TPTP Problem File: NUM977_5.p
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%------------------------------------------------------------------------------
% File : NUM977_5 : TPTP v9.0.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 120
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_120 [Bla13]
% Status : Theorem
% Rating : 0.00 v6.4.0
% Syntax : Number of formulae : 148 ( 56 unt; 32 typ; 0 def)
% Number of atoms : 209 ( 67 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 119 ( 26 ~; 2 |; 10 &)
% ( 31 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 183 ( 165 !; 0 ?; 183 :)
% ( 18 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:24:45
%------------------------------------------------------------------------------
%----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_fun,type,
fun: ( $tType * $tType ) > $tType ).
%----Explicit typings (28)
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_Rings_Osemiring__1,type,
semiring_1:
!>[A: $tType] : $o ).
tff(sy_cl_Nat_Osemiring__char__0,type,
semiring_char_0:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Olinordered__idom,type,
linordered_idom:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Olinordered__semidom,type,
linordered_semidom:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Olinordered__ab__group__add,type,
linord219039673up_add:
!>[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_Groups_Ozero__class_Ozero,type,
zero_zero:
!>[A: $tType] : 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_TwoSquares__Mirabelle__poiayhyqls_Ois__sum2sq,type,
twoSqu1567020053sum2sq: int > $o ).
tff(sy_c_aa,type,
aa:
!>[A: $tType,B: $tType] : ( ( fun(A,B) * A ) > B ) ).
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_t____,type,
t: int ).
tff(sy_v_tn____,type,
tn: nat ).
%----Relevant facts (98)
tff(fact_0_t1,axiom,
ord_less(int,one_one(int),t) ).
tff(fact_1_nQ1,axiom,
~ twoSqu1567020053sum2sq(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,zero_zero(nat))))) ).
tff(fact_2__C0_C,axiom,
ord_less(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_3_p,axiom,
zprime(plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ).
tff(fact_4_is__mult__sum2sq,axiom,
! [Y: int,X: int] :
( twoSqu1567020053sum2sq(X)
=> ( twoSqu1567020053sum2sq(Y)
=> twoSqu1567020053sum2sq(times_times(int,X,Y)) ) ) ).
tff(fact_5_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_6_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_7_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_8_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_9_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_10_less__special_I4_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [X1: int] :
( ord_less(A,number_number_of(A,X1),one_one(A))
<=> ord_less(int,X1,bit1(pls)) ) ) ).
tff(fact_11_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_12_less__special_I1_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y1: int] :
( ord_less(A,zero_zero(A),number_number_of(A,Y1))
<=> ord_less(int,pls,Y1) ) ) ).
tff(fact_13_less__special_I3_J,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [X1: int] :
( ord_less(A,number_number_of(A,X1),zero_zero(A))
<=> ord_less(int,X1,pls) ) ) ).
tff(fact_14_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_15_numeral__1__eq__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_16_of__nat__0__less__iff,axiom,
! [A: $tType] :
( linordered_semidom(A)
=> ! [N: nat] :
( ord_less(A,zero_zero(A),semiring_1_of_nat(A,N))
<=> ord_less(nat,zero_zero(nat),N) ) ) ).
tff(fact_17_tn0,axiom,
ord_less(nat,zero_zero(nat),tn) ).
tff(fact_18_eq__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& ring_char_0(A) )
=> ! [Y1: int,X1: int] :
( ( number_number_of(A,X1) = number_number_of(A,Y1) )
<=> ( X1 = Y1 ) ) ) ).
tff(fact_19_add__is__0,axiom,
! [N: nat,Ma: nat] :
( ( plus_plus(nat,Ma,N) = zero_zero(nat) )
<=> ( ( Ma = zero_zero(nat) )
& ( N = zero_zero(nat) ) ) ) ).
tff(fact_20_rel__simps_I51_J,axiom,
! [L1: int,K1: int] :
( ( bit1(K1) = bit1(L1) )
<=> ( K1 = L1 ) ) ).
tff(fact_21_rel__simps_I48_J,axiom,
! [L1: int,K1: int] :
( ( bit0(K1) = bit0(L1) )
<=> ( K1 = L1 ) ) ).
tff(fact_22_nat__add__left__cancel__less,axiom,
! [N: nat,Ma: nat,K1: nat] :
( ord_less(nat,plus_plus(nat,K1,Ma),plus_plus(nat,K1,N))
<=> ord_less(nat,Ma,N) ) ).
tff(fact_23_of__nat__eq__iff,axiom,
! [A: $tType] :
( semiring_char_0(A)
=> ! [N: nat,Ma: nat] :
( ( semiring_1_of_nat(A,Ma) = semiring_1_of_nat(A,N) )
<=> ( Ma = N ) ) ) ).
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,
! [K: int] : ( bit1(K) != pls ) ).
tff(fact_26_rel__simps_I39_J,axiom,
! [L: int] : ( pls != bit1(L) ) ).
tff(fact_27_rel__simps_I50_J,axiom,
! [L: int,K: int] : ( bit1(K) != bit0(L) ) ).
tff(fact_28_rel__simps_I49_J,axiom,
! [L: int,K: int] : ( bit0(K) != bit1(L) ) ).
tff(fact_29_rel__simps_I44_J,axiom,
! [K1: int] :
( ( bit0(K1) = pls )
<=> ( K1 = pls ) ) ).
tff(fact_30_rel__simps_I38_J,axiom,
! [L1: int] :
( ( pls = bit0(L1) )
<=> ( pls = L1 ) ) ).
tff(fact_31_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_32_add__gr__0,axiom,
! [N: nat,Ma: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,Ma,N))
<=> ( ord_less(nat,zero_zero(nat),Ma)
| ord_less(nat,zero_zero(nat),N) ) ) ).
tff(fact_33_less__zeroE,axiom,
! [N1: nat] : ~ ord_less(nat,N1,zero_zero(nat)) ).
tff(fact_34_less__nat__zero__code,axiom,
! [N1: nat] : ~ ord_less(nat,N1,zero_zero(nat)) ).
tff(fact_35_neq0__conv,axiom,
! [N: nat] :
( ( N != zero_zero(nat) )
<=> ord_less(nat,zero_zero(nat),N) ) ).
tff(fact_36_rel__simps_I17_J,axiom,
! [L1: int,K1: int] :
( ord_less(int,bit1(K1),bit1(L1))
<=> ord_less(int,K1,L1) ) ).
tff(fact_37_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_38_rel__simps_I14_J,axiom,
! [L1: int,K1: int] :
( ord_less(int,bit0(K1),bit0(L1))
<=> ord_less(int,K1,L1) ) ).
tff(fact_39_of__nat__add,axiom,
! [A: $tType] :
( semiring_1(A)
=> ! [N1: nat,M: nat] : ( semiring_1_of_nat(A,plus_plus(nat,M,N1)) = plus_plus(A,semiring_1_of_nat(A,M),semiring_1_of_nat(A,N1)) ) ) ).
tff(fact_40_of__nat__1,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( semiring_1_of_nat(A,one_one(nat)) = one_one(A) ) ) ).
tff(fact_41_mult__Pls,axiom,
! [W1: int] : ( times_times(int,pls,W1) = pls ) ).
tff(fact_42_mult__Bit0,axiom,
! [L: int,K: int] : ( times_times(int,bit0(K),L) = bit0(times_times(int,K,L)) ) ).
tff(fact_43_add__Bit0__Bit0,axiom,
! [L: int,K: int] : ( plus_plus(int,bit0(K),bit0(L)) = bit0(plus_plus(int,K,L)) ) ).
tff(fact_44_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_45_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_46_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_47_number__of__Pls,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_48_less__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Y1: int,X1: int] :
( ord_less(A,number_number_of(A,X1),number_number_of(A,Y1))
<=> ord_less(int,X1,Y1) ) ) ).
tff(fact_49_mult__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A,W1: int,V: int] : ( times_times(A,number_number_of(A,V),times_times(A,number_number_of(A,W1),Z)) = times_times(A,number_number_of(A,times_times(int,V,W1)),Z) ) ) ).
tff(fact_50_arith__simps_I32_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W1: int,V: int] : ( times_times(A,number_number_of(A,V),number_number_of(A,W1)) = number_number_of(A,times_times(int,V,W1)) ) ) ).
tff(fact_51_of__nat__0,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( semiring_1_of_nat(A,zero_zero(nat)) = zero_zero(A) ) ) ).
tff(fact_52_add__number__of__left,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [Z: A,W1: int,V: int] : ( plus_plus(A,number_number_of(A,V),plus_plus(A,number_number_of(A,W1),Z)) = plus_plus(A,number_number_of(A,plus_plus(int,V,W1)),Z) ) ) ).
tff(fact_53_add__number__of__eq,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W1: int,V: int] : ( plus_plus(A,number_number_of(A,V),number_number_of(A,W1)) = number_number_of(A,plus_plus(int,V,W1)) ) ) ).
tff(fact_54_rel__simps_I12_J,axiom,
! [K1: int] :
( ord_less(int,bit1(K1),pls)
<=> ord_less(int,K1,pls) ) ).
tff(fact_55_rel__simps_I16_J,axiom,
! [L1: int,K1: int] :
( ord_less(int,bit1(K1),bit0(L1))
<=> ord_less(int,K1,L1) ) ).
tff(fact_56_of__nat__less__iff,axiom,
! [A: $tType] :
( linordered_semidom(A)
=> ! [N: nat,Ma: nat] :
( ord_less(A,semiring_1_of_nat(A,Ma),semiring_1_of_nat(A,N))
<=> ord_less(nat,Ma,N) ) ) ).
tff(fact_57_rel__simps_I10_J,axiom,
! [K1: int] :
( ord_less(int,bit0(K1),pls)
<=> ord_less(int,K1,pls) ) ).
tff(fact_58_rel__simps_I4_J,axiom,
! [K1: int] :
( ord_less(int,pls,bit0(K1))
<=> ord_less(int,pls,K1) ) ).
tff(fact_59_add__Bit1__Bit0,axiom,
! [L: int,K: int] : ( plus_plus(int,bit1(K),bit0(L)) = bit1(plus_plus(int,K,L)) ) ).
tff(fact_60_add__Bit0__Bit1,axiom,
! [L: int,K: int] : ( plus_plus(int,bit0(K),bit1(L)) = bit1(plus_plus(int,K,L)) ) ).
tff(fact_61_less__not__refl,axiom,
! [N1: nat] : ~ ord_less(nat,N1,N1) ).
tff(fact_62_not__add__less1,axiom,
! [J: nat,I: nat] : ~ ord_less(nat,plus_plus(nat,I,J),I) ).
tff(fact_63_not__add__less2,axiom,
! [I: nat,J: nat] : ~ ord_less(nat,plus_plus(nat,J,I),I) ).
tff(fact_64_nat__neq__iff,axiom,
! [N: nat,Ma: nat] :
( ( Ma != N )
<=> ( ord_less(nat,Ma,N)
| ord_less(nat,N,Ma) ) ) ).
tff(fact_65_linorder__neqE__nat,axiom,
! [Y: nat,X: nat] :
( ( X != Y )
=> ( ~ ord_less(nat,X,Y)
=> ord_less(nat,Y,X) ) ) ).
tff(fact_66_less__irrefl__nat,axiom,
! [N1: nat] : ~ ord_less(nat,N1,N1) ).
tff(fact_67_less__not__refl2,axiom,
! [M: nat,N1: nat] :
( ord_less(nat,N1,M)
=> ( M != N1 ) ) ).
tff(fact_68_less__not__refl3,axiom,
! [T: nat,S: nat] :
( ord_less(nat,S,T)
=> ( S != T ) ) ).
tff(fact_69_trans__less__add1,axiom,
! [M: nat,J: nat,I: nat] :
( ord_less(nat,I,J)
=> ord_less(nat,I,plus_plus(nat,J,M)) ) ).
tff(fact_70_trans__less__add2,axiom,
! [M: nat,J: nat,I: nat] :
( ord_less(nat,I,J)
=> ord_less(nat,I,plus_plus(nat,M,J)) ) ).
tff(fact_71_add__less__mono1,axiom,
! [K: nat,J: nat,I: nat] :
( ord_less(nat,I,J)
=> ord_less(nat,plus_plus(nat,I,K),plus_plus(nat,J,K)) ) ).
tff(fact_72_add__less__mono,axiom,
! [L: nat,K: nat,J: nat,I: nat] :
( ord_less(nat,I,J)
=> ( ord_less(nat,K,L)
=> ord_less(nat,plus_plus(nat,I,K),plus_plus(nat,J,L)) ) ) ).
tff(fact_73_less__add__eq__less,axiom,
! [N1: nat,M: nat,L: nat,K: nat] :
( ord_less(nat,K,L)
=> ( ( plus_plus(nat,M,L) = plus_plus(nat,K,N1) )
=> ord_less(nat,M,N1) ) ) ).
tff(fact_74_add__lessD1,axiom,
! [K: nat,J: nat,I: nat] :
( ord_less(nat,plus_plus(nat,I,J),K)
=> ord_less(nat,I,K) ) ).
tff(fact_75_nat__less__cases,axiom,
! [P: fun(nat,fun(nat,bool)),N: nat,Ma: nat] :
( ( ord_less(nat,Ma,N)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N),Ma)) )
=> ( ( ( Ma = N )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N),Ma)) )
=> ( ( ord_less(nat,N,Ma)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N),Ma)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N),Ma)) ) ) ) ).
tff(fact_76_add__eq__self__zero,axiom,
! [N1: nat,M: nat] :
( ( plus_plus(nat,M,N1) = M )
=> ( N1 = zero_zero(nat) ) ) ).
tff(fact_77_Nat_Oadd__0__right,axiom,
! [M: nat] : ( plus_plus(nat,M,zero_zero(nat)) = M ) ).
tff(fact_78_plus__nat_Oadd__0,axiom,
! [N1: nat] : ( plus_plus(nat,zero_zero(nat),N1) = N1 ) ).
tff(fact_79_gr0I,axiom,
! [N1: nat] :
( ( N1 != zero_zero(nat) )
=> ord_less(nat,zero_zero(nat),N1) ) ).
tff(fact_80_gr__implies__not0,axiom,
! [N1: nat,M: nat] :
( ord_less(nat,M,N1)
=> ( N1 != zero_zero(nat) ) ) ).
tff(fact_81_not__less0,axiom,
! [N1: nat] : ~ ord_less(nat,N1,zero_zero(nat)) ).
tff(fact_82_Pls__def,axiom,
pls = zero_zero(int) ).
tff(fact_83_zero__less__int__conv,axiom,
! [N: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,N))
<=> ord_less(nat,zero_zero(nat),N) ) ).
tff(fact_84_zadd__int__left,axiom,
! [Z: int,N1: nat,M: nat] : ( plus_plus(int,semiring_1_of_nat(int,M),plus_plus(int,semiring_1_of_nat(int,N1),Z)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,M,N1)),Z) ) ).
tff(fact_85_zadd__int,axiom,
! [N1: nat,M: nat] : ( plus_plus(int,semiring_1_of_nat(int,M),semiring_1_of_nat(int,N1)) = semiring_1_of_nat(int,plus_plus(nat,M,N1)) ) ).
tff(fact_86_zless__int,axiom,
! [N: nat,Ma: nat] :
( ord_less(int,semiring_1_of_nat(int,Ma),semiring_1_of_nat(int,N))
<=> ord_less(nat,Ma,N) ) ).
tff(fact_87_bin__less__0__simps_I4_J,axiom,
! [W: int] :
( ord_less(int,bit1(W),zero_zero(int))
<=> ord_less(int,W,zero_zero(int)) ) ).
tff(fact_88_bin__less__0__simps_I1_J,axiom,
~ ord_less(int,pls,zero_zero(int)) ).
tff(fact_89_bin__less__0__simps_I3_J,axiom,
! [W: int] :
( ord_less(int,bit0(W),zero_zero(int))
<=> ord_less(int,W,zero_zero(int)) ) ).
tff(fact_90_int__1,axiom,
semiring_1_of_nat(int,one_one(nat)) = one_one(int) ).
tff(fact_91_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls) ).
tff(fact_92_zmult__zless__mono2,axiom,
! [K: int,J: int,I: int] :
( ord_less(int,I,J)
=> ( ord_less(int,zero_zero(int),K)
=> ord_less(int,times_times(int,K,I),times_times(int,K,J)) ) ) ).
tff(fact_93_int__eq__0__conv,axiom,
! [N: nat] :
( ( semiring_1_of_nat(int,N) = zero_zero(int) )
<=> ( N = zero_zero(nat) ) ) ).
tff(fact_94_int__0,axiom,
semiring_1_of_nat(int,zero_zero(nat)) = zero_zero(int) ).
tff(fact_95_odd__nonzero,axiom,
! [Z: int] : ( plus_plus(int,plus_plus(int,one_one(int),Z),Z) != zero_zero(int) ) ).
tff(fact_96_int__less__0__conv,axiom,
! [K: nat] : ~ ord_less(int,semiring_1_of_nat(int,K),zero_zero(int)) ).
tff(fact_97_pos__zmult__eq__1__iff,axiom,
! [N: int,Ma: int] :
( ord_less(int,zero_zero(int),Ma)
=> ( ( times_times(int,Ma,N) = one_one(int) )
<=> ( ( Ma = one_one(int) )
& ( N = one_one(int) ) ) ) ) ).
%----Arities (14)
tff(arity_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
linord219039673up_add(int) ).
tff(arity_Int_Oint___Rings_Olinordered__semidom,axiom,
linordered_semidom(int) ).
tff(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int) ).
tff(arity_Int_Oint___Nat_Osemiring__char__0,axiom,
semiring_char_0(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___Int_Onumber,axiom,
number(int) ).
tff(arity_Nat_Onat___Rings_Olinordered__semidom,axiom,
linordered_semidom(nat) ).
tff(arity_Nat_Onat___Nat_Osemiring__char__0,axiom,
semiring_char_0(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 (2)
tff(conj_0,hypothesis,
$true ).
tff(conj_1,conjecture,
~ twoSqu1567020053sum2sq(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,zero_zero(nat))))) ).
%------------------------------------------------------------------------------