TPTP Problem File: NUN013_5.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : NUN013_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 195
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_195 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 150 ( 60 unt; 35 typ; 0 def)
% Number of atoms : 191 ( 88 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 86 ( 10 ~; 1 |; 11 &)
% ( 20 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 16 ( 11 >; 5 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 0 prp; 1-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-3 aty)
% Number of variables : 194 ( 176 !; 2 ?; 194 :)
% ( 16 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:26:29
%------------------------------------------------------------------------------
%----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 (32)
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_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_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_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_m1____,type,
m1: int ).
tff(sy_v_r____,type,
r: int ).
tff(sy_v_s____,type,
s: int ).
tff(sy_v_sa____,type,
sa: int ).
tff(sy_v_t____,type,
t: int ).
tff(sy_v_v____,type,
v: int ).
tff(sy_v_w____,type,
w: int ).
%----Relevant facts (98)
tff(fact_0__096_Ir_A_K_Av_A_L_As_A_K_Aw_A_L_Am1_J_A_094_A2_A_L_A_Ir_A_K_Aw_A_N_As_A_K_Av_J_A_094_A2_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_Am1_096,axiom,
plus_plus(int,power_power(int,plus_plus(int,plus_plus(int,times_times(int,r,v),times_times(int,sa,w)),m1),number_number_of(nat,bit0(bit1(pls)))),power_power(int,minus_minus(int,times_times(int,r,w),times_times(int,sa,v)),number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),m1) ).
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_is__mult__sum2sq,axiom,
! [Y: int,X: int] :
( twoSqu1567020053sum2sq(X)
=> ( twoSqu1567020053sum2sq(Y)
=> twoSqu1567020053sum2sq(times_times(int,X,Y)) ) ) ).
tff(fact_3_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_4_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_5_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_6_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_7_mult__Bit1,axiom,
! [L1: int,K3: int] : times_times(int,bit1(K3),L1) = plus_plus(int,bit0(times_times(int,K3,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,K3: int] : plus_plus(int,bit0(K3),bit1(L1)) = bit1(plus_plus(int,K3,L1)) ).
tff(fact_10_add__Bit1__Bit0,axiom,
! [L1: int,K3: int] : plus_plus(int,bit1(K3),bit0(L1)) = bit1(plus_plus(int,K3,L1)) ).
tff(fact_11_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_12_add__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z1: A,W: int,V: int] : plus_plus(A,number_number_of(A,V),plus_plus(A,number_number_of(A,W),Z1)) = plus_plus(A,number_number_of(A,plus_plus(int,V,W)),Z1) ) ).
tff(fact_13_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_14_mult__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z1: A,W: int,V: int] : times_times(A,number_number_of(A,V),times_times(A,number_number_of(A,W),Z1)) = times_times(A,number_number_of(A,times_times(int,V,W)),Z1) ) ).
tff(fact_15_eq__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& ring_char_0(A) )
=> ! [Ya: int,Xa: int] :
( ( number_number_of(A,Xa) = number_number_of(A,Ya) )
<=> ( Xa = Ya ) ) ) ).
tff(fact_16_rel__simps_I51_J,axiom,
! [L: int,K: int] :
( ( bit1(K) = bit1(L) )
<=> ( K = L ) ) ).
tff(fact_17_rel__simps_I48_J,axiom,
! [L: int,K: int] :
( ( bit0(K) = bit0(L) )
<=> ( K = L ) ) ).
tff(fact_18_rel__simps_I46_J,axiom,
! [K3: int] : bit1(K3) != pls ).
tff(fact_19_rel__simps_I39_J,axiom,
! [L1: int] : pls != bit1(L1) ).
tff(fact_20_rel__simps_I50_J,axiom,
! [L1: int,K3: int] : bit1(K3) != bit0(L1) ).
tff(fact_21_rel__simps_I49_J,axiom,
! [L1: int,K3: int] : bit0(K3) != bit1(L1) ).
tff(fact_22_rel__simps_I44_J,axiom,
! [K: int] :
( ( bit0(K) = pls )
<=> ( K = pls ) ) ).
tff(fact_23_rel__simps_I38_J,axiom,
! [L: int] :
( ( pls = bit0(L) )
<=> ( pls = L ) ) ).
tff(fact_24_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_25_mult__Pls,axiom,
! [W: int] : times_times(int,pls,W) = pls ).
tff(fact_26_mult__Bit0,axiom,
! [L1: int,K3: int] : times_times(int,bit0(K3),L1) = bit0(times_times(int,K3,L1)) ).
tff(fact_27_add__Bit0__Bit0,axiom,
! [L1: int,K3: int] : plus_plus(int,bit0(K3),bit0(L1)) = bit0(plus_plus(int,K3,L1)) ).
tff(fact_28_diff__bin__simps_I7_J,axiom,
! [L1: int,K3: int] : minus_minus(int,bit0(K3),bit0(L1)) = bit0(minus_minus(int,K3,L1)) ).
tff(fact_29_left__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& semiring(B1) )
=> ! [V: int,B: B1,A1: B1] : times_times(B1,plus_plus(B1,A1,B),number_number_of(B1,V)) = plus_plus(B1,times_times(B1,A1,number_number_of(B1,V)),times_times(B1,B,number_number_of(B1,V))) ) ).
tff(fact_30_right__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& semiring(B1) )
=> ! [C: B1,B: B1,V: int] : times_times(B1,number_number_of(B1,V),plus_plus(B1,B,C)) = plus_plus(B1,times_times(B1,number_number_of(B1,V),B),times_times(B1,number_number_of(B1,V),C)) ) ).
tff(fact_31_left__diff__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& ring(B1) )
=> ! [V: int,B: B1,A1: B1] : times_times(B1,minus_minus(B1,A1,B),number_number_of(B1,V)) = minus_minus(B1,times_times(B1,A1,number_number_of(B1,V)),times_times(B1,B,number_number_of(B1,V))) ) ).
tff(fact_32_right__diff__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& ring(B1) )
=> ! [C: B1,B: B1,V: int] : times_times(B1,number_number_of(B1,V),minus_minus(B1,B,C)) = minus_minus(B1,times_times(B1,number_number_of(B1,V),B),times_times(B1,number_number_of(B1,V),C)) ) ).
tff(fact_33_t1,axiom,
ord_less(int,one_one(int),t) ).
tff(fact_34_diff__bin__simps_I10_J,axiom,
! [L1: int,K3: int] : minus_minus(int,bit1(K3),bit1(L1)) = bit0(minus_minus(int,K3,L1)) ).
tff(fact_35_diff__bin__simps_I9_J,axiom,
! [L1: int,K3: int] : minus_minus(int,bit1(K3),bit0(L1)) = bit1(minus_minus(int,K3,L1)) ).
tff(fact_36_diff__bin__simps_I3_J,axiom,
! [L1: int] : minus_minus(int,pls,bit0(L1)) = bit0(minus_minus(int,pls,L1)) ).
tff(fact_37_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_38_calculation_I2_J,axiom,
( ( t = one_one(int) )
=> ? [X1: int,Y1: int] : plus_plus(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y1,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_39_zpower__zpower,axiom,
! [Z1: nat,Y: nat,X: int] : power_power(int,power_power(int,X,Y),Z1) = power_power(int,X,times_times(nat,Y,Z1)) ).
tff(fact_40_number__of__diff,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V: int] : number_number_of(A,minus_minus(int,V,W)) = minus_minus(A,number_number_of(A,V),number_number_of(A,W)) ) ).
tff(fact_41_diff__bin__simps_I1_J,axiom,
! [K3: int] : minus_minus(int,K3,pls) = K3 ).
tff(fact_42_int__distrib_I3_J,axiom,
! [W: int,Z2: int,Z11: int] : times_times(int,minus_minus(int,Z11,Z2),W) = minus_minus(int,times_times(int,Z11,W),times_times(int,Z2,W)) ).
tff(fact_43_int__distrib_I4_J,axiom,
! [Z2: int,Z11: int,W: int] : times_times(int,W,minus_minus(int,Z11,Z2)) = minus_minus(int,times_times(int,W,Z11),times_times(int,W,Z2)) ).
tff(fact_44_number__of__reorient,axiom,
! [A: $tType] :
( number(A)
=> ! [Xa: A,Wa: int] :
( ( number_number_of(A,Wa) = Xa )
<=> ( Xa = number_number_of(A,Wa) ) ) ) ).
tff(fact_45_number__of__is__id,axiom,
! [K3: int] : number_number_of(int,K3) = K3 ).
tff(fact_46_add__number__of__diff1,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [C: A,W: int,V: int] : plus_plus(A,number_number_of(A,V),minus_minus(A,number_number_of(A,W),C)) = minus_minus(A,number_number_of(A,plus_plus(int,V,W)),C) ) ).
tff(fact_47_add__Pls__right,axiom,
! [K3: int] : plus_plus(int,K3,pls) = K3 ).
tff(fact_48_add__Pls,axiom,
! [K3: int] : plus_plus(int,pls,K3) = K3 ).
tff(fact_49_Bit0__def,axiom,
! [K3: int] : bit0(K3) = plus_plus(int,K3,K3) ).
tff(fact_50_times__numeral__code_I5_J,axiom,
! [W: int,V: int] : times_times(int,number_number_of(int,V),number_number_of(int,W)) = number_number_of(int,times_times(int,V,W)) ).
tff(fact_51_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_52_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_53_plus__numeral__code_I9_J,axiom,
! [W: int,V: int] : plus_plus(int,number_number_of(int,V),number_number_of(int,W)) = number_number_of(int,plus_plus(int,V,W)) ).
tff(fact_54_add__numeral__0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : plus_plus(A,number_number_of(A,pls),A1) = A1 ) ).
tff(fact_55_add__numeral__0__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : plus_plus(A,A1,number_number_of(A,pls)) = A1 ) ).
tff(fact_56_number__of__mult,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V: int] : number_number_of(A,times_times(int,V,W)) = times_times(A,number_number_of(A,V),number_number_of(A,W)) ) ).
tff(fact_57_number__of__add,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int,V: int] : number_number_of(A,plus_plus(int,V,W)) = plus_plus(A,number_number_of(A,V),number_number_of(A,W)) ) ).
tff(fact_58_Bit1__def,axiom,
! [K3: int] : bit1(K3) = plus_plus(int,plus_plus(int,one_one(int),K3),K3) ).
tff(fact_59_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_60_mult__numeral__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : times_times(A,number_number_of(A,bit1(pls)),A1) = A1 ) ).
tff(fact_61_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_62_semiring__numeral__1__eq__1,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_63_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)) ).
tff(fact_64_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_65_semiring__mult__2,axiom,
! [A: $tType] :
( number_semiring(A)
=> ! [Z1: A] : times_times(A,number_number_of(A,bit0(bit1(pls))),Z1) = plus_plus(A,Z1,Z1) ) ).
tff(fact_66_mult__2,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z1: A] : times_times(A,number_number_of(A,bit0(bit1(pls))),Z1) = plus_plus(A,Z1,Z1) ) ).
tff(fact_67_semiring__mult__2__right,axiom,
! [A: $tType] :
( number_semiring(A)
=> ! [Z1: A] : times_times(A,Z1,number_number_of(A,bit0(bit1(pls)))) = plus_plus(A,Z1,Z1) ) ).
tff(fact_68_mult__2__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z1: A] : times_times(A,Z1,number_number_of(A,bit0(bit1(pls)))) = plus_plus(A,Z1,Z1) ) ).
tff(fact_69_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_70_power2__eq__square__number__of,axiom,
! [B1: $tType] :
( ( monoid_mult(B1)
& number(B1) )
=> ! [W: int] : power_power(B1,number_number_of(B1,W),number_number_of(nat,bit0(bit1(pls)))) = times_times(B1,number_number_of(B1,W),number_number_of(B1,W)) ) ).
tff(fact_71_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_72_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_73_zdiff__power3,axiom,
! [B: int,A1: int] : power_power(int,minus_minus(int,A1,B),number_number_of(nat,bit1(bit1(pls)))) = minus_minus(int,plus_plus(int,minus_minus(int,power_power(int,A1,number_number_of(nat,bit1(bit1(pls)))),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),power_power(int,A1,number_number_of(nat,bit0(bit1(pls))))),B)),times_times(int,times_times(int,number_number_of(int,bit1(bit1(pls))),A1),power_power(int,B,number_number_of(nat,bit0(bit1(pls)))))),power_power(int,B,number_number_of(nat,bit1(bit1(pls))))) ).
tff(fact_74_zdiff__power2,axiom,
! [B: int,A1: int] : power_power(int,minus_minus(int,A1,B),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),B)),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))) ).
tff(fact_75_power2__diff,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Y: A,X: A] : power_power(A,minus_minus(A,X,Y),number_number_of(nat,bit0(bit1(pls)))) = minus_minus(A,plus_plus(A,power_power(A,X,number_number_of(nat,bit0(bit1(pls)))),power_power(A,Y,number_number_of(nat,bit0(bit1(pls))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),X),Y)) ) ).
tff(fact_76_t__l__p,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_77_zspecial__product,axiom,
! [B: int,A1: int] : times_times(int,plus_plus(int,A1,B),minus_minus(int,A1,B)) = minus_minus(int,power_power(int,A1,number_number_of(nat,bit0(bit1(pls)))),power_power(int,B,number_number_of(nat,bit0(bit1(pls))))) ).
tff(fact_78_rel__simps_I17_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit1(K),bit1(L))
<=> ord_less(int,K,L) ) ).
tff(fact_79_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_80_rel__simps_I14_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit0(K),bit0(L))
<=> ord_less(int,K,L) ) ).
tff(fact_81_less__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Ya: int,Xa: int] :
( ord_less(A,number_number_of(A,Xa),number_number_of(A,Ya))
<=> ord_less(int,Xa,Ya) ) ) ).
tff(fact_82_rel__simps_I12_J,axiom,
! [K: int] :
( ord_less(int,bit1(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_83_rel__simps_I16_J,axiom,
! [L: int,K: int] :
( ord_less(int,bit1(K),bit0(L))
<=> ord_less(int,K,L) ) ).
tff(fact_84_rel__simps_I4_J,axiom,
! [K: int] :
( ord_less(int,pls,bit0(K))
<=> ord_less(int,pls,K) ) ).
tff(fact_85_rel__simps_I10_J,axiom,
! [K: int] :
( ord_less(int,bit0(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_86_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat) ).
tff(fact_87_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)) ) ) ) ) ) ).
tff(fact_88_less__special_I2_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Ya: int] :
( ord_less(A,one_one(A),number_number_of(A,Ya))
<=> ord_less(int,bit1(pls),Ya) ) ) ).
tff(fact_89_less__special_I4_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Xa: int] :
( ord_less(A,number_number_of(A,Xa),one_one(A))
<=> ord_less(int,Xa,bit1(pls)) ) ) ).
tff(fact_90__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_91_less__int__code_I16_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit1(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_92_less__int__code_I13_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit0(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_93_less__number__of__int__code,axiom,
! [L: int,K: int] :
( ord_less(int,number_number_of(int,K),number_number_of(int,L))
<=> ord_less(int,K,L) ) ).
tff(fact_94_less__int__code_I15_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_95_zless__add1__eq,axiom,
! [Z: int,Wa: int] :
( ord_less(int,Wa,plus_plus(int,Z,one_one(int)))
<=> ( ord_less(int,Wa,Z)
| ( Wa = Z ) ) ) ).
tff(fact_96_Numeral1__eq1__nat,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)) ).
tff(fact_97_semiring__norm_I110_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ( one_one(A) = number_number_of(A,bit1(pls)) ) ) ).
%----Arities (14)
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___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___Int_Onumber__semiring,axiom,
number_semiring(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) ).
%----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,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),m1)) ).
%------------------------------------------------------------------------------