TPTP Problem File: NUM975_5.p
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%------------------------------------------------------------------------------
% File : NUM975_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 115
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_115 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 149 ( 65 unt; 31 typ; 0 def)
% Number of atoms : 189 ( 116 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 6 ~; 5 |; 4 &)
% ( 18 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 13 ( 10 >; 3 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 0 prp; 1-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 183 ( 165 !; 0 ?; 183 :)
% ( 18 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:24:41
%------------------------------------------------------------------------------
%----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_Groups_Ozero,type,
zero:
!>[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_Int_Onumber__semiring,type,
number_semiring:
!>[A: $tType] : $o ).
tff(sy_cl_Nat_Osemiring__char__0,type,
semiring_char_0:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ocancel__semigroup__add,type,
cancel_semigroup_add:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Oring__no__zero__divisors,type,
ring_n68954251visors:
!>[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_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 ).
%----Relevant facts (97)
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_is__mult__sum2sq,axiom,
! [Y1: int,X1: int] :
( twoSqu1567020053sum2sq(X1)
=> ( twoSqu1567020053sum2sq(Y1)
=> twoSqu1567020053sum2sq(times_times(int,X1,Y1)) ) ) ).
tff(fact_2_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_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_add__Bit0__Bit1,axiom,
! [L: int,K: int] : plus_plus(int,bit0(K),bit1(L)) = bit1(plus_plus(int,K,L)) ).
tff(fact_9_add__Bit1__Bit0,axiom,
! [L: int,K: int] : plus_plus(int,bit1(K),bit0(L)) = bit1(plus_plus(int,K,L)) ).
tff(fact_10_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_11_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_12_of__nat__0,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( semiring_1_of_nat(A,zero_zero(nat)) = zero_zero(A) ) ) ).
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_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_15_add__is__0,axiom,
! [N1: nat,Ma: nat] :
( ( plus_plus(nat,Ma,N1) = zero_zero(nat) )
<=> ( ( Ma = zero_zero(nat) )
& ( N1 = zero_zero(nat) ) ) ) ).
tff(fact_16_mult__cancel2,axiom,
! [N1: nat,K1: nat,Ma: nat] :
( ( times_times(nat,Ma,K1) = times_times(nat,N1,K1) )
<=> ( ( Ma = N1 )
| ( K1 = zero_zero(nat) ) ) ) ).
tff(fact_17_mult__cancel1,axiom,
! [N1: nat,Ma: nat,K1: nat] :
( ( times_times(nat,K1,Ma) = times_times(nat,K1,N1) )
<=> ( ( Ma = N1 )
| ( K1 = zero_zero(nat) ) ) ) ).
tff(fact_18_mult__is__0,axiom,
! [N1: nat,Ma: nat] :
( ( times_times(nat,Ma,N1) = zero_zero(nat) )
<=> ( ( Ma = zero_zero(nat) )
| ( N1 = zero_zero(nat) ) ) ) ).
tff(fact_19_mult__0__right,axiom,
! [M: nat] : times_times(nat,M,zero_zero(nat)) = zero_zero(nat) ).
tff(fact_20_mult__0,axiom,
! [N: nat] : times_times(nat,zero_zero(nat),N) = zero_zero(nat) ).
tff(fact_21_rel__simps_I51_J,axiom,
! [L1: int,K1: int] :
( ( bit1(K1) = bit1(L1) )
<=> ( K1 = L1 ) ) ).
tff(fact_22_rel__simps_I48_J,axiom,
! [L1: int,K1: int] :
( ( bit0(K1) = bit0(L1) )
<=> ( K1 = L1 ) ) ).
tff(fact_23_of__nat__eq__iff,axiom,
! [A: $tType] :
( semiring_char_0(A)
=> ! [N1: nat,Ma: nat] :
( ( semiring_1_of_nat(A,Ma) = semiring_1_of_nat(A,N1) )
<=> ( Ma = N1 ) ) ) ).
tff(fact_24_double__eq__0__iff,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A1: A] :
( ( plus_plus(A,A1,A1) = zero_zero(A) )
<=> ( A1 = 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_of__nat__add,axiom,
! [A: $tType] :
( semiring_1(A)
=> ! [N: nat,M: nat] : semiring_1_of_nat(A,plus_plus(nat,M,N)) = plus_plus(A,semiring_1_of_nat(A,M),semiring_1_of_nat(A,N)) ) ).
tff(fact_33_of__nat__1,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( semiring_1_of_nat(A,one_one(nat)) = one_one(A) ) ) ).
tff(fact_34_mult__Pls,axiom,
! [W: int] : times_times(int,pls,W) = pls ).
tff(fact_35_mult__Bit0,axiom,
! [L: int,K: int] : times_times(int,bit0(K),L) = bit0(times_times(int,K,L)) ).
tff(fact_36_add__Bit0__Bit0,axiom,
! [L: int,K: int] : plus_plus(int,bit0(K),bit0(L)) = bit0(plus_plus(int,K,L)) ).
tff(fact_37_left__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& semiring(B1) )
=> ! [V: int,B2: B1,A2: B1] : times_times(B1,plus_plus(B1,A2,B2),number_number_of(B1,V)) = plus_plus(B1,times_times(B1,A2,number_number_of(B1,V)),times_times(B1,B2,number_number_of(B1,V))) ) ).
tff(fact_38_right__distrib__number__of,axiom,
! [B1: $tType] :
( ( number(B1)
& semiring(B1) )
=> ! [C1: B1,B2: B1,V: int] : times_times(B1,number_number_of(B1,V),plus_plus(B1,B2,C1)) = plus_plus(B1,times_times(B1,number_number_of(B1,V),B2),times_times(B1,number_number_of(B1,V),C1)) ) ).
tff(fact_39_number__of__Pls,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_40_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_41_t1,axiom,
ord_less(int,one_one(int),t) ).
tff(fact_42_mult__eq__self__implies__10,axiom,
! [N: nat,M: nat] :
( ( M = times_times(nat,M,N) )
=> ( ( N = one_one(nat) )
| ( M = zero_zero(nat) ) ) ) ).
tff(fact_43_add__eq__self__zero,axiom,
! [N: nat,M: nat] :
( ( plus_plus(nat,M,N) = M )
=> ( N = zero_zero(nat) ) ) ).
tff(fact_44_Nat_Oadd__0__right,axiom,
! [M: nat] : plus_plus(nat,M,zero_zero(nat)) = M ).
tff(fact_45_plus__nat_Oadd__0,axiom,
! [N: nat] : plus_plus(nat,zero_zero(nat),N) = N ).
tff(fact_46_Pls__def,axiom,
pls = zero_zero(int) ).
tff(fact_47_zmult__int,axiom,
! [N: nat,M: nat] : times_times(int,semiring_1_of_nat(int,M),semiring_1_of_nat(int,N)) = semiring_1_of_nat(int,times_times(nat,M,N)) ).
tff(fact_48_int__mult,axiom,
! [N: nat,M: nat] : semiring_1_of_nat(int,times_times(nat,M,N)) = times_times(int,semiring_1_of_nat(int,M),semiring_1_of_nat(int,N)) ).
tff(fact_49_zadd__int__left,axiom,
! [Z: int,N: nat,M: nat] : plus_plus(int,semiring_1_of_nat(int,M),plus_plus(int,semiring_1_of_nat(int,N),Z)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,M,N)),Z) ).
tff(fact_50_zadd__int,axiom,
! [N: nat,M: nat] : plus_plus(int,semiring_1_of_nat(int,M),semiring_1_of_nat(int,N)) = semiring_1_of_nat(int,plus_plus(nat,M,N)) ).
tff(fact_51_int__1,axiom,
semiring_1_of_nat(int,one_one(nat)) = one_one(int) ).
tff(fact_52_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls) ).
tff(fact_53_int__eq__0__conv,axiom,
! [N1: nat] :
( ( semiring_1_of_nat(int,N1) = zero_zero(int) )
<=> ( N1 = zero_zero(nat) ) ) ).
tff(fact_54_int__0,axiom,
semiring_1_of_nat(int,zero_zero(nat)) = zero_zero(int) ).
tff(fact_55_odd__nonzero,axiom,
! [Z: int] : plus_plus(int,plus_plus(int,one_one(int),Z),Z) != zero_zero(int) ).
tff(fact_56_number__of__reorient,axiom,
! [A: $tType] :
( number(A)
=> ! [X: A,W1: int] :
( ( number_number_of(A,W1) = X )
<=> ( X = number_number_of(A,W1) ) ) ) ).
tff(fact_57_number__of__is__id,axiom,
! [K: int] : number_number_of(int,K) = K ).
tff(fact_58_int__int__eq,axiom,
! [N1: nat,Ma: nat] :
( ( semiring_1_of_nat(int,Ma) = semiring_1_of_nat(int,N1) )
<=> ( Ma = N1 ) ) ).
tff(fact_59_of__nat__mult,axiom,
! [A: $tType] :
( semiring_1(A)
=> ! [N: nat,M: nat] : semiring_1_of_nat(A,times_times(nat,M,N)) = times_times(A,semiring_1_of_nat(A,M),semiring_1_of_nat(A,N)) ) ).
tff(fact_60_add__Pls__right,axiom,
! [K: int] : plus_plus(int,K,pls) = K ).
tff(fact_61_add__Pls,axiom,
! [K: int] : plus_plus(int,pls,K) = K ).
tff(fact_62_Bit0__def,axiom,
! [K: int] : bit0(K) = plus_plus(int,K,K) ).
tff(fact_63_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_64_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_65_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_66_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_67_semiring__numeral__0__eq__0,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_68_add__numeral__0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : plus_plus(A,number_number_of(A,pls),A2) = A2 ) ).
tff(fact_69_add__numeral__0__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : plus_plus(A,A2,number_number_of(A,pls)) = A2 ) ).
tff(fact_70_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_71_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_72_Bit1__def,axiom,
! [K: int] : bit1(K) = plus_plus(int,plus_plus(int,one_one(int),K),K) ).
tff(fact_73_number__of__int,axiom,
! [A: $tType] :
( number_semiring(A)
=> ! [N: nat] : number_number_of(A,semiring_1_of_nat(int,N)) = semiring_1_of_nat(A,N) ) ).
tff(fact_74_number__of__Bit0,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [W: int] : number_number_of(A,bit0(W)) = plus_plus(A,plus_plus(A,zero_zero(A),number_number_of(A,W)),number_number_of(A,W)) ) ).
tff(fact_75_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_76_mult__numeral__1,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : times_times(A,number_number_of(A,bit1(pls)),A2) = A2 ) ).
tff(fact_77_mult__numeral__1__right,axiom,
! [A: $tType] :
( number_ring(A)
=> ! [A2: A] : times_times(A,A2,number_number_of(A,bit1(pls))) = A2 ) ).
tff(fact_78_semiring__numeral__1__eq__1,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,bit1(pls)) = one_one(A) ) ) ).
tff(fact_79_one__is__num__one,axiom,
one_one(int) = number_number_of(int,bit1(pls)) ).
tff(fact_80_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_81_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_82_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_83_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_84_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_85_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_86_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_87_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))) ).
tff(fact_88_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_89_zprime__2,axiom,
zprime(number_number_of(int,bit0(bit1(pls)))) ).
tff(fact_90_transfer__int__nat__numerals_I3_J,axiom,
number_number_of(int,bit0(bit1(pls))) = semiring_1_of_nat(int,number_number_of(nat,bit0(bit1(pls)))) ).
tff(fact_91_nat__numeral__1__eq__1,axiom,
number_number_of(nat,bit1(pls)) = one_one(nat) ).
tff(fact_92_nat__number__of__Pls,axiom,
number_number_of(nat,pls) = zero_zero(nat) ).
tff(fact_93_double__zero__sym,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A1: A] :
( ( zero_zero(A) = plus_plus(A,A1,A1) )
<=> ( A1 = zero_zero(A) ) ) ) ).
tff(fact_94_mult__eq__0__iff,axiom,
! [A: $tType] :
( ring_n68954251visors(A)
=> ! [B: A,A1: A] :
( ( times_times(A,A1,B) = zero_zero(A) )
<=> ( ( A1 = zero_zero(A) )
| ( B = zero_zero(A) ) ) ) ) ).
tff(fact_95_add__left__cancel,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C: A,B: A,A1: A] :
( ( plus_plus(A,A1,B) = plus_plus(A,A1,C) )
<=> ( B = C ) ) ) ).
tff(fact_96_add__right__cancel,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C: A,A1: A,B: A] :
( ( plus_plus(A,B,A1) = plus_plus(A,C,A1) )
<=> ( B = C ) ) ) ).
%----Arities (18)
tff(arity_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
linord219039673up_add(int) ).
tff(arity_Int_Oint___Rings_Oring__no__zero__divisors,axiom,
ring_n68954251visors(int) ).
tff(arity_Int_Oint___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(int) ).
tff(arity_Int_Oint___Nat_Osemiring__char__0,axiom,
semiring_char_0(int) ).
tff(arity_Int_Oint___Int_Onumber__semiring,axiom,
number_semiring(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___Groups_Ozero,axiom,
zero(int) ).
tff(arity_Int_Oint___Int_Onumber,axiom,
number(int) ).
tff(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat) ).
tff(arity_Nat_Onat___Nat_Osemiring__char__0,axiom,
semiring_char_0(nat) ).
tff(arity_Nat_Onat___Int_Onumber__semiring,axiom,
number_semiring(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___Groups_Ozero,axiom,
zero(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)),plus_plus(int,one_one(int),semiring_1_of_nat(int,zero_zero(nat))))) ).
%------------------------------------------------------------------------------