TPTP Problem File: NUM961_5.p
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%------------------------------------------------------------------------------
% File : NUM961_5 : TPTP v9.0.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 86
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_86 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 147 ( 61 unt; 34 typ; 0 def)
% Number of atoms : 188 ( 61 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 94 ( 19 ~; 0 |; 14 &)
% ( 35 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 20 ( 12 >; 8 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 0 prp; 1-3 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 144 ( 126 !; 0 ?; 144 :)
% ( 18 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:24:01
%------------------------------------------------------------------------------
%----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 (31)
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_Rings_Olinordered__idom,type,
linordered_idom:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Olinordered__ab__group__add,type,
linord219039673up_add:
!>[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_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : A ).
tff(sy_c_IntPrimes_Ozcong,type,
zcong: ( int * int * int ) > $o ).
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_OMin,type,
min: 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_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_s1____,type,
s1: int ).
tff(sy_v_s____,type,
s: int ).
tff(sy_v_t____,type,
t: int ).
%----Relevant facts (97)
tff(fact_0__096s_A_060_061_A4_A_K_Am_A_L_A1_A_N_A1_096,axiom,
ord_less_eq(int,s,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))) ).
tff(fact_1_s0p,axiom,
( ord_less_eq(int,zero_zero(int),s)
& ord_less(int,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
& zcong(s1,s,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ).
tff(fact_2_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_3_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_4__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_5__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_6_p,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_7__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096,axiom,
zcong(power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),power_power(int,s1,number_number_of(nat,bit0(bit1(pls)))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_8_p0,axiom,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_9__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_10_power2__eq__square__number__of,axiom,
! [B: $tType] :
( ( monoid_mult(B)
& number(B) )
=> ! [W: int] : ( power_power(B,number_number_of(B,W),number_number_of(nat,bit0(bit1(pls)))) = times_times(B,number_number_of(B,W),number_number_of(B,W)) ) ) ).
tff(fact_11_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_12_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_13_add__special_I3_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [V: int] : ( plus_plus(A,number_number_of(A,V),one_one(A)) = number_number_of(A,plus_plus(int,V,bit1(pls))) ) ) ).
tff(fact_14_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_15_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_16_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_17_s1,axiom,
zcong(power_power(int,s1,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_18_mult__Bit1,axiom,
! [L1: int,K1: int] : ( times_times(int,bit1(K1),L1) = plus_plus(int,bit0(times_times(int,K1,L1)),L1) ) ).
tff(fact_19_numeral__1__eq__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_20_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_21_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_22_rel__simps_I51_J,axiom,
! [L: int,K: int] :
( ( bit1(K) = bit1(L) )
<=> ( K = L ) ) ).
tff(fact_23_rel__simps_I48_J,axiom,
! [L: int,K: int] :
( ( bit0(K) = bit0(L) )
<=> ( K = L ) ) ).
tff(fact_24_double__eq__0__iff,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A2: A] :
( ( plus_plus(A,A2,A2) = zero_zero(A) )
<=> ( A2 = zero_zero(A) ) ) ) ).
tff(fact_25_rel__simps_I46_J,axiom,
! [K1: int] : ( bit1(K1) != pls ) ).
tff(fact_26_rel__simps_I39_J,axiom,
! [L1: int] : ( pls != bit1(L1) ) ).
tff(fact_27_rel__simps_I50_J,axiom,
! [L1: int,K1: int] : ( bit1(K1) != bit0(L1) ) ).
tff(fact_28_rel__simps_I49_J,axiom,
! [L1: int,K1: int] : ( bit0(K1) != bit1(L1) ) ).
tff(fact_29_rel__simps_I44_J,axiom,
! [K: int] :
( ( bit0(K) = pls )
<=> ( K = pls ) ) ).
tff(fact_30_rel__simps_I38_J,axiom,
! [L: int] :
( ( pls = bit0(L) )
<=> ( pls = L ) ) ).
tff(fact_31_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_32_rel__simps_I17_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit1(K),bit1(L))
<=> ord_less(int,K,L) ) ).
tff(fact_33_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_34_rel__simps_I14_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit0(K),bit0(L))
<=> ord_less(int,K,L) ) ).
tff(fact_35_rel__simps_I34_J,axiom,
! [L: int,K: int] :
( ord_less_eq(int,bit1(K),bit1(L))
<=> ord_less_eq(int,K,L) ) ).
tff(fact_36_rel__simps_I19_J,axiom,
ord_less_eq(int,pls,pls) ).
tff(fact_37_rel__simps_I31_J,axiom,
! [L: int,K: int] :
( ord_less_eq(int,bit0(K),bit0(L))
<=> ord_less_eq(int,K,L) ) ).
tff(fact_38_mult__Pls,axiom,
! [W: int] : ( times_times(int,pls,W) = pls ) ).
tff(fact_39_mult__Bit0,axiom,
! [L1: int,K1: int] : ( times_times(int,bit0(K1),L1) = bit0(times_times(int,K1,L1)) ) ).
tff(fact_40_add__Bit0__Bit0,axiom,
! [L1: int,K1: int] : ( plus_plus(int,bit0(K1),bit0(L1)) = bit0(plus_plus(int,K1,L1)) ) ).
tff(fact_41_diff__bin__simps_I7_J,axiom,
! [L1: int,K1: int] : ( minus_minus(int,bit0(K1),bit0(L1)) = bit0(minus_minus(int,K1,L1)) ) ).
tff(fact_42_rel__simps_I47_J,axiom,
! [K: int] :
( ( bit1(K) = min )
<=> ( K = min ) ) ).
tff(fact_43_rel__simps_I43_J,axiom,
! [L: int] :
( ( min = bit1(L) )
<=> ( min = L ) ) ).
tff(fact_44_Bit1__Min,axiom,
bit1(min) = min ).
tff(fact_45_rel__simps_I37_J,axiom,
pls != min ).
tff(fact_46_rel__simps_I40_J,axiom,
min != pls ).
tff(fact_47_rel__simps_I45_J,axiom,
! [K1: int] : ( bit0(K1) != min ) ).
tff(fact_48_rel__simps_I42_J,axiom,
! [L1: int] : ( min != bit0(L1) ) ).
tff(fact_49_rel__simps_I7_J,axiom,
~ ord_less(int,min,min) ).
tff(fact_50_rel__simps_I24_J,axiom,
ord_less_eq(int,min,min) ).
tff(fact_51_left__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& semiring(B) )
=> ! [V: int,B1: B,A1: B] : ( times_times(B,plus_plus(B,A1,B1),number_number_of(B,V)) = plus_plus(B,times_times(B,A1,number_number_of(B,V)),times_times(B,B1,number_number_of(B,V))) ) ) ).
tff(fact_52_right__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& semiring(B) )
=> ! [C: B,B1: B,V: int] : ( times_times(B,number_number_of(B,V),plus_plus(B,B1,C)) = plus_plus(B,times_times(B,number_number_of(B,V),B1),times_times(B,number_number_of(B,V),C)) ) ) ).
tff(fact_53_number__of__Pls,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_54_left__diff__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& ring(B) )
=> ! [V: int,B1: B,A1: B] : ( times_times(B,minus_minus(B,A1,B1),number_number_of(B,V)) = minus_minus(B,times_times(B,A1,number_number_of(B,V)),times_times(B,B1,number_number_of(B,V))) ) ) ).
tff(fact_55_right__diff__distrib__number__of,axiom,
! [B: $tType] :
( ( number(B)
& ring(B) )
=> ! [C: B,B1: B,V: int] : ( times_times(B,number_number_of(B,V),minus_minus(B,B1,C)) = minus_minus(B,times_times(B,number_number_of(B,V),B1),times_times(B,number_number_of(B,V),C)) ) ) ).
tff(fact_56_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_57_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_58_mult__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A,W: int,V: int] : ( times_times(A,number_number_of(A,V),times_times(A,number_number_of(A,W),Z)) = times_times(A,number_number_of(A,times_times(int,V,W)),Z) ) ) ).
tff(fact_59_arith__simps_I32_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V: int] : ( times_times(A,number_number_of(A,V),number_number_of(A,W)) = number_number_of(A,times_times(int,V,W)) ) ) ).
tff(fact_60_add__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A,W: int,V: int] : ( plus_plus(A,number_number_of(A,V),plus_plus(A,number_number_of(A,W),Z)) = plus_plus(A,number_number_of(A,plus_plus(int,V,W)),Z) ) ) ).
tff(fact_61_add__number__of__eq,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V: int] : ( plus_plus(A,number_number_of(A,V),number_number_of(A,W)) = number_number_of(A,plus_plus(int,V,W)) ) ) ).
tff(fact_62_rel__simps_I12_J,axiom,
! [K: int] :
( ord_less(int,bit1(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_63_rel__simps_I16_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit1(K),bit0(L))
<=> ord_less(int,K,L) ) ).
tff(fact_64_rel__simps_I10_J,axiom,
! [K: int] :
( ord_less(int,bit0(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_65_rel__simps_I4_J,axiom,
! [K: int] :
( ord_less(int,pls,bit0(K))
<=> ord_less(int,pls,K) ) ).
tff(fact_66_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat) ).
tff(fact_67_rel__simps_I22_J,axiom,
! [K: int] :
( ord_less_eq(int,pls,bit1(K))
<=> ord_less_eq(int,pls,K) ) ).
tff(fact_68_rel__simps_I32_J,axiom,
! [L: int,K: int] :
( ord_less_eq(int,bit0(K),bit1(L))
<=> ord_less_eq(int,K,L) ) ).
tff(fact_69_rel__simps_I27_J,axiom,
! [K: int] :
( ord_less_eq(int,bit0(K),pls)
<=> ord_less_eq(int,K,pls) ) ).
tff(fact_70_rel__simps_I21_J,axiom,
! [K: int] :
( ord_less_eq(int,pls,bit0(K))
<=> ord_less_eq(int,pls,K) ) ).
tff(fact_71_add__Bit1__Bit0,axiom,
! [L1: int,K1: int] : ( plus_plus(int,bit1(K1),bit0(L1)) = bit1(plus_plus(int,K1,L1)) ) ).
tff(fact_72_add__Bit0__Bit1,axiom,
! [L1: int,K1: int] : ( plus_plus(int,bit0(K1),bit1(L1)) = bit1(plus_plus(int,K1,L1)) ) ).
tff(fact_73_le__nat__number__of,axiom,
! [V3: int,V2: int] :
( ord_less_eq(nat,number_number_of(nat,V2),number_number_of(nat,V3))
<=> ( ~ ord_less_eq(int,V2,V3)
=> ord_less_eq(int,V2,pls) ) ) ).
tff(fact_74_diff__bin__simps_I10_J,axiom,
! [L1: int,K1: int] : ( minus_minus(int,bit1(K1),bit1(L1)) = bit0(minus_minus(int,K1,L1)) ) ).
tff(fact_75_diff__bin__simps_I9_J,axiom,
! [L1: int,K1: int] : ( minus_minus(int,bit1(K1),bit0(L1)) = bit1(minus_minus(int,K1,L1)) ) ).
tff(fact_76_diff__bin__simps_I3_J,axiom,
! [L1: int] : ( minus_minus(int,pls,bit0(L1)) = bit0(minus_minus(int,pls,L1)) ) ).
tff(fact_77__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
minus_minus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min)) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) ).
tff(fact_78_rel__simps_I13_J,axiom,
! [K: int] :
( ord_less(int,bit1(K),min)
<=> ord_less(int,K,min) ) ).
tff(fact_79_rel__simps_I9_J,axiom,
! [K: int] :
( ord_less(int,min,bit1(K))
<=> ord_less(int,min,K) ) ).
tff(fact_80_rel__simps_I3_J,axiom,
~ ord_less(int,pls,min) ).
tff(fact_81_rel__simps_I6_J,axiom,
ord_less(int,min,pls) ).
tff(fact_82_rel__simps_I8_J,axiom,
! [K: int] :
( ord_less(int,min,bit0(K))
<=> ord_less(int,min,K) ) ).
tff(fact_83_rel__simps_I30_J,axiom,
! [K: int] :
( ord_less_eq(int,bit1(K),min)
<=> ord_less_eq(int,K,min) ) ).
tff(fact_84_rel__simps_I26_J,axiom,
! [K: int] :
( ord_less_eq(int,min,bit1(K))
<=> ord_less_eq(int,min,K) ) ).
tff(fact_85_rel__simps_I20_J,axiom,
~ ord_less_eq(int,pls,min) ).
tff(fact_86_rel__simps_I23_J,axiom,
ord_less_eq(int,min,pls) ).
tff(fact_87_rel__simps_I28_J,axiom,
! [K: int] :
( ord_less_eq(int,bit0(K),min)
<=> ord_less_eq(int,K,min) ) ).
tff(fact_88__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_89__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_90_s,axiom,
zcong(power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),number_number_of(int,min),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_91_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_92_rel__simps_I29_J,axiom,
! [K: int] :
( ord_less_eq(int,bit1(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_93_rel__simps_I5_J,axiom,
! [K: int] :
( ord_less(int,pls,bit1(K))
<=> ord_less_eq(int,pls,K) ) ).
tff(fact_94_rel__simps_I33_J,axiom,
! [L: int,K: int] :
( ord_less_eq(int,bit1(K),bit0(L))
<=> ord_less(int,K,L) ) ).
tff(fact_95_rel__simps_I15_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit0(K),bit1(L))
<=> ord_less_eq(int,K,L) ) ).
tff(fact_96_add__nat__number__of,axiom,
! [V1: int,V: int] :
( ( ord_less(int,V,pls)
=> ( plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V1)) = number_number_of(nat,V1) ) )
& ( ~ ord_less(int,V,pls)
=> ( ( ord_less(int,V1,pls)
=> ( plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V1)) = number_number_of(nat,V) ) )
& ( ~ ord_less(int,V1,pls)
=> ( plus_plus(nat,number_number_of(nat,V),number_number_of(nat,V1)) = number_number_of(nat,plus_plus(int,V,V1)) ) ) ) ) ) ).
%----Arities (13)
tff(arity_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
linord219039673up_add(int) ).
tff(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(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___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) ).
%----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,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),power_power(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)),number_number_of(nat,bit0(bit1(pls))))) ).
%------------------------------------------------------------------------------