TPTP Problem File: NUN003_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NUN003_5 : TPTP v9.0.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 171
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_171 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 164 ( 79 unt; 39 typ; 0 def)
% Number of atoms : 179 ( 103 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 11 ~; 0 |; 6 &)
% ( 6 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 16 ( 11 >; 5 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 0 prp; 1-3 aty)
% Number of functors : 23 ( 23 usr; 14 con; 0-3 aty)
% Number of variables : 196 ( 177 !; 2 ?; 196 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:26:01
%------------------------------------------------------------------------------
%----Should-be-implicit typings (4)
tff(ty_tc_HOL_Obool,type,
bool: $tType ).
tff(ty_tc_Int_Oint,type,
int: $tType ).
tff(ty_tc_Nat_Onat,type,
nat: $tType ).
tff(ty_tc_RealDef_Oreal,type,
real: $tType ).
%----Explicit typings (35)
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_Ocomm__semiring__1,type,
comm_semiring_1:
!>[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_Nat_Osemiring__1__class_Oof__nat,type,
semiring_1_of_nat:
!>[A: $tType] : ( nat > 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_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_n____,type,
n: nat ).
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 ).
tff(sy_v_x____,type,
x: int ).
tff(sy_v_y____,type,
y: int ).
%----Relevant facts (98)
tff(fact_0_p,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_1_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_2_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_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)
=> ! [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_5_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_6_mult__Bit1,axiom,
! [L: int,K: int] : ( times_times(int,bit1(K),L) = plus_plus(int,bit0(times_times(int,K,L)),L) ) ).
tff(fact_7_numeral__1__eq__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_8_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_9_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_10_power2__diff,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Y1: A,X1: A] : ( power_power(A,minus_minus(A,X1,Y1),number_number_of(nat,bit0(bit1(pls)))) = minus_minus(A,plus_plus(A,power_power(A,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(A,Y1,number_number_of(nat,bit0(bit1(pls))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),X1),Y1)) ) ) ).
tff(fact_11_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_12_zadd__power2,axiom,
! [B: int,A1: int] : ( power_power(int,plus_plus(int,A1,B),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(int,plus_plus(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_13_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_14_rel__simps_I51_J,axiom,
! [L1: int,K1: int] :
( ( bit1(K1) = bit1(L1) )
<=> ( K1 = L1 ) ) ).
tff(fact_15_rel__simps_I48_J,axiom,
! [L1: int,K1: int] :
( ( bit0(K1) = bit0(L1) )
<=> ( K1 = L1 ) ) ).
tff(fact_16_rel__simps_I46_J,axiom,
! [K: int] : ( bit1(K) != pls ) ).
tff(fact_17_rel__simps_I39_J,axiom,
! [L: int] : ( pls != bit1(L) ) ).
tff(fact_18_rel__simps_I50_J,axiom,
! [L: int,K: int] : ( bit1(K) != bit0(L) ) ).
tff(fact_19_rel__simps_I49_J,axiom,
! [L: int,K: int] : ( bit0(K) != bit1(L) ) ).
tff(fact_20_rel__simps_I44_J,axiom,
! [K1: int] :
( ( bit0(K1) = pls )
<=> ( K1 = pls ) ) ).
tff(fact_21_rel__simps_I38_J,axiom,
! [L1: int] :
( ( pls = bit0(L1) )
<=> ( pls = L1 ) ) ).
tff(fact_22_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_23_mult__Pls,axiom,
! [W: int] : ( times_times(int,pls,W) = pls ) ).
tff(fact_24_mult__Bit0,axiom,
! [L: int,K: int] : ( times_times(int,bit0(K),L) = bit0(times_times(int,K,L)) ) ).
tff(fact_25_add__Bit0__Bit0,axiom,
! [L: int,K: int] : ( plus_plus(int,bit0(K),bit0(L)) = bit0(plus_plus(int,K,L)) ) ).
tff(fact_26_diff__bin__simps_I7_J,axiom,
! [L: int,K: int] : ( minus_minus(int,bit0(K),bit0(L)) = bit0(minus_minus(int,K,L)) ) ).
tff(fact_27_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_28_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_29_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_30_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_31_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_32_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_33_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_34_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_35_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat) ).
tff(fact_36_add__Bit1__Bit0,axiom,
! [L: int,K: int] : ( plus_plus(int,bit1(K),bit0(L)) = bit1(plus_plus(int,K,L)) ) ).
tff(fact_37_add__Bit0__Bit1,axiom,
! [L: int,K: int] : ( plus_plus(int,bit0(K),bit1(L)) = bit1(plus_plus(int,K,L)) ) ).
tff(fact_38_diff__bin__simps_I10_J,axiom,
! [L: int,K: int] : ( minus_minus(int,bit1(K),bit1(L)) = bit0(minus_minus(int,K,L)) ) ).
tff(fact_39_diff__bin__simps_I9_J,axiom,
! [L: int,K: int] : ( minus_minus(int,bit1(K),bit0(L)) = bit1(minus_minus(int,K,L)) ) ).
tff(fact_40_diff__bin__simps_I3_J,axiom,
! [L: int] : ( minus_minus(int,pls,bit0(L)) = bit0(minus_minus(int,pls,L)) ) ).
tff(fact_41_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_42_zpower__zpower,axiom,
! [Z: nat,Y1: nat,X1: int] : ( power_power(int,power_power(int,X1,Y1),Z) = power_power(int,X1,times_times(nat,Y1,Z)) ) ).
tff(fact_43_nat__mult__2,axiom,
! [Z: nat] : ( times_times(nat,number_number_of(nat,bit0(bit1(pls))),Z) = plus_plus(nat,Z,Z) ) ).
tff(fact_44_nat__mult__2__right,axiom,
! [Z: nat] : ( times_times(nat,Z,number_number_of(nat,bit0(bit1(pls)))) = plus_plus(nat,Z,Z) ) ).
tff(fact_45_Numeral1__eq1__nat,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)) ).
tff(fact_46_zprime__2,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))) ).
tff(fact_47_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_48_number__of__is__id,axiom,
! [K: int] : ( number_number_of(int,K) = K ) ).
tff(fact_49_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_50_add__Pls__right,axiom,
! [K: int] : ( plus_plus(int,K,pls) = K ) ).
tff(fact_51_add__Pls,axiom,
! [K: int] : ( plus_plus(int,pls,K) = K ) ).
tff(fact_52_Bit0__def,axiom,
! [K: int] : ( bit0(K) = plus_plus(int,K,K) ) ).
tff(fact_53_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_54_diff__bin__simps_I1_J,axiom,
! [K: int] : ( minus_minus(int,K,pls) = K ) ).
tff(fact_55_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_56_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_57_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_58_int__distrib_I3_J,axiom,
! [W: int,Z2: int,Z1: int] : ( times_times(int,minus_minus(int,Z1,Z2),W) = minus_minus(int,times_times(int,Z1,W),times_times(int,Z2,W)) ) ).
tff(fact_59_int__distrib_I4_J,axiom,
! [Z2: int,Z1: int,W: int] : ( times_times(int,W,minus_minus(int,Z1,Z2)) = minus_minus(int,times_times(int,W,Z1),times_times(int,W,Z2)) ) ).
tff(fact_60_add__numeral__0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : ( plus_plus(A,number_number_of(A,pls),A1) = A1 ) ) ).
tff(fact_61_add__numeral__0__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A1: A] : ( plus_plus(A,A1,number_number_of(A,pls)) = A1 ) ) ).
tff(fact_62_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_63_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_64_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_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)
=> ! [A1: A] : ( times_times(A,number_number_of(A,bit1(pls)),A1) = A1 ) ) ).
tff(fact_68_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_69_semiring__numeral__1__eq__1,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_70_semiring__norm_I110_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ( one_one(A) = number_number_of(A,bit1(pls)) ) ) ).
tff(fact_71_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_72_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)) ).
tff(fact_73_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_74_power3__eq__cube,axiom,
! [A: $tType] :
( monoid_mult(A)
=> ! [A1: A] : ( power_power(A,A1,number_number_of(nat,bit1(bit1(pls)))) = times_times(A,times_times(A,A1,A1),A1) ) ) ).
tff(fact_75_quartic__square__square,axiom,
! [X1: int] : ( power_power(int,power_power(int,X1,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X1,number_number_of(nat,bit0(bit0(bit1(pls))))) ) ).
tff(fact_76_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_77_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_78_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_79_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_80_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_81_power2__eq__square,axiom,
! [A: $tType] :
( monoid_mult(A)
=> ! [A1: A] : ( power_power(A,A1,number_number_of(nat,bit0(bit1(pls)))) = times_times(A,A1,A1) ) ) ).
tff(fact_82_cube__square,axiom,
! [A1: int] : ( times_times(int,A1,power_power(int,A1,number_number_of(nat,bit0(bit1(pls))))) = power_power(int,A1,number_number_of(nat,bit1(bit1(pls)))) ) ).
tff(fact_83_power2__sum,axiom,
! [A: $tType] :
( number_semiring(A)
=> ! [Y1: A,X1: A] : ( power_power(A,plus_plus(A,X1,Y1),number_number_of(nat,bit0(bit1(pls)))) = plus_plus(A,plus_plus(A,power_power(A,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(A,Y1,number_number_of(nat,bit0(bit1(pls))))),times_times(A,times_times(A,number_number_of(A,bit0(bit1(pls))),X1),Y1)) ) ) ).
tff(fact_84_zadd__power3,axiom,
! [B: int,A1: int] : ( power_power(int,plus_plus(int,A1,B),number_number_of(nat,bit1(bit1(pls)))) = plus_plus(int,plus_plus(int,plus_plus(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_85_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_86_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [A: $tType] :
( comm_semiring_1(A)
=> ! [N: nat,X1: A] : ( power_power(A,X1,times_times(nat,number_number_of(nat,bit0(bit1(pls))),N)) = times_times(A,power_power(A,X1,N),power_power(A,X1,N)) ) ) ).
tff(fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [A: $tType] :
( comm_semiring_1(A)
=> ! [X1: A] : ( times_times(A,X1,X1) = power_power(A,X1,number_number_of(nat,bit0(bit1(pls)))) ) ) ).
tff(fact_88__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_89_m1,axiom,
plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) = times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1) ).
tff(fact_90_power__one,axiom,
! [A: $tType] :
( monoid_mult(A)
=> ! [N: nat] : ( power_power(A,one_one(A),N) = one_one(A) ) ) ).
tff(fact_91_calculation_I2_J,axiom,
( ( t = one_one(int) )
=> ? [X: int,Y: int] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,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_92_diff__square,axiom,
! [Y1: nat,X1: nat] : ( minus_minus(nat,power_power(nat,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(nat,Y1,number_number_of(nat,bit0(bit1(pls))))) = times_times(nat,plus_plus(nat,X1,Y1),minus_minus(nat,X1,Y1)) ) ).
tff(fact_93_four__x__squared,axiom,
! [X1: real] : ( times_times(real,number_number_of(real,bit0(bit0(bit1(pls)))),power_power(real,X1,number_number_of(nat,bit0(bit1(pls))))) = power_power(real,times_times(real,number_number_of(real,bit0(bit1(pls))),X1),number_number_of(nat,bit0(bit1(pls)))) ) ).
tff(fact_94_t1,axiom,
ord_less(int,one_one(int),t) ).
tff(fact_95__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_A_I1_A_L_Aint_An_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X: int,Y: int] : ( plus_plus(int,power_power(int,X,number_number_of(nat,bit0(bit1(pls)))),power_power(int,Y,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)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ) ).
tff(fact_96__096_B_Bthesis_O_A_I_B_Bm1_O_Av_A_094_A2_A_L_Aw_A_094_A2_A_061_A_I1_A_L_Aint_An_J_A_K_Am1_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [M1: int] : ( plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))) != times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),M1) ) ).
tff(fact_97_xy,axiom,
plus_plus(int,power_power(int,x,number_number_of(nat,bit0(bit1(pls)))),power_power(int,y,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)),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ).
%----Arities (24)
tff(arity_Int_Oint___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(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___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(nat) ).
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) ).
tff(arity_RealDef_Oreal___Rings_Ocomm__semiring__1,axiom,
comm_semiring_1(real) ).
tff(arity_RealDef_Oreal___Int_Onumber__semiring,axiom,
number_semiring(real) ).
tff(arity_RealDef_Oreal___Groups_Omonoid__mult,axiom,
monoid_mult(real) ).
tff(arity_RealDef_Oreal___Rings_Osemiring__1,axiom,
semiring_1(real) ).
tff(arity_RealDef_Oreal___Int_Oring__char__0,axiom,
ring_char_0(real) ).
tff(arity_RealDef_Oreal___Int_Onumber__ring,axiom,
number_ring(real) ).
tff(arity_RealDef_Oreal___Rings_Osemiring,axiom,
semiring(real) ).
tff(arity_RealDef_Oreal___Rings_Oring,axiom,
ring(real) ).
tff(arity_RealDef_Oreal___Int_Onumber,axiom,
number(real) ).
%----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,
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) ).
%------------------------------------------------------------------------------