TPTP Problem File: NUM934_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUM934_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 39
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_39 [Bla13]
% Status : Theorem
% Rating : 0.33 v7.4.0, 0.50 v7.1.0, 1.00 v6.4.0
% Syntax : Number of formulae : 137 ( 42 unt; 24 typ; 0 def)
% Number of atoms : 214 ( 65 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 113 ( 12 ~; 1 |; 14 &)
% ( 44 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 13 ( 9 >; 4 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 0 prp; 1-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 189 ( 176 !; 0 ?; 189 :)
% ( 13 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:22:53
%------------------------------------------------------------------------------
%----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 (21)
tff(sy_cl_Int_Onumber,type,
number:
!>[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_Orderings_Olinorder,type,
linorder:
!>[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_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_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,type,
ord_less:
!>[A: $tType] : ( ( A * A ) > $o ) ).
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 (98)
tff(fact_0__0961_A_060_061_Am_096,axiom,
ord_less_eq(int,one_one(int),m) ).
tff(fact_1_p,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_2_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_3_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_4_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_5_less__special_I2_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y: int] :
( ord_less(A,one_one(A),number_number_of(A,Y))
<=> ord_less(int,bit1(pls),Y) ) ) ).
tff(fact_6_less__special_I4_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [X: int] :
( ord_less(A,number_number_of(A,X),one_one(A))
<=> ord_less(int,X,bit1(pls)) ) ) ).
tff(fact_7_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_8_numeral__1__eq__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_9_add__Bit0__Bit1,axiom,
! [L1: int,K: int] : plus_plus(int,bit0(K),bit1(L1)) = bit1(plus_plus(int,K,L1)) ).
tff(fact_10_add__Bit1__Bit0,axiom,
! [L1: int,K: int] : plus_plus(int,bit1(K),bit0(L1)) = bit1(plus_plus(int,K,L1)) ).
tff(fact_11_rel__simps_I4_J,axiom,
! [K3: int] :
( ord_less(int,pls,bit0(K3))
<=> ord_less(int,pls,K3) ) ).
tff(fact_12_rel__simps_I10_J,axiom,
! [K3: int] :
( ord_less(int,bit0(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_13_rel__simps_I16_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit1(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_14_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_15_rel__simps_I51_J,axiom,
! [L: int,K3: int] :
( ( bit1(K3) = bit1(L) )
<=> ( K3 = L ) ) ).
tff(fact_16_rel__simps_I48_J,axiom,
! [L: int,K3: int] :
( ( bit0(K3) = bit0(L) )
<=> ( K3 = L ) ) ).
tff(fact_17_rel__simps_I46_J,axiom,
! [K: int] : bit1(K) != pls ).
tff(fact_18_rel__simps_I39_J,axiom,
! [L1: int] : pls != bit1(L1) ).
tff(fact_19_rel__simps_I50_J,axiom,
! [L1: int,K: int] : bit1(K) != bit0(L1) ).
tff(fact_20_rel__simps_I49_J,axiom,
! [L1: int,K: int] : bit0(K) != bit1(L1) ).
tff(fact_21_rel__simps_I44_J,axiom,
! [K3: int] :
( ( bit0(K3) = pls )
<=> ( K3 = pls ) ) ).
tff(fact_22_rel__simps_I38_J,axiom,
! [L: int] :
( ( pls = bit0(L) )
<=> ( pls = L ) ) ).
tff(fact_23_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_24_rel__simps_I17_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit1(K3),bit1(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_25_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_26_rel__simps_I14_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit0(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_27_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_28_rel__simps_I19_J,axiom,
ord_less_eq(int,pls,pls) ).
tff(fact_29_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_30_mult__Pls,axiom,
! [W: int] : times_times(int,pls,W) = pls ).
tff(fact_31_mult__Bit0,axiom,
! [L1: int,K: int] : times_times(int,bit0(K),L1) = bit0(times_times(int,K,L1)) ).
tff(fact_32_add__Bit0__Bit0,axiom,
! [L1: int,K: int] : plus_plus(int,bit0(K),bit0(L1)) = bit0(plus_plus(int,K,L1)) ).
tff(fact_33_left__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& semiring(B) )
=> ! [V2: int,B1: B,A1: B] : times_times(B,plus_plus(B,A1,B1),number_number_of(B,V2)) = plus_plus(B,times_times(B,A1,number_number_of(B,V2)),times_times(B,B1,number_number_of(B,V2))) ) ).
tff(fact_34_right__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& semiring(B) )
=> ! [C: B,B1: B,V2: int] : times_times(B,number_number_of(B,V2),plus_plus(B,B1,C)) = plus_plus(B,times_times(B,number_number_of(B,V2),B1),times_times(B,number_number_of(B,V2),C)) ) ).
tff(fact_35_less__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y: int,X: int] :
( ord_less(A,number_number_of(A,X),number_number_of(A,Y))
<=> ord_less(int,X,Y) ) ) ).
tff(fact_36_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_37_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_38_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_39_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_40_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_41_rel__simps_I12_J,axiom,
! [K3: int] :
( ord_less(int,bit1(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_42_rel__simps_I22_J,axiom,
! [K3: int] :
( ord_less_eq(int,pls,bit1(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_43_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_44_rel__simps_I27_J,axiom,
! [K3: int] :
( ord_less_eq(int,bit0(K3),pls)
<=> ord_less_eq(int,K3,pls) ) ).
tff(fact_45_rel__simps_I21_J,axiom,
! [K3: int] :
( ord_less_eq(int,pls,bit0(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_46_rel__simps_I29_J,axiom,
! [K3: int] :
( ord_less_eq(int,bit1(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_47_rel__simps_I5_J,axiom,
! [K3: int] :
( ord_less(int,pls,bit1(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_48_rel__simps_I33_J,axiom,
! [L: int,K3: int] :
( ord_less_eq(int,bit1(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_49_rel__simps_I15_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit0(K3),bit1(L))
<=> ord_less_eq(int,K3,L) ) ).
tff(fact_50_zle__add1__eq__le,axiom,
! [Z1: int,W1: int] :
( ord_less(int,W1,plus_plus(int,Z1,one_one(int)))
<=> ord_less_eq(int,W1,Z1) ) ).
tff(fact_51_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_52_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_53_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_54_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_55_less__int__def,axiom,
! [W1: int,Z1: int] :
( ord_less(int,Z1,W1)
<=> ( ord_less_eq(int,Z1,W1)
& ( Z1 != W1 ) ) ) ).
tff(fact_56_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_57_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_58_le__number__of__eq__not__less,axiom,
! [A: $tType] :
( ( number(A)
& linorder(A) )
=> ! [W1: int,V: int] :
( ord_less_eq(A,number_number_of(A,V),number_number_of(A,W1))
<=> ~ ord_less(A,number_number_of(A,W1),number_number_of(A,V)) ) ) ).
tff(fact_59_number__of__is__id,axiom,
! [K: int] : number_number_of(int,K) = K ).
tff(fact_60_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_61_less__eq__int__code_I15_J,axiom,
! [K2: int,K1: int] :
( ord_less_eq(int,bit1(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_62_less__int__code_I14_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit0(K1),bit1(K2))
<=> ord_less_eq(int,K1,K2) ) ).
tff(fact_63_zless__imp__add1__zle,axiom,
! [Z: int,W: int] :
( ord_less(int,W,Z)
=> ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) ).
tff(fact_64_add1__zle__eq,axiom,
! [Z1: int,W1: int] :
( ord_less_eq(int,plus_plus(int,W1,one_one(int)),Z1)
<=> ord_less(int,W1,Z1) ) ).
tff(fact_65_less__int__code_I16_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit1(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_66_less__int__code_I13_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit0(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_67_add__Pls__right,axiom,
! [K: int] : plus_plus(int,K,pls) = K ).
tff(fact_68_add__Pls,axiom,
! [K: int] : plus_plus(int,pls,K) = K ).
tff(fact_69_Bit0__def,axiom,
! [K: int] : bit0(K) = plus_plus(int,K,K) ).
tff(fact_70_less__number__of__int__code,axiom,
! [L: int,K3: int] :
( ord_less(int,number_number_of(int,K3),number_number_of(int,L))
<=> ord_less(int,K3,L) ) ).
tff(fact_71_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_72_int__distrib_I1_J,axiom,
! [W: int,Z2: int,Z11: int] : times_times(int,plus_plus(int,Z11,Z2),W) = plus_plus(int,times_times(int,Z11,W),times_times(int,Z2,W)) ).
tff(fact_73_int__distrib_I2_J,axiom,
! [Z2: int,Z11: int,W: int] : times_times(int,W,plus_plus(int,Z11,Z2)) = plus_plus(int,times_times(int,W,Z11),times_times(int,W,Z2)) ).
tff(fact_74_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_75_add__numeral__0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : plus_plus(A,number_number_of(A,pls),A1) = A1 ) ).
tff(fact_76_add__numeral__0__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : plus_plus(A,A1,number_number_of(A,pls)) = A1 ) ).
tff(fact_77_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_78_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_79_less__int__code_I15_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_80_Bit1__def,axiom,
! [K: int] : bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K) ).
tff(fact_81_zless__add1__eq,axiom,
! [Z1: int,W1: int] :
( ord_less(int,W1,plus_plus(int,Z1,one_one(int)))
<=> ( ord_less(int,W1,Z1)
| ( W1 = Z1 ) ) ) ).
tff(fact_82_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_83_mult__numeral__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : times_times(A,number_number_of(A,bit1(pls)),A1) = A1 ) ).
tff(fact_84_mult__numeral__1__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : times_times(A,A1,number_number_of(A,bit1(pls))) = A1 ) ).
tff(fact_85_semiring__numeral__1__eq__1,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_86_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)) ).
tff(fact_87_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_88_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_89_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_90_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_91_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_92_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_93_add__nat__number__of,axiom,
! [V3: int,V2: int] :
( ( ord_less(int,V2,pls)
=> ( plus_plus(nat,number_number_of(nat,V2),number_number_of(nat,V3)) = number_number_of(nat,V3) ) )
& ( ~ ord_less(int,V2,pls)
=> ( ( ord_less(int,V3,pls)
=> ( plus_plus(nat,number_number_of(nat,V2),number_number_of(nat,V3)) = number_number_of(nat,V2) ) )
& ( ~ ord_less(int,V3,pls)
=> ( plus_plus(nat,number_number_of(nat,V2),number_number_of(nat,V3)) = number_number_of(nat,plus_plus(int,V2,V3)) ) ) ) ) ) ).
tff(fact_94_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_95_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_96_zprime__2,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))) ).
tff(fact_97_less__nat__number__of,axiom,
! [V1: int,V: int] :
( ord_less(nat,number_number_of(nat,V),number_number_of(nat,V1))
<=> ( ( ord_less(int,V,V1)
=> ord_less(int,pls,V1) )
& ord_less(int,V,V1) ) ) ).
%----Arities (12)
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___Orderings_Olinorder,axiom,
linorder(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___Int_Onumber,axiom,
number(int) ).
tff(arity_Nat_Onat___Int_Onumber__semiring,axiom,
number_semiring(nat) ).
tff(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat) ).
tff(arity_Nat_Onat___Rings_Osemiring,axiom,
semiring(nat) ).
tff(arity_Nat_Onat___Int_Onumber,axiom,
number(nat) ).
tff(arity_HOL_Obool___Orderings_Olinorder,axiom,
linorder(bool) ).
%----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(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
%------------------------------------------------------------------------------