,neg_Z,Phi_2)) ) ).
tff(fact_57_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)) ) ).
tff(fact_58_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)) = aa(fm(A),fm(A),aa(fm(A),fun(fm(A),fm(A)),c_Logic_Oand(A),amap_fm(B,A,H,Phi_1)),amap_fm(B,A,H,Phi_2)) ) ).
tff(fact_59_zero__reorient,axiom,
! [A: $tType] :
( zero(A)
=> ! [Xa: A] :
( ( zero_zero(A) = Xa )
<=> ( Xa = zero_zero(A) ) ) ) ).
tff(fact_60_not__Cons__self2,axiom,
! [A: $tType,Xs: list(A),X2: A] : ( cons(A,X2,Xs) != Xs ) ).
tff(fact_61_not__Cons__self,axiom,
! [A: $tType,X2: A,Xs: list(A)] : ( Xs != cons(A,X2,Xs) ) ).
tff(fact_62_Z_OI__nnf,axiom,
! [Xsa: list(int),Phi: fm(atom)] :
( interpret(atom,int,i_Z,nnf(atom,neg_Z,Phi),Xsa)
<=> interpret(atom,int,i_Z,Phi,Xsa) ) ).
tff(fact_63_list__conj__def,axiom,
! [A: $tType,Fs: list(fm(A))] : ( list_conj(A,Fs) = foldr(fm(A),fm(A),c_Logic_Oand(A),Fs,trueF(A)) ) ).
tff(fact_64_Z_Onnf_Osimps_I12_J,axiom,
! [Va: fm(atom)] : ( nnf(atom,neg_Z,neg(atom,exQ(atom,Va))) = neg(atom,exQ(atom,Va)) ) ).
tff(fact_65_Z_Olift__nnf__qe_Osimps_I4_J,axiom,
! [Phi: fm(atom),Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,exQ(atom,Phi)) = aa(fm(atom),fm(atom),Qe,nnf(atom,neg_Z,lift_nnf_qe(atom,neg_Z,Qe,Phi))) ) ).
tff(fact_66_Z_Onnf_Osimps_I4_J,axiom,
nnf(atom,neg_Z,neg(atom,falseF(atom))) = trueF(atom) ).
tff(fact_67_fm_Osimps_I5_J,axiom,
! [A: $tType,Fm5: fm(A),Fm4: fm(A)] :
( ( exQ(A,Fm4) = exQ(A,Fm5) )
<=> ( Fm4 = Fm5 ) ) ).
tff(fact_68_interpret_Osimps_I2_J,axiom,
! [A: $tType,B: $tType,Xsa: list(B),H: fun(A,fun(list(B),bool))] : ~ interpret(A,B,H,falseF(A),Xsa) ).
tff(fact_69_amap__fm_Osimps_I2_J,axiom,
! [B: $tType,A: $tType,H: fun(B,fm(A))] : ( amap_fm(B,A,H,falseF(B)) = falseF(A) ) ).
tff(fact_70_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)
<=> ? [X1: B] : interpret(A,B,H,Phi,cons(B,X1,Xsa)) ) ).
tff(fact_71_Z_Onnf_Osimps_I10_J,axiom,
nnf(atom,neg_Z,falseF(atom)) = falseF(atom) ).
tff(fact_72_Z_Olift__nnf__qe_Osimps_I6_J,axiom,
! [Qe: fun(fm(atom),fm(atom))] : ( lift_nnf_qe(atom,neg_Z,Qe,falseF(atom)) = falseF(atom) ) ).
tff(fact_73_Z_Onnf_Osimps_I13_J,axiom,
! [V: fm(atom)] : ( nnf(atom,neg_Z,exQ(atom,V)) = exQ(atom,V) ) ).
tff(fact_74_ext,axiom,
! [B: $tType,A: $tType,G: fun(A,B),F: fun(A,B)] :
( ! [X: A] : ( aa(A,B,F,X) = aa(A,B,G,X) )
=> ( F = G ) ) ).
tff(fact_75_mem__def,axiom,
! [A: $tType,A3: fun(A,bool),Xa: A] :
( member(A,Xa,A3)
<=> pp(aa(A,bool,A3,Xa)) ) ).
tff(fact_76_Z_Onnf_Osimps_I3_J,axiom,
nnf(atom,neg_Z,neg(atom,trueF(atom))) = falseF(atom) ).
tff(fact_77_fm_Osimps_I27_J,axiom,
! [A: $tType,Fm: fm(A)] : ( exQ(A,Fm) != falseF(A) ) ).
tff(fact_78_fm_Osimps_I26_J,axiom,
! [A: $tType,Fm: fm(A)] : ( falseF(A) != exQ(A,Fm) ) ).
tff(fact_79_fm_Osimps_I24_J,axiom,
! [A: $tType,Fm: fm(A)] : ( falseF(A) != neg(A,Fm) ) ).
tff(fact_80_fm_Osimps_I25_J,axiom,
! [A: $tType,Fm: fm(A)] : ( neg(A,Fm) != falseF(A) ) ).
tff(fact_81_fm_Osimps_I6_J,axiom,
! [A: $tType] : ( trueF(A) != falseF(A) ) ).
tff(fact_82_fm_Osimps_I7_J,axiom,
! [A: $tType] : ( falseF(A) != trueF(A) ) ).
tff(fact_83_fm_Osimps_I18_J,axiom,
! [A: $tType,A2: A] : ( falseF(A) != atom1(A,A2) ) ).
tff(fact_84_fm_Osimps_I19_J,axiom,
! [A: $tType,A2: A] : ( atom1(A,A2) != falseF(A) ) ).
tff(fact_85_fm_Osimps_I22_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( falseF(A) != c_Logic_Ofm_OOr(A,Fm11,Fm21) ) ).
tff(fact_86_fm_Osimps_I23_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OOr(A,Fm11,Fm21) != falseF(A) ) ).
tff(fact_87_fm_Osimps_I20_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( falseF(A) != c_Logic_Ofm_OAnd(A,Fm11,Fm21) ) ).
tff(fact_88_fm_Osimps_I21_J,axiom,
! [A: $tType,Fm21: fm(A),Fm11: fm(A)] : ( c_Logic_Ofm_OAnd(A,Fm11,Fm21) != falseF(A) ) ).
tff(fact_89_fm_Osimps_I47_J,axiom,
! [A: $tType,Fm3: fm(A),Fm: fm(A)] : ( exQ(A,Fm) != neg(A,Fm3) ) ).
tff(fact_90_fm_Osimps_I46_J,axiom,
! [A: $tType,Fm: fm(A),Fm3: fm(A)] : ( neg(A,Fm3) != exQ(A,Fm) ) ).
tff(fact_91_fm_Osimps_I16_J,axiom,
! [A: $tType,Fm: fm(A)] : ( trueF(A) != exQ(A,Fm) ) ).
tff(fact_92_fm_Osimps_I17_J,axiom,
! [A: $tType,Fm: fm(A)] : ( exQ(A,Fm) != trueF(A) ) ).
tff(fact_93_fm_Osimps_I35_J,axiom,
! [A: $tType,A1: A,Fm: fm(A)] : ( exQ(A,Fm) != atom1(A,A1) ) ).
tff(fact_94_fm_Osimps_I34_J,axiom,
! [A: $tType,Fm: fm(A),A1: A] : ( atom1(A,A1) != exQ(A,Fm) ) ).
tff(fact_95_fm_Osimps_I45_J,axiom,
! [A: $tType,Fm2: fm(A),Fm1: fm(A),Fm: fm(A)] : ( exQ(A,Fm) != c_Logic_Ofm_OOr(A,Fm1,Fm2) ) ).
tff(fact_96_fm_Osimps_I44_J,axiom,
! [A: $tType,Fm: fm(A),Fm2: fm(A),Fm1: fm(A)] : ( c_Logic_Ofm_OOr(A,Fm1,Fm2) != exQ(A,Fm) ) ).
tff(fact_97_fm_Osimps_I41_J,axiom,
! [A: $tType,Fm2: fm(A),Fm1: fm(A),Fm: fm(A)] : ( exQ(A,Fm) != c_Logic_Ofm_OAnd(A,Fm1,Fm2) ) ).
tff(fact_98_fm_Osimps_I40_J,axiom,
! [A: $tType,Fm: fm(A),Fm2: fm(A),Fm1: fm(A)] : ( c_Logic_Ofm_OAnd(A,Fm1,Fm2) != exQ(A,Fm) ) ).
%----Arities (1)
tff(arity_Int_Oint___Groups_Ozero,axiom,
zero(int) ).
%----Helper facts (2)
tff(help_pp_1_1_U,axiom,
~ pp(fFalse) ).
tff(help_pp_2_1_U,axiom,
pp(fTrue) ).
%----Conjectures (1)
tff(conj_0,conjecture,
interpret(atom,int,i_Z,qEpres896714165pres_1(as),xs) ).
%------------------------------------------------------------------------------