TPTP Problem File: NUN002_5.p
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%------------------------------------------------------------------------------
% File : NUN002_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Number Theory
% Problem : Sum of two squares line 168
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : s2s_168 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 164 ( 63 unt; 39 typ; 0 def)
% Number of atoms : 215 ( 66 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 103 ( 13 ~; 2 |; 7 &)
% ( 46 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 193 ( 167 !; 0 ?; 193 :)
% ( 26 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:25:59
%------------------------------------------------------------------------------
%----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 (36)
tff(sy_cl_Groups_Oone,type,
one:
!>[A: $tType] : $o ).
tff(sy_cl_Int_Onumber,type,
number:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Oring,type,
ring:
!>[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_Omult__zero,type,
mult_zero:
!>[A: $tType] : $o ).
tff(sy_cl_Groups_Ogroup__add,type,
group_add:
!>[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_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_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
ordere236663937imp_le:
!>[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_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_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_Orderings_Oord__class_Oless__eq,type,
ord_less_eq:
!>[A: $tType] : ( ( A * A ) > $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_m1____,type,
m1: int ).
tff(sy_v_n____,type,
n: nat ).
tff(sy_v_t____,type,
t: int ).
%----Relevant facts (95)
tff(fact_0_t1,axiom,
ord_less(int,one_one(int),t) ).
tff(fact_1__096_126_Am1_A_060_A1_A_L_Aint_An_096,axiom,
~ ord_less(int,m1,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ).
tff(fact_2_n1pos,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ).
tff(fact_3_contr,axiom,
ord_less(int,times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1))),zero_zero(int)) ).
tff(fact_4__096_N1_A_060_A_I1_A_L_Aint_An_J_A_K_A_I2_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_J_096,axiom,
ord_less(int,number_number_of(int,min),times_times(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),minus_minus(int,times_times(int,number_number_of(int,bit0(bit1(pls))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)))) ).
tff(fact_5_of__nat__1,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( semiring_1_of_nat(A,one_one(nat)) = one_one(A) ) ) ).
tff(fact_6_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_7_of__nat__less__iff,axiom,
! [A: $tType] :
( linordered_semidom(A)
=> ! [Na: nat,Ma: nat] :
( ord_less(A,semiring_1_of_nat(A,Ma),semiring_1_of_nat(A,Na))
<=> ord_less(nat,Ma,Na) ) ) ).
tff(fact_8_add__less__cancel__right,axiom,
! [A: $tType] :
( ordere236663937imp_le(A)
=> ! [B2: A,C1: A,A2: A] :
( ord_less(A,plus_plus(A,A2,C1),plus_plus(A,B2,C1))
<=> ord_less(A,A2,B2) ) ) ).
tff(fact_9_add__less__cancel__left,axiom,
! [A: $tType] :
( ordere236663937imp_le(A)
=> ! [B2: A,A2: A,C1: A] :
( ord_less(A,plus_plus(A,C1,A2),plus_plus(A,C1,B2))
<=> ord_less(A,A2,B2) ) ) ).
tff(fact_10_zless__add1__eq,axiom,
! [Z1: int,Wa: int] :
( ord_less(int,Wa,plus_plus(int,Z1,one_one(int)))
<=> ( ord_less(int,Wa,Z1)
| ( Wa = Z1 ) ) ) ).
tff(fact_11_less__add__one,axiom,
! [A: $tType] :
( linordered_semidom(A)
=> ! [A1: A] : ord_less(A,A1,plus_plus(A,A1,one_one(A))) ) ).
tff(fact_12_tpos,axiom,
ord_less_eq(int,one_one(int),t) ).
tff(fact_13_of__nat__eq__iff,axiom,
! [A: $tType] :
( semiring_char_0(A)
=> ! [Na: nat,Ma: nat] :
( ( semiring_1_of_nat(A,Ma) = semiring_1_of_nat(A,Na) )
<=> ( Ma = Na ) ) ) ).
tff(fact_14_add__right__cancel,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C1: A,A2: A,B2: A] :
( ( plus_plus(A,B2,A2) = plus_plus(A,C1,A2) )
<=> ( B2 = C1 ) ) ) ).
tff(fact_15_add__left__cancel,axiom,
! [A: $tType] :
( cancel_semigroup_add(A)
=> ! [C1: A,B2: A,A2: A] :
( ( plus_plus(A,A2,B2) = plus_plus(A,A2,C1) )
<=> ( B2 = C1 ) ) ) ).
tff(fact_16_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_17_rel__simps_I51_J,axiom,
! [L1: int,K: int] :
( ( bit1(K) = bit1(L1) )
<=> ( K = L1 ) ) ).
tff(fact_18_rel__simps_I48_J,axiom,
! [L1: int,K: int] :
( ( bit0(K) = bit0(L1) )
<=> ( K = L1 ) ) ).
tff(fact_19_nat__add__left__cancel,axiom,
! [Na: nat,Ma: nat,K: nat] :
( ( plus_plus(nat,K,Ma) = plus_plus(nat,K,Na) )
<=> ( Ma = Na ) ) ).
tff(fact_20_nat__add__right__cancel,axiom,
! [Na: nat,K: nat,Ma: nat] :
( ( plus_plus(nat,Ma,K) = plus_plus(nat,Na,K) )
<=> ( Ma = Na ) ) ).
tff(fact_21_n0,axiom,
ord_less(nat,zero_zero(nat),n) ).
tff(fact_22_mult__eq__0__iff,axiom,
! [A: $tType] :
( ring_n68954251visors(A)
=> ! [B2: A,A2: A] :
( ( times_times(A,A2,B2) = zero_zero(A) )
<=> ( ( A2 = zero_zero(A) )
| ( B2 = zero_zero(A) ) ) ) ) ).
tff(fact_23_mult__zero__right,axiom,
! [A: $tType] :
( mult_zero(A)
=> ! [A1: A] : times_times(A,A1,zero_zero(A)) = zero_zero(A) ) ).
tff(fact_24_mult__zero__left,axiom,
! [A: $tType] :
( mult_zero(A)
=> ! [A1: A] : times_times(A,zero_zero(A),A1) = zero_zero(A) ) ).
tff(fact_25_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_26_double__zero__sym,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A2: A] :
( ( zero_zero(A) = plus_plus(A,A2,A2) )
<=> ( A2 = zero_zero(A) ) ) ) ).
tff(fact_27_add__le__cancel__left,axiom,
! [A: $tType] :
( ordere236663937imp_le(A)
=> ! [B2: A,A2: A,C1: A] :
( ord_less_eq(A,plus_plus(A,C1,A2),plus_plus(A,C1,B2))
<=> ord_less_eq(A,A2,B2) ) ) ).
tff(fact_28_add__le__cancel__right,axiom,
! [A: $tType] :
( ordere236663937imp_le(A)
=> ! [B2: A,C1: A,A2: A] :
( ord_less_eq(A,plus_plus(A,A2,C1),plus_plus(A,B2,C1))
<=> ord_less_eq(A,A2,B2) ) ) ).
tff(fact_29_diff__self,axiom,
! [A: $tType] :
( group_add(A)
=> ! [A1: A] : minus_minus(A,A1,A1) = zero_zero(A) ) ).
tff(fact_30_rel__simps_I46_J,axiom,
! [K1: int] : bit1(K1) != pls ).
tff(fact_31_rel__simps_I39_J,axiom,
! [L: int] : pls != bit1(L) ).
tff(fact_32_of__nat__0,axiom,
! [A: $tType] :
( semiring_1(A)
=> ( semiring_1_of_nat(A,zero_zero(nat)) = zero_zero(A) ) ) ).
tff(fact_33_rel__simps_I50_J,axiom,
! [L: int,K1: int] : bit1(K1) != bit0(L) ).
tff(fact_34_rel__simps_I49_J,axiom,
! [L: int,K1: int] : bit0(K1) != bit1(L) ).
tff(fact_35_rel__simps_I44_J,axiom,
! [K: int] :
( ( bit0(K) = pls )
<=> ( K = pls ) ) ).
tff(fact_36_rel__simps_I38_J,axiom,
! [L1: int] :
( ( pls = bit0(L1) )
<=> ( pls = L1 ) ) ).
tff(fact_37_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_38_of__nat__le__iff,axiom,
! [A: $tType] :
( linordered_semidom(A)
=> ! [Na: nat,Ma: nat] :
( ord_less_eq(A,semiring_1_of_nat(A,Ma),semiring_1_of_nat(A,Na))
<=> ord_less_eq(nat,Ma,Na) ) ) ).
tff(fact_39_rel__simps_I17_J,axiom,
! [L1: int,K: int] :
( ord_less(int,bit1(K),bit1(L1))
<=> ord_less(int,K,L1) ) ).
tff(fact_40_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_41_rel__simps_I14_J,axiom,
! [L1: int,K: int] :
( ord_less(int,bit0(K),bit0(L1))
<=> ord_less(int,K,L1) ) ).
tff(fact_42_rel__simps_I34_J,axiom,
! [L1: int,K: int] :
( ord_less_eq(int,bit1(K),bit1(L1))
<=> ord_less_eq(int,K,L1) ) ).
tff(fact_43_rel__simps_I19_J,axiom,
ord_less_eq(int,pls,pls) ).
tff(fact_44_mult__Pls,axiom,
! [W: int] : times_times(int,pls,W) = pls ).
tff(fact_45_rel__simps_I31_J,axiom,
! [L1: int,K: int] :
( ord_less_eq(int,bit0(K),bit0(L1))
<=> ord_less_eq(int,K,L1) ) ).
tff(fact_46_mult__Bit0,axiom,
! [L: int,K1: int] : times_times(int,bit0(K1),L) = bit0(times_times(int,K1,L)) ).
tff(fact_47_add__Bit0__Bit0,axiom,
! [L: int,K1: int] : plus_plus(int,bit0(K1),bit0(L)) = bit0(plus_plus(int,K1,L)) ).
tff(fact_48_nat__add__left__cancel__less,axiom,
! [Na: nat,Ma: nat,K: nat] :
( ord_less(nat,plus_plus(nat,K,Ma),plus_plus(nat,K,Na))
<=> ord_less(nat,Ma,Na) ) ).
tff(fact_49_diff__bin__simps_I7_J,axiom,
! [L: int,K1: int] : minus_minus(int,bit0(K1),bit0(L)) = bit0(minus_minus(int,K1,L)) ).
tff(fact_50_rel__simps_I47_J,axiom,
! [K: int] :
( ( bit1(K) = min )
<=> ( K = min ) ) ).
tff(fact_51_rel__simps_I43_J,axiom,
! [L1: int] :
( ( min = bit1(L1) )
<=> ( min = L1 ) ) ).
tff(fact_52_Bit1__Min,axiom,
bit1(min) = min ).
tff(fact_53_rel__simps_I37_J,axiom,
pls != min ).
tff(fact_54_rel__simps_I40_J,axiom,
min != pls ).
tff(fact_55_rel__simps_I45_J,axiom,
! [K1: int] : bit0(K1) != min ).
tff(fact_56_rel__simps_I42_J,axiom,
! [L: int] : min != bit0(L) ).
tff(fact_57_rel__simps_I7_J,axiom,
~ ord_less(int,min,min) ).
tff(fact_58_rel__simps_I24_J,axiom,
ord_less_eq(int,min,min) ).
tff(fact_59__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096,axiom,
ord_less_eq(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)) ).
tff(fact_60_double__add__le__zero__iff__single__add__le__zero,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A2: A] :
( ord_less_eq(A,plus_plus(A,A2,A2),zero_zero(A))
<=> ord_less_eq(A,A2,zero_zero(A)) ) ) ).
tff(fact_61_zero__le__double__add__iff__zero__le__single__add,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A2: A] :
( ord_less_eq(A,zero_zero(A),plus_plus(A,A2,A2))
<=> ord_less_eq(A,zero_zero(A),A2) ) ) ).
tff(fact_62_double__add__less__zero__iff__single__add__less__zero,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A2: A] :
( ord_less(A,plus_plus(A,A2,A2),zero_zero(A))
<=> ord_less(A,A2,zero_zero(A)) ) ) ).
tff(fact_63_zero__less__double__add__iff__zero__less__single__add,axiom,
! [A: $tType] :
( linord219039673up_add(A)
=> ! [A2: A] :
( ord_less(A,zero_zero(A),plus_plus(A,A2,A2))
<=> ord_less(A,zero_zero(A),A2) ) ) ).
tff(fact_64_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_65_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_66_number__of__Pls,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_67_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_68_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_69_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_70_le__number__of,axiom,
! [A: $tType] :
( ( number_ring(A)
& linordered_idom(A) )
=> ! [Ya: int,Xa: int] :
( ord_less_eq(A,number_number_of(A,Xa),number_number_of(A,Ya))
<=> ord_less_eq(int,Xa,Ya) ) ) ).
tff(fact_71_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_72_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_73_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_74_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_75_rel__simps_I12_J,axiom,
! [K: int] :
( ord_less(int,bit1(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_76_rel__simps_I16_J,axiom,
! [L1: int,K: int] :
( ord_less(int,bit1(K),bit0(L1))
<=> ord_less(int,K,L1) ) ).
tff(fact_77_rel__simps_I10_J,axiom,
! [K: int] :
( ord_less(int,bit0(K),pls)
<=> ord_less(int,K,pls) ) ).
tff(fact_78_rel__simps_I4_J,axiom,
! [K: int] :
( ord_less(int,pls,bit0(K))
<=> ord_less(int,pls,K) ) ).
tff(fact_79_rel__simps_I22_J,axiom,
! [K: int] :
( ord_less_eq(int,pls,bit1(K))
<=> ord_less_eq(int,pls,K) ) ).
tff(fact_80_rel__simps_I32_J,axiom,
! [L1: int,K: int] :
( ord_less_eq(int,bit0(K),bit1(L1))
<=> ord_less_eq(int,K,L1) ) ).
tff(fact_81_rel__simps_I27_J,axiom,
! [K: int] :
( ord_less_eq(int,bit0(K),pls)
<=> ord_less_eq(int,K,pls) ) ).
tff(fact_82_rel__simps_I21_J,axiom,
! [K: int] :
( ord_less_eq(int,pls,bit0(K))
<=> ord_less_eq(int,pls,K) ) ).
tff(fact_83_add__Bit1__Bit0,axiom,
! [L: int,K1: int] : plus_plus(int,bit1(K1),bit0(L)) = bit1(plus_plus(int,K1,L)) ).
tff(fact_84_add__Bit0__Bit1,axiom,
! [L: int,K1: int] : plus_plus(int,bit0(K1),bit1(L)) = bit1(plus_plus(int,K1,L)) ).
tff(fact_85_diff__bin__simps_I10_J,axiom,
! [L: int,K1: int] : minus_minus(int,bit1(K1),bit1(L)) = bit0(minus_minus(int,K1,L)) ).
tff(fact_86_diff__bin__simps_I9_J,axiom,
! [L: int,K1: int] : minus_minus(int,bit1(K1),bit0(L)) = bit1(minus_minus(int,K1,L)) ).
tff(fact_87_diff__bin__simps_I3_J,axiom,
! [L: int] : minus_minus(int,pls,bit0(L)) = bit0(minus_minus(int,pls,L)) ).
tff(fact_88_rel__simps_I13_J,axiom,
! [K: int] :
( ord_less(int,bit1(K),min)
<=> ord_less(int,K,min) ) ).
tff(fact_89_rel__simps_I9_J,axiom,
! [K: int] :
( ord_less(int,min,bit1(K))
<=> ord_less(int,min,K) ) ).
tff(fact_90_rel__simps_I3_J,axiom,
~ ord_less(int,pls,min) ).
tff(fact_91_rel__simps_I6_J,axiom,
ord_less(int,min,pls) ).
tff(fact_92_rel__simps_I8_J,axiom,
! [K: int] :
( ord_less(int,min,bit0(K))
<=> ord_less(int,min,K) ) ).
tff(fact_93_rel__simps_I30_J,axiom,
! [K: int] :
( ord_less_eq(int,bit1(K),min)
<=> ord_less_eq(int,K,min) ) ).
tff(fact_94_rel__simps_I26_J,axiom,
! [K: int] :
( ord_less_eq(int,min,bit1(K))
<=> ord_less_eq(int,min,K) ) ).
%----Arities (27)
tff(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(int) ).
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___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___Groups_Ogroup__add,axiom,
group_add(int) ).
tff(arity_Int_Oint___Rings_Omult__zero,axiom,
mult_zero(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___Rings_Oring,axiom,
ring(int) ).
tff(arity_Int_Oint___Int_Onumber,axiom,
number(int) ).
tff(arity_Int_Oint___Groups_Oone,axiom,
one(int) ).
tff(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
ordere236663937imp_le(nat) ).
tff(arity_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
cancel_semigroup_add(nat) ).
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_Omult__zero,axiom,
mult_zero(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) ).
tff(arity_Nat_Onat___Groups_Oone,axiom,
one(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,
$false ).
%------------------------------------------------------------------------------