TPTP Problem File: NUM959_5.p
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%------------------------------------------------------------------------------
% File : NUM959_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 84
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_84 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 147 ( 56 unt; 31 typ; 0 def)
% Number of atoms : 206 ( 61 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 104 ( 14 ~; 1 |; 16 &)
% ( 43 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 18 ( 12 >; 6 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 0 prp; 1-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 180 ( 163 !; 0 ?; 180 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:23:56
%------------------------------------------------------------------------------
%----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 (28)
tff(sy_cl_Int_Onumber,type,
number:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Oring,type,
ring:
!>[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_Rings_Osemiring__1,type,
semiring_1:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Omonoid__mult,type,
monoid_mult:
!>[A: $tType] : $o ).
tff(sy_cl_Orderings_Olinorder,type,
linorder:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Olinordered__idom,type,
linordered_idom:
!>[A: $tType] : $o ).
tff(sy_c_Groups_Ominus__class_Ominus,type,
minus_minus:
!>[A: $tType] : ( ( A * A ) > A ) ).
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_Power_Opower__class_Opower,type,
power_power:
!>[A: $tType] : ( ( A * nat ) > A ) ).
tff(sy_c_TwoSquares__Mirabelle__poiayhyqls_Ois__sum2sq,type,
twoSqu1567020053sum2sq: int > $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 ).
tff(sy_v_s____,type,
s: int ).
tff(sy_v_t____,type,
t: int ).
%----Relevant facts (98)
tff(fact_0_t,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) ).
tff(fact_1__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [T: int] : plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) != times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),T) ).
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__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_061_As_A_094_A2_A_L_A1_096,axiom,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) ).
tff(fact_4_power2__eq__square__number__of,axiom,
! [B: $tType] :
( ( monoid_mult(B)
& number(B) )
=> ! [W1: int] : power_power(B,number_number_of(B,W1),number_number_of(nat,bit0(bit1(pls)))) = times_times(B,number_number_of(B,W1),number_number_of(B,W1)) ) ).
tff(fact_5_one__power2,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( power_power(A,one_one(A),number_number_of(nat,bit0(bit1(pls)))) = one_one(A) ) ) ).
tff(fact_6_add__special_I2_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W1: int] : plus_plus(A,one_one(A),number_number_of(A,W1)) = number_number_of(A,plus_plus(int,bit1(pls),W1)) ) ).
tff(fact_7_add__special_I3_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [V1: int] : plus_plus(A,number_number_of(A,V1),one_one(A)) = number_number_of(A,plus_plus(int,V1,bit1(pls))) ) ).
tff(fact_8_le__special_I2_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y1: int] :
( ord_less_eq(A,one_one(A),number_number_of(A,Y1))
<=> ord_less_eq(int,bit1(pls),Y1) ) ) ).
tff(fact_9_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_10_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_11_calculation,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int))) ).
tff(fact_12_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_13_numeral__1__eq__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_14_zdiff__power2,axiom,
! [B1: int,A1: int] : power_power(int,minus_minus(int,A1,B1),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,minus_minus(int,power_power(int,A1,number_number_of(nat,bit0(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit0(bit1(pls))),A1),B1)),power_power(int,B1,number_number_of(nat,bit0(bit1(pls))))) ).
tff(fact_15_eq__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& ring_char_0(A) )
=> ! [Y1: int,X: int] :
( ( number_number_of(A,X) = number_number_of(A,Y1) )
<=> ( X = Y1 ) ) ) ).
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__096_126_At_A_060_A4_A_K_Am_A_L_A1_096,axiom,
~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
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_I17_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit1(K3),bit1(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_27_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_28_rel__simps_I14_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit0(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_29_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_30_rel__simps_I19_J,axiom,
ord_less_eq(int,pls,pls) ).
tff(fact_31_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_32_mult__Pls,axiom,
! [W1: int] : times_times(int,pls,W1) = pls ).
tff(fact_33_mult__Bit0,axiom,
! [L1: int,K: int] : times_times(int,bit0(K),L1) = bit0(times_times(int,K,L1)) ).
tff(fact_34_add__Bit0__Bit0,axiom,
! [L1: int,K: int] : plus_plus(int,bit0(K),bit0(L1)) = bit0(plus_plus(int,K,L1)) ).
tff(fact_35_diff__bin__simps_I7_J,axiom,
! [L1: int,K: int] : minus_minus(int,bit0(K),bit0(L1)) = bit0(minus_minus(int,K,L1)) ).
tff(fact_36_left__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& semiring(B) )
=> ! [V1: int,B1: B,A1: B] : times_times(B,plus_plus(B,A1,B1),number_number_of(B,V1)) = plus_plus(B,times_times(B,A1,number_number_of(B,V1)),times_times(B,B1,number_number_of(B,V1))) ) ).
tff(fact_37_right__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& semiring(B) )
=> ! [C: B,B1: B,V1: int] : times_times(B,number_number_of(B,V1),plus_plus(B,B1,C)) = plus_plus(B,times_times(B,number_number_of(B,V1),B1),times_times(B,number_number_of(B,V1),C)) ) ).
tff(fact_38_left__diff__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& ring(B) )
=> ! [V1: int,B1: B,A1: B] : times_times(B,minus_minus(B,A1,B1),number_number_of(B,V1)) = minus_minus(B,times_times(B,A1,number_number_of(B,V1)),times_times(B,B1,number_number_of(B,V1))) ) ).
tff(fact_39_right__diff__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& ring(B) )
=> ! [C: B,B1: B,V1: int] : times_times(B,number_number_of(B,V1),minus_minus(B,B1,C)) = minus_minus(B,times_times(B,number_number_of(B,V1),B1),times_times(B,number_number_of(B,V1),C)) ) ).
tff(fact_40_less__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y1: int,X: int] :
( ord_less(A,number_number_of(A,X),number_number_of(A,Y1))
<=> ord_less(int,X,Y1) ) ) ).
tff(fact_41_le__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y1: int,X: int] :
( ord_less_eq(A,number_number_of(A,X),number_number_of(A,Y1))
<=> ord_less_eq(int,X,Y1) ) ) ).
tff(fact_42_mult__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z1: A,W1: int,V1: int] : times_times(A,number_number_of(A,V1),times_times(A,number_number_of(A,W1),Z1)) = times_times(A,number_number_of(A,times_times(int,V1,W1)),Z1) ) ).
tff(fact_43_arith__simps_I32_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W1: int,V1: int] : times_times(A,number_number_of(A,V1),number_number_of(A,W1)) = number_number_of(A,times_times(int,V1,W1)) ) ).
tff(fact_44_add__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z1: A,W1: int,V1: int] : plus_plus(A,number_number_of(A,V1),plus_plus(A,number_number_of(A,W1),Z1)) = plus_plus(A,number_number_of(A,plus_plus(int,V1,W1)),Z1) ) ).
tff(fact_45_add__number__of__eq,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W1: int,V1: int] : plus_plus(A,number_number_of(A,V1),number_number_of(A,W1)) = number_number_of(A,plus_plus(int,V1,W1)) ) ).
tff(fact_46_rel__simps_I12_J,axiom,
! [K3: int] :
( ord_less(int,bit1(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_47_rel__simps_I16_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit1(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_48_rel__simps_I10_J,axiom,
! [K3: int] :
( ord_less(int,bit0(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_49_rel__simps_I4_J,axiom,
! [K3: int] :
( ord_less(int,pls,bit0(K3))
<=> ord_less(int,pls,K3) ) ).
tff(fact_50_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat) ).
tff(fact_51_rel__simps_I22_J,axiom,
! [K3: int] :
( ord_less_eq(int,pls,bit1(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_52_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_53_rel__simps_I27_J,axiom,
! [K3: int] :
( ord_less_eq(int,bit0(K3),pls)
<=> ord_less_eq(int,K3,pls) ) ).
tff(fact_54_rel__simps_I21_J,axiom,
! [K3: int] :
( ord_less_eq(int,pls,bit0(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_55_add__Bit1__Bit0,axiom,
! [L1: int,K: int] : plus_plus(int,bit1(K),bit0(L1)) = bit1(plus_plus(int,K,L1)) ).
tff(fact_56_add__Bit0__Bit1,axiom,
! [L1: int,K: int] : plus_plus(int,bit0(K),bit1(L1)) = bit1(plus_plus(int,K,L1)) ).
tff(fact_57_le__nat__number__of,axiom,
! [V3: int,V: int] :
( ord_less_eq(nat,number_number_of(nat,V),number_number_of(nat,V3))
<=> ( ~ ord_less_eq(int,V,V3)
=> ord_less_eq(int,V,pls) ) ) ).
tff(fact_58_diff__bin__simps_I10_J,axiom,
! [L1: int,K: int] : minus_minus(int,bit1(K),bit1(L1)) = bit0(minus_minus(int,K,L1)) ).
tff(fact_59_diff__bin__simps_I9_J,axiom,
! [L1: int,K: int] : minus_minus(int,bit1(K),bit0(L1)) = bit1(minus_minus(int,K,L1)) ).
tff(fact_60_diff__bin__simps_I3_J,axiom,
! [L1: int] : minus_minus(int,pls,bit0(L1)) = bit0(minus_minus(int,pls,L1)) ).
tff(fact_61__096_I4_A_K_Am_A_L_A1_J_A_K_A_I4_A_K_Am_A_L_A1_A_N_A1_J_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ).
tff(fact_62__0964_A_K_Am_A_L_A1_A_N_A1_A_060_At_096,axiom,
ord_less(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),t) ).
tff(fact_63_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_64_rel__simps_I29_J,axiom,
! [K3: int] :
( ord_less_eq(int,bit1(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_65_rel__simps_I5_J,axiom,
! [K3: int] :
( ord_less(int,pls,bit1(K3))
<=> ord_less_eq(int,pls,K3) ) ).
tff(fact_66_rel__simps_I33_J,axiom,
! [L: int,K3: int] :
( ord_less_eq(int,bit1(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_67_rel__simps_I15_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit0(K3),bit1(L))
<=> ord_less_eq(int,K3,L) ) ).
tff(fact_68_add__nat__number__of,axiom,
! [V2: int,V1: int] :
( ( ord_less(int,V1,pls)
=> ( plus_plus(nat,number_number_of(nat,V1),number_number_of(nat,V2)) = number_number_of(nat,V2) ) )
& ( ~ ord_less(int,V1,pls)
=> ( ( ord_less(int,V2,pls)
=> ( plus_plus(nat,number_number_of(nat,V1),number_number_of(nat,V2)) = number_number_of(nat,V1) ) )
& ( ~ ord_less(int,V2,pls)
=> ( plus_plus(nat,number_number_of(nat,V1),number_number_of(nat,V2)) = number_number_of(nat,plus_plus(int,V1,V2)) ) ) ) ) ) ).
tff(fact_69_zle__add1__eq__le,axiom,
! [Z: int,W: int] :
( ord_less(int,W,plus_plus(int,Z,one_one(int)))
<=> ord_less_eq(int,W,Z) ) ).
tff(fact_70_zle__diff1__eq,axiom,
! [Z: int,W: int] :
( ord_less_eq(int,W,minus_minus(int,Z,one_one(int)))
<=> ord_less(int,W,Z) ) ).
tff(fact_71_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_72_less__special_I2_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y1: int] :
( ord_less(A,one_one(A),number_number_of(A,Y1))
<=> ord_less(int,bit1(pls),Y1) ) ) ).
tff(fact_73_qf1pt,axiom,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ).
tff(fact_74_less__int__code_I16_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit1(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_75_less__int__code_I13_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit0(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_76_less__int__def,axiom,
! [W: int,Z: int] :
( ord_less(int,Z,W)
<=> ( ord_less_eq(int,Z,W)
& ( Z != W ) ) ) ).
tff(fact_77_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_78_zpower__zpower,axiom,
! [Z1: nat,Y: nat,X1: int] : power_power(int,power_power(int,X1,Y),Z1) = power_power(int,X1,times_times(nat,Y,Z1)) ).
tff(fact_79_le__number__of__eq__not__less,axiom,
! [A: $tType] :
( ( number(A)
& linorder(A) )
=> ! [W: int,V: int] :
( ord_less_eq(A,number_number_of(A,V),number_number_of(A,W))
<=> ~ ord_less(A,number_number_of(A,W),number_number_of(A,V)) ) ) ).
tff(fact_80_less__int__code_I15_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_81_zless__add1__eq,axiom,
! [Z: int,W: int] :
( ord_less(int,W,plus_plus(int,Z,one_one(int)))
<=> ( ord_less(int,W,Z)
| ( W = Z ) ) ) ).
tff(fact_82_nat__mult__2,axiom,
! [Z1: nat] : times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z1) = plus_plus(nat,Z1,Z1) ).
tff(fact_83_nat__mult__2__right,axiom,
! [Z1: nat] : times_times(nat,Z1,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,Z1,Z1) ).
tff(fact_84_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_85_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_86_Numeral1__eq1__nat,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)) ).
tff(fact_87_zless__imp__add1__zle,axiom,
! [Z1: int,W1: int] :
( ord_less(int,W1,Z1)
=> ord_less_eq(int,plus_plus(int,W1,one_one(int)),Z1) ) ).
tff(fact_88_add1__zle__eq,axiom,
! [Z: int,W: int] :
( ord_less_eq(int,plus_plus(int,W,one_one(int)),Z)
<=> ord_less(int,W,Z) ) ).
tff(fact_89_zprime__2,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))) ).
tff(fact_90_number__of__reorient,axiom,
! [A: $tType] :
( number(A)
=> ! [X: A,W: int] :
( ( number_number_of(A,W) = X )
<=> ( X = number_number_of(A,W) ) ) ) ).
tff(fact_91_number__of__is__id,axiom,
! [K: int] : number_number_of(int,K) = K ).
tff(fact_92_power__even__eq,axiom,
! [A: $tType] :
( monoid_mult(A)
=> ! [N: nat,A1: A] : power_power(A,A1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)) = power_power(A,power_power(A,A1,N),number_number_of(nat,bit0(bit1(pls)))) ) ).
tff(fact_93_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_94_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_95_add__Pls__right,axiom,
! [K: int] : plus_plus(int,K,pls) = K ).
tff(fact_96_add__Pls,axiom,
! [K: int] : plus_plus(int,pls,K) = K ).
tff(fact_97_Bit0__def,axiom,
! [K: int] : bit0(K) = plus_plus(int,K,K) ).
%----Arities (15)
tff(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int) ).
tff(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int) ).
tff(arity_Int_Oint___Groups_Omonoid__mult,axiom,
monoid_mult(int) ).
tff(arity_Int_Oint___Rings_Osemiring__1,axiom,
semiring_1(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___Rings_Oring,axiom,
ring(int) ).
tff(arity_Int_Oint___Int_Onumber,axiom,
number(int) ).
tff(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat) ).
tff(arity_Nat_Onat___Groups_Omonoid__mult,axiom,
monoid_mult(nat) ).
tff(arity_Nat_Onat___Rings_Osemiring__1,axiom,
semiring_1(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_eq(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),plus_plus(int,minus_minus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),number_number_of(int,bit0(bit1(pls))))) ).
%------------------------------------------------------------------------------