TPTP Problem File: NUM932_5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUM932_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 36
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_36 [Bla13]
% Status : Theorem
% Rating : 0.33 v7.4.0, 0.50 v7.1.0, 0.67 v6.4.0
% Syntax : Number of formulae : 145 ( 56 unt; 28 typ; 0 def)
% Number of atoms : 205 ( 80 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 98 ( 10 ~; 0 |; 9 &)
% ( 32 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 11 ( 8 >; 3 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 0 prp; 1-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 181 ( 164 !; 0 ?; 181 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:22:48
%------------------------------------------------------------------------------
%----Should-be-implicit typings (3)
tff(ty_tc_HOL_Obool,type,
bool: $tType ).
tff(ty_tc_Int_Oint,type,
int: $tType ).
tff(ty_tc_Nat_Onat,type,
nat: $tType ).
%----Explicit typings (25)
tff(sy_cl_Groups_Oone,type,
one:
!>[A: $tType] : $o ).
tff(sy_cl_Int_Onumber,type,
number:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ozero,type,
zero:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Osemiring,type,
semiring:
!>[A: $tType] : $o ).
tff(sy_cl_Int_Onumber__ring,type,
number_ring:
!>[A: $tType] : $o ).
tff(sy_cl_Int_Oring__char__0,type,
ring_char_0:
!>[A: $tType] : $o ).
tff(sy_cl_Int_Onumber__semiring,type,
number_semiring:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Olinordered__idom,type,
linordered_idom:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ocancel__semigroup__add,type,
cancel_semigroup_add:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Olinordered__ab__group__add,type,
linord219039673up_add:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
ordere236663937imp_le:
!>[A: $tType] : $o ).
tff(sy_c_Groups_Oone__class_Oone,type,
one_one:
!>[A: $tType] : A ).
tff(sy_c_Groups_Oplus__class_Oplus,type,
plus_plus:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_Groups_Otimes__class_Otimes,type,
times_times:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_IntPrimes_Ozprime,type,
zprime: int > $o ).
tff(sy_c_Int_OBit0,type,
bit0: int > int ).
tff(sy_c_Int_OBit1,type,
bit1: int > int ).
tff(sy_c_Int_OPls,type,
pls: int ).
tff(sy_c_Int_Onumber__class_Onumber__of,type,
number_number_of:
!>[A: $tType] : ( int > A ) ).
tff(sy_c_Orderings_Oord__class_Oless__eq,type,
ord_less_eq:
!>[A: $tType] : ( ( A * A ) > $o ) ).
tff(sy_c_fFalse,type,
fFalse: bool ).
tff(sy_c_fTrue,type,
fTrue: bool ).
tff(sy_c_pp,type,
pp: bool > $o ).
tff(sy_v_m,type,
m: int ).
%----Relevant facts (96)
tff(fact_0__096m_A_060_061_A0_096,axiom,
ord_less_eq(int,m,zero_zero(int)) ).
tff(fact_1__096_126_A1_A_060_061_Am_096,axiom,
~ ord_less_eq(int,one_one(int),m) ).
tff(fact_2_p,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_3_add__special_I2_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int] : plus_plus(A,one_one(A),number_number_of(A,W)) = number_number_of(A,plus_plus(int,bit1(pls),W)) ) ).
tff(fact_4_add__special_I3_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [V2: int] : plus_plus(A,number_number_of(A,V2),one_one(A)) = number_number_of(A,plus_plus(int,V2,bit1(pls))) ) ).
tff(fact_5_le__special_I2_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y: int] :
( ord_less_eq(A,one_one(A),number_number_of(A,Y))
<=> ord_less_eq(int,bit1(pls),Y) ) ) ).
tff(fact_6_le__special_I4_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [X: int] :
( ord_less_eq(A,number_number_of(A,X),one_one(A))
<=> ord_less_eq(int,X,bit1(pls)) ) ) ).
tff(fact_7_one__add__one__is__two,axiom,
! [A: $tType] :
( number_ring(A)
=> ( plus_plus(A,one_one(A),one_one(A)) = number_number_of(A,bit0(bit1(pls))) ) ) ).
tff(fact_8_mult__Bit1,axiom,
! [L1: int,K: int] : times_times(int,bit1(K),L1) = plus_plus(int,bit0(times_times(int,K,L1)),L1) ).
tff(fact_9_numeral__1__eq__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_10_add__Bit0__Bit1,axiom,
! [L1: int,K: int] : plus_plus(int,bit0(K),bit1(L1)) = bit1(plus_plus(int,K,L1)) ).
tff(fact_11_add__Bit1__Bit0,axiom,
! [L1: int,K: int] : plus_plus(int,bit1(K),bit0(L1)) = bit1(plus_plus(int,K,L1)) ).
tff(fact_12_rel__simps_I21_J,axiom,
! [K3: int] :
( ord_less_eq(int,pls,bit0(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_13_rel__simps_I27_J,axiom,
! [K3: int] :
( ord_less_eq(int,bit0(K3),pls)
<=> ord_less_eq(int,K3,pls) ) ).
tff(fact_14_rel__simps_I32_J,axiom,
! [L: int,K3: int] :
( ord_less_eq(int,bit0(K3),bit1(L))
<=> ord_less_eq(int,K3,L) ) ).
tff(fact_15_eq__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& ring_char_0(A) )
=> ! [Y: int,X: int] :
( ( number_number_of(A,X) = number_number_of(A,Y) )
<=> ( X = Y ) ) ) ).
tff(fact_16_rel__simps_I51_J,axiom,
! [L: int,K3: int] :
( ( bit1(K3) = bit1(L) )
<=> ( K3 = L ) ) ).
tff(fact_17_rel__simps_I48_J,axiom,
! [L: int,K3: int] :
( ( bit0(K3) = bit0(L) )
<=> ( K3 = L ) ) ).
tff(fact_18_double__eq__0__iff,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A1: A] :
( ( plus_plus(A,A1,A1) = zero_zero(A) )
<=> ( A1 = zero_zero(A) ) ) ) ).
tff(fact_19_rel__simps_I46_J,axiom,
! [K: int] : bit1(K) != pls ).
tff(fact_20_rel__simps_I39_J,axiom,
! [L1: int] : pls != bit1(L1) ).
tff(fact_21_rel__simps_I50_J,axiom,
! [L1: int,K: int] : bit1(K) != bit0(L1) ).
tff(fact_22_rel__simps_I49_J,axiom,
! [L1: int,K: int] : bit0(K) != bit1(L1) ).
tff(fact_23_rel__simps_I44_J,axiom,
! [K3: int] :
( ( bit0(K3) = pls )
<=> ( K3 = pls ) ) ).
tff(fact_24_rel__simps_I38_J,axiom,
! [L: int] :
( ( pls = bit0(L) )
<=> ( pls = L ) ) ).
tff(fact_25_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_26_rel__simps_I34_J,axiom,
! [L: int,K3: int] :
( ord_less_eq(int,bit1(K3),bit1(L))
<=> ord_less_eq(int,K3,L) ) ).
tff(fact_27_rel__simps_I19_J,axiom,
ord_less_eq(int,pls,pls) ).
tff(fact_28_rel__simps_I31_J,axiom,
! [L: int,K3: int] :
( ord_less_eq(int,bit0(K3),bit0(L))
<=> ord_less_eq(int,K3,L) ) ).
tff(fact_29_mult__Pls,axiom,
! [W: int] : times_times(int,pls,W) = pls ).
tff(fact_30_mult__Bit0,axiom,
! [L1: int,K: int] : times_times(int,bit0(K),L1) = bit0(times_times(int,K,L1)) ).
tff(fact_31_add__Bit0__Bit0,axiom,
! [L1: int,K: int] : plus_plus(int,bit0(K),bit0(L1)) = bit0(plus_plus(int,K,L1)) ).
tff(fact_32_left__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& semiring(B1) )
=> ! [V2: int,B2: B1,A2: B1] : times_times(B1,plus_plus(B1,A2,B2),number_number_of(B1,V2)) = plus_plus(B1,times_times(B1,A2,number_number_of(B1,V2)),times_times(B1,B2,number_number_of(B1,V2))) ) ).
tff(fact_33_right__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& semiring(B1) )
=> ! [C1: B1,B2: B1,V2: int] : times_times(B1,number_number_of(B1,V2),plus_plus(B1,B2,C1)) = plus_plus(B1,times_times(B1,number_number_of(B1,V2),B2),times_times(B1,number_number_of(B1,V2),C1)) ) ).
tff(fact_34_number__of__Pls,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_35_le__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y: int,X: int] :
( ord_less_eq(A,number_number_of(A,X),number_number_of(A,Y))
<=> ord_less_eq(int,X,Y) ) ) ).
tff(fact_36_mult__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A,W: int,V2: int] : times_times(A,number_number_of(A,V2),times_times(A,number_number_of(A,W),Z)) = times_times(A,number_number_of(A,times_times(int,V2,W)),Z) ) ).
tff(fact_37_arith__simps_I32_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V2: int] : times_times(A,number_number_of(A,V2),number_number_of(A,W)) = number_number_of(A,times_times(int,V2,W)) ) ).
tff(fact_38_add__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A,W: int,V2: int] : plus_plus(A,number_number_of(A,V2),plus_plus(A,number_number_of(A,W),Z)) = plus_plus(A,number_number_of(A,plus_plus(int,V2,W)),Z) ) ).
tff(fact_39_add__number__of__eq,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V2: int] : plus_plus(A,number_number_of(A,V2),number_number_of(A,W)) = number_number_of(A,plus_plus(int,V2,W)) ) ).
tff(fact_40_rel__simps_I22_J,axiom,
! [K3: int] :
( ord_less_eq(int,pls,bit1(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_41_le__special_I3_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [X: int] :
( ord_less_eq(A,number_number_of(A,X),zero_zero(A))
<=> ord_less_eq(int,X,pls) ) ) ).
tff(fact_42_le__special_I1_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y: int] :
( ord_less_eq(A,zero_zero(A),number_number_of(A,Y))
<=> ord_less_eq(int,pls,Y) ) ) ).
tff(fact_43_Pls__def,axiom,
pls = zero_zero(int) ).
tff(fact_44_number__of__reorient,axiom,
! [A: $tType] :
( number(A)
=> ! [X: A,W1: int] :
( ( number_number_of(A,W1) = X )
<=> ( X = number_number_of(A,W1) ) ) ) ).
tff(fact_45_number__of__is__id,axiom,
! [K: int] : number_number_of(int,K) = K ).
tff(fact_46_semiring__numeral__0__eq__0,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_47_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls) ).
tff(fact_48_odd__nonzero,axiom,
! [Z: int] : plus_plus(int,plus_plus(int,one_one(int),Z),Z) != zero_zero(int) ).
tff(fact_49_number__of__Bit0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int] : number_number_of(A,bit0(W)) = plus_plus(A,plus_plus(A,zero_zero(A),number_number_of(A,W)),number_number_of(A,W)) ) ).
tff(fact_50_less__eq__int__code_I16_J,axiom,
! [K2: int,K1: int] :
( ord_less_eq(int,bit1(K1),bit1(K2))
<=> ord_less_eq(int,K1,K2) ) ).
tff(fact_51_less__eq__int__code_I13_J,axiom,
! [K2: int,K1: int] :
( ord_less_eq(int,bit0(K1),bit0(K2))
<=> ord_less_eq(int,K1,K2) ) ).
tff(fact_52_add__Pls__right,axiom,
! [K: int] : plus_plus(int,K,pls) = K ).
tff(fact_53_add__Pls,axiom,
! [K: int] : plus_plus(int,pls,K) = K ).
tff(fact_54_Bit0__def,axiom,
! [K: int] : bit0(K) = plus_plus(int,K,K) ).
tff(fact_55_less__eq__number__of__int__code,axiom,
! [L: int,K3: int] :
( ord_less_eq(int,number_number_of(int,K3),number_number_of(int,L))
<=> ord_less_eq(int,K3,L) ) ).
tff(fact_56_times__numeral__code_I5_J,axiom,
! [W: int,V2: int] : times_times(int,number_number_of(int,V2),number_number_of(int,W)) = number_number_of(int,times_times(int,V2,W)) ).
tff(fact_57_int__distrib_I1_J,axiom,
! [W: int,Z2: int,Z1: int] : times_times(int,plus_plus(int,Z1,Z2),W) = plus_plus(int,times_times(int,Z1,W),times_times(int,Z2,W)) ).
tff(fact_58_int__distrib_I2_J,axiom,
! [Z2: int,Z1: int,W: int] : times_times(int,W,plus_plus(int,Z1,Z2)) = plus_plus(int,times_times(int,W,Z1),times_times(int,W,Z2)) ).
tff(fact_59_plus__numeral__code_I9_J,axiom,
! [W: int,V2: int] : plus_plus(int,number_number_of(int,V2),number_number_of(int,W)) = number_number_of(int,plus_plus(int,V2,W)) ).
tff(fact_60_add__numeral__0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : plus_plus(A,number_number_of(A,pls),A2) = A2 ) ).
tff(fact_61_add__numeral__0__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : plus_plus(A,A2,number_number_of(A,pls)) = A2 ) ).
tff(fact_62_number__of__mult,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V2: int] : number_number_of(A,times_times(int,V2,W)) = times_times(A,number_number_of(A,V2),number_number_of(A,W)) ) ).
tff(fact_63_number__of__add,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V2: int] : number_number_of(A,plus_plus(int,V2,W)) = plus_plus(A,number_number_of(A,V2),number_number_of(A,W)) ) ).
tff(fact_64_less__eq__int__code_I14_J,axiom,
! [K2: int,K1: int] :
( ord_less_eq(int,bit0(K1),bit1(K2))
<=> ord_less_eq(int,K1,K2) ) ).
tff(fact_65_Bit1__def,axiom,
! [K: int] : bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K) ).
tff(fact_66_number__of__Bit1,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int] : number_number_of(A,bit1(W)) = plus_plus(A,plus_plus(A,one_one(A),number_number_of(A,W)),number_number_of(A,W)) ) ).
tff(fact_67_mult__numeral__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : times_times(A,number_number_of(A,bit1(pls)),A2) = A2 ) ).
tff(fact_68_mult__numeral__1__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : times_times(A,A2,number_number_of(A,bit1(pls))) = A2 ) ).
tff(fact_69_semiring__numeral__1__eq__1,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_70_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)) ).
tff(fact_71_double__number__of__Bit0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int] : times_times(A,plus_plus(A,one_one(A),one_one(A)),number_number_of(A,W)) = number_number_of(A,bit0(W)) ) ).
tff(fact_72_semiring__mult__2,axiom,
! [A: $tType] :
( number_semiring(A)
=> ! [Z: A] : times_times(A,number_number_of(A,bit0(bit1(pls))),Z) = plus_plus(A,Z,Z) ) ).
tff(fact_73_mult__2,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A] : times_times(A,number_number_of(A,bit0(bit1(pls))),Z) = plus_plus(A,Z,Z) ) ).
tff(fact_74_semiring__mult__2__right,axiom,
! [A: $tType] :
( number_semiring(A)
=> ! [Z: A] : times_times(A,Z,number_number_of(A,bit0(bit1(pls)))) = plus_plus(A,Z,Z) ) ).
tff(fact_75_mult__2__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A] : times_times(A,Z,number_number_of(A,bit0(bit1(pls)))) = plus_plus(A,Z,Z) ) ).
tff(fact_76_semiring__one__add__one__is__two,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( plus_plus(A,one_one(A),one_one(A)) = number_number_of(A,bit0(bit1(pls))) ) ) ).
tff(fact_77_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_78_double__add__le__zero__iff__single__add__le__zero,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A1: A] :
( ord_less_eq(A,plus_plus(A,A1,A1),zero_zero(A))
<=> ord_less_eq(A,A1,zero_zero(A)) ) ) ).
tff(fact_79_zero__le__double__add__iff__zero__le__single__add,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A1: A] :
( ord_less_eq(A,zero_zero(A),plus_plus(A,A1,A1))
<=> ord_less_eq(A,zero_zero(A),A1) ) ) ).
tff(fact_80_prime__g__5,axiom,
! [P: int] :
( zprime(P)
=> ( ( P != number_number_of(int,bit0(bit1(pls))) )
=> ( ( P != number_number_of(int,bit1(bit1(pls))) )
=> ord_less_eq(int,number_number_of(int,bit1(bit0(bit1(pls)))),P) ) ) ) ).
tff(fact_81_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(bit1(pls)))) ).
tff(fact_82_zprime__2,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))) ).
tff(fact_83_number__of1,axiom,
! [N: int] :
( ord_less_eq(int,zero_zero(int),number_number_of(int,N))
=> ( ord_less_eq(int,zero_zero(int),number_number_of(int,bit0(N)))
& ord_less_eq(int,zero_zero(int),number_number_of(int,bit1(N))) ) ) ).
tff(fact_84_le__nat__number__of,axiom,
! [V1: int,V: int] :
( ord_less_eq(nat,number_number_of(nat,V),number_number_of(nat,V1))
<=> ( ~ ord_less_eq(int,V,V1)
=> ord_less_eq(int,V,pls) ) ) ).
tff(fact_85_add__left__cancel,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C: A,B: A,A1: A] :
( ( plus_plus(A,A1,B) = plus_plus(A,A1,C) )
<=> ( B = C ) ) ) ).
tff(fact_86_add__right__cancel,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C: A,A1: A,B: A] :
( ( plus_plus(A,B,A1) = plus_plus(A,C,A1) )
<=> ( B = C ) ) ) ).
tff(fact_87_double__zero__sym,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A1: A] :
( ( zero_zero(A) = plus_plus(A,A1,A1) )
<=> ( A1 = zero_zero(A) ) ) ) ).
tff(fact_88_add__le__cancel__right,axiom,
! [A: $tType] :
( ordere236663937imp_le(A)
=> ! [B: A,C: A,A1: A] :
( ord_less_eq(A,plus_plus(A,A1,C),plus_plus(A,B,C))
<=> ord_less_eq(A,A1,B) ) ) ).
tff(fact_89_add__le__cancel__left,axiom,
! [A: $tType] :
( ordere236663937imp_le(A)
=> ! [B: A,A1: A,C: A] :
( ord_less_eq(A,plus_plus(A,C,A1),plus_plus(A,C,B))
<=> ord_less_eq(A,A1,B) ) ) ).
tff(fact_90_nat__number__of__Pls,axiom,
number_number_of(nat,pls) = zero_zero(nat) ).
tff(fact_91_eq__0__number__of,axiom,
! [V: int] :
( ( zero_zero(nat) = number_number_of(nat,V) )
<=> ord_less_eq(int,V,pls) ) ).
tff(fact_92_eq__number__of__0,axiom,
! [V: int] :
( ( number_number_of(nat,V) = zero_zero(nat) )
<=> ord_less_eq(int,V,pls) ) ).
tff(fact_93_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat) ).
tff(fact_94_semiring__norm_I113_J,axiom,
zero_zero(nat) = number_number_of(nat,pls) ).
tff(fact_95_nat__mult__2__right,axiom,
! [Z: nat] : times_times(nat,Z,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,Z,Z) ).
%----Arities (18)
tff(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(int) ).
tff(arity_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
linord219039673up_add(int) ).
tff(arity_Int_Oint___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(int) ).
tff(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int) ).
tff(arity_Int_Oint___Int_Onumber__semiring,axiom,
number_semiring(int) ).
tff(arity_Int_Oint___Int_Oring__char__0,axiom,
ring_char_0(int) ).
tff(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int) ).
tff(arity_Int_Oint___Rings_Osemiring,axiom,
semiring(int) ).
tff(arity_Int_Oint___Groups_Ozero,axiom,
zero(int) ).
tff(arity_Int_Oint___Int_Onumber,axiom,
number(int) ).
tff(arity_Int_Oint___Groups_Oone,axiom,
one(int) ).
tff(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(nat) ).
tff(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat) ).
tff(arity_Nat_Onat___Int_Onumber__semiring,axiom,
number_semiring(nat) ).
tff(arity_Nat_Onat___Rings_Osemiring,axiom,
semiring(nat) ).
tff(arity_Nat_Onat___Groups_Ozero,axiom,
zero(nat) ).
tff(arity_Nat_Onat___Int_Onumber,axiom,
number(nat) ).
tff(arity_Nat_Onat___Groups_Oone,axiom,
one(nat) ).
%----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,
ord_less_eq(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)) ).
%------------------------------------------------------------------------------