TPTP Problem File: SWW484_5.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWW484_5 : TPTP v8.2.0. Released v6.0.0.
% Domain : Software Verification
% Problem : Fundamental Theorem of Algebra line 63
% Version : Especial.
% English :
% Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% : [Bla13] Blanchette (2011), Email to Geoff Sutcliffe
% Source : [Bla13]
% Names : fta_63 [Bla13]
% Status : Unknown
% Rating : 1.00 v6.4.0
% Syntax : Number of formulae : 171 ( 58 unt; 34 typ; 0 def)
% Number of atoms : 298 ( 60 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 198 ( 37 ~; 8 |; 19 &)
% ( 34 <=>; 100 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 0 prp; 1-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 230 ( 208 !; 0 ?; 230 :)
% ( 22 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_UNK_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2011-12-13 16:14:36
%------------------------------------------------------------------------------
%----Should-be-implicit typings (5)
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 ).
tff(ty_tc_fun,type,
fun: ( $tType * $tType ) > $tType ).
%----Explicit typings (29)
tff(sy_cl_Int_Onumber,type,
number:
!>[A: $tType] : $o ).
tff(sy_cl_Fields_Ofield,type,
field:
!>[A: $tType] : $o ).
tff(sy_cl_Orderings_Oord,type,
ord:
!>[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_Orderings_Oorder,type,
order:
!>[A: $tType] : $o ).
tff(sy_cl_Orderings_Olinorder,type,
linorder:
!>[A: $tType] : $o ).
tff(sy_cl_Orderings_Opreorder,type,
preorder:
!>[A: $tType] : $o ).
tff(sy_cl_Int_Onumber__semiring,type,
number_semiring:
!>[A: $tType] : $o ).
tff(sy_cl_Fields_Odivision__ring,type,
division_ring:
!>[A: $tType] : $o ).
tff(sy_cl_Rings_Olinordered__idom,type,
linordered_idom:
!>[A: $tType] : $o ).
tff(sy_cl_Fields_Olinordered__field,type,
linordered_field:
!>[A: $tType] : $o ).
tff(sy_cl_Fields_Ofield__inverse__zero,type,
field_inverse_zero:
!>[A: $tType] : $o ).
tff(sy_cl_Fields_Odivision__ring__inverse__zero,type,
divisi14063676e_zero:
!>[A: $tType] : $o ).
tff(sy_cl_Fields_Olinordered__field__inverse__zero,type,
linord1117847801e_zero:
!>[A: $tType] : $o ).
tff(sy_c_Fields_Oinverse__class_Odivide,type,
inverse_divide:
!>[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_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_Orderings_Oord__class_Omin,type,
ord_min:
!>[A: $tType] : ( ( A * A ) > A ) ).
tff(sy_c_aa,type,
aa:
!>[A: $tType,B2: $tType] : ( ( fun(A,B2) * A ) > B2 ) ).
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_d1,type,
d1: real ).
tff(sy_v_d2,type,
d2: real ).
%----Relevant facts (98)
tff(fact_0_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_1_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_2_number__of__Pls,axiom,
! [A: $tType] :
( number_ring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_3_half__gt__zero__iff,axiom,
! [A: $tType] :
( ( linord1117847801e_zero(A)
& number_ring(A) )
=> ! [R1: A] :
( ord_less(A,zero_zero(A),inverse_divide(A,R1,number_number_of(A,bit0(bit1(pls)))))
<=> ord_less(A,zero_zero(A),R1) ) ) ).
tff(fact_4_half__gt__zero,axiom,
! [A: $tType] :
( ( linord1117847801e_zero(A)
& number_ring(A) )
=> ! [R: A] :
( ord_less(A,zero_zero(A),R)
=> ord_less(A,zero_zero(A),inverse_divide(A,R,number_number_of(A,bit0(bit1(pls))))) ) ) ).
tff(fact_5_min__less__iff__conj,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y1: A,X1: A,Z1: A] :
( ord_less(A,Z1,ord_min(A,X1,Y1))
<=> ( ord_less(A,Z1,X1)
& ord_less(A,Z1,Y1) ) ) ) ).
tff(fact_6_Bit0__Pls,axiom,
bit0(pls) = pls ).
tff(fact_7_rel__simps_I38_J,axiom,
! [L: int] :
( ( pls = bit0(L) )
<=> ( pls = L ) ) ).
tff(fact_8_rel__simps_I44_J,axiom,
! [K3: int] :
( ( bit0(K3) = pls )
<=> ( K3 = pls ) ) ).
tff(fact_9_rel__simps_I49_J,axiom,
! [L1: int,K: int] : bit0(K) != bit1(L1) ).
tff(fact_10_rel__simps_I50_J,axiom,
! [L1: int,K: int] : bit1(K) != bit0(L1) ).
tff(fact_11_rel__simps_I39_J,axiom,
! [L1: int] : pls != bit1(L1) ).
tff(fact_12_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_13_rel__simps_I51_J,axiom,
! [L: int,K3: int] :
( ( bit1(K3) = bit1(L) )
<=> ( K3 = L ) ) ).
tff(fact_14_rel__simps_I48_J,axiom,
! [L: int,K3: int] :
( ( bit0(K3) = bit0(L) )
<=> ( K3 = L ) ) ).
tff(fact_15_rel__simps_I46_J,axiom,
! [K: int] : bit1(K) != pls ).
tff(fact_16_rel__simps_I17_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit1(K3),bit1(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_17_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls) ).
tff(fact_18_rel__simps_I14_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit0(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_19_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_20_rel__simps_I12_J,axiom,
! [K3: int] :
( ord_less(int,bit1(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_21_rel__simps_I16_J,axiom,
! [L: int,K3: int] :
( ord_less(int,bit1(K3),bit0(L))
<=> ord_less(int,K3,L) ) ).
tff(fact_22_rel__simps_I10_J,axiom,
! [K3: int] :
( ord_less(int,bit0(K3),pls)
<=> ord_less(int,K3,pls) ) ).
tff(fact_23_rel__simps_I4_J,axiom,
! [K3: int] :
( ord_less(int,pls,bit0(K3))
<=> ord_less(int,pls,K3) ) ).
tff(fact_24_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls) ).
tff(fact_25_bin__less__0__simps_I1_J,axiom,
~ ord_less(int,pls,zero_zero(int)) ).
tff(fact_26_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_27_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_28_less__number__of__int__code,axiom,
! [L: int,K3: int] :
( ord_less(int,number_number_of(int,K3),number_number_of(int,L))
<=> ord_less(int,K3,L) ) ).
tff(fact_29_less__int__code_I16_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit1(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_30_less__int__code_I13_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit0(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_31_Pls__def,axiom,
pls = zero_zero(int) ).
tff(fact_32_less__int__code_I15_J,axiom,
! [K2: int,K1: int] :
( ord_less(int,bit1(K1),bit0(K2))
<=> ord_less(int,K1,K2) ) ).
tff(fact_33_linorder__cases,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y: A,X: A] :
( ~ ord_less(A,X,Y)
=> ( ( X != Y )
=> ord_less(A,Y,X) ) ) ) ).
tff(fact_34_order__less__asym,axiom,
! [A: $tType] :
( preorder(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
=> ~ ord_less(A,Y,X) ) ) ).
tff(fact_35_order__less__trans,axiom,
! [A: $tType] :
( preorder(A)
=> ! [Z: A,Y: A,X: A] :
( ord_less(A,X,Y)
=> ( ord_less(A,Y,Z)
=> ord_less(A,X,Z) ) ) ) ).
tff(fact_36_ord__less__eq__trans,axiom,
! [A: $tType] :
( ord(A)
=> ! [C: A,B: A,A1: A] :
( ord_less(A,A1,B)
=> ( ( B = C )
=> ord_less(A,A1,C) ) ) ) ).
tff(fact_37_ord__eq__less__trans,axiom,
! [A: $tType] :
( ord(A)
=> ! [C: A,B: A,A1: A] :
( ( A1 = B )
=> ( ord_less(A,B,C)
=> ord_less(A,A1,C) ) ) ) ).
tff(fact_38_order__less__asym_H,axiom,
! [A: $tType] :
( preorder(A)
=> ! [B: A,A1: A] :
( ord_less(A,A1,B)
=> ~ ord_less(A,B,A1) ) ) ).
tff(fact_39_order__less__imp__triv,axiom,
! [A: $tType] :
( preorder(A)
=> ! [P: bool,Y1: A,X1: A] :
( ord_less(A,X1,Y1)
=> ( ord_less(A,Y1,X1)
=> pp(P) ) ) ) ).
tff(fact_40_order__less__imp__not__eq2,axiom,
! [A: $tType] :
( order(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
=> ( Y != X ) ) ) ).
tff(fact_41_order__less__imp__not__eq,axiom,
! [A: $tType] :
( order(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
=> ( X != Y ) ) ) ).
tff(fact_42_order__less__imp__not__less,axiom,
! [A: $tType] :
( preorder(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
=> ~ ord_less(A,Y,X) ) ) ).
tff(fact_43_order__less__not__sym,axiom,
! [A: $tType] :
( preorder(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
=> ~ ord_less(A,Y,X) ) ) ).
tff(fact_44_less__imp__neq,axiom,
! [A: $tType] :
( order(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
=> ( X != Y ) ) ) ).
tff(fact_45_linorder__neqE,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y: A,X: A] :
( ( X != Y )
=> ( ~ ord_less(A,X,Y)
=> ord_less(A,Y,X) ) ) ) ).
tff(fact_46_linorder__antisym__conv3,axiom,
! [A: $tType] :
( linorder(A)
=> ! [X1: A,Y1: A] :
( ~ ord_less(A,Y1,X1)
=> ( ~ ord_less(A,X1,Y1)
<=> ( X1 = Y1 ) ) ) ) ).
tff(fact_47_linorder__less__linear,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,Y)
| ( X = Y )
| ord_less(A,Y,X) ) ) ).
tff(fact_48_not__less__iff__gr__or__eq,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y1: A,X1: A] :
( ~ ord_less(A,X1,Y1)
<=> ( ord_less(A,Y1,X1)
| ( X1 = Y1 ) ) ) ) ).
tff(fact_49_linorder__neq__iff,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y1: A,X1: A] :
( ( X1 != Y1 )
<=> ( ord_less(A,X1,Y1)
| ord_less(A,Y1,X1) ) ) ) ).
tff(fact_50_order__less__irrefl,axiom,
! [A: $tType] :
( preorder(A)
=> ! [X: A] : ~ ord_less(A,X,X) ) ).
tff(fact_51_number__of__reorient,axiom,
! [A: $tType] :
( number(A)
=> ! [X1: A,W: int] :
( ( number_number_of(A,W) = X1 )
<=> ( X1 = number_number_of(A,W) ) ) ) ).
tff(fact_52_min__less__iff__disj,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Z1: A,Y1: A,X1: A] :
( ord_less(A,ord_min(A,X1,Y1),Z1)
<=> ( ord_less(A,X1,Z1)
| ord_less(A,Y1,Z1) ) ) ) ).
tff(fact_53_semiring__numeral__0__eq__0,axiom,
! [A: $tType] :
( number_semiring(A)
=> ( number_number_of(A,pls) = zero_zero(A) ) ) ).
tff(fact_54_divide__Numeral0,axiom,
! [A: $tType] :
( ( field_inverse_zero(A)
& number_ring(A) )
=> ! [X: A] : inverse_divide(A,X,number_number_of(A,pls)) = zero_zero(A) ) ).
tff(fact_55_divide__Numeral1,axiom,
! [A: $tType] :
( ( field(A)
& number_ring(A) )
=> ! [X: A] : inverse_divide(A,X,number_number_of(A,bit1(pls))) = X ) ).
tff(fact_56_divide__numeral__1,axiom,
! [A: $tType] :
( ( field(A)
& number_ring(A) )
=> ! [A1: A] : inverse_divide(A,A1,number_number_of(A,bit1(pls))) = A1 ) ).
tff(fact_57_less__0__number__of,axiom,
! [V: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,V))
<=> ord_less(int,pls,V) ) ).
tff(fact_58_less__nat__number__of,axiom,
! [V1: int,V: int] :
( ord_less(nat,number_number_of(nat,V),number_number_of(nat,V1))
<=> ( ( ord_less(int,V,V1)
=> ord_less(int,pls,V1) )
& ord_less(int,V,V1) ) ) ).
tff(fact_59_divide__zero,axiom,
! [A: $tType] :
( divisi14063676e_zero(A)
=> ! [A1: A] : inverse_divide(A,A1,zero_zero(A)) = zero_zero(A) ) ).
tff(fact_60_divide__zero__left,axiom,
! [A: $tType] :
( division_ring(A)
=> ! [A1: A] : inverse_divide(A,zero_zero(A),A1) = zero_zero(A) ) ).
tff(fact_61_pos2,axiom,
ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))) ).
tff(fact_62_semiring__norm_I112_J,axiom,
! [A: $tType] :
( number_ring(A)
=> ( zero_zero(A) = number_number_of(A,pls) ) ) ).
tff(fact_63_divide__strict__right__mono__neg,axiom,
! [A: $tType] :
( linordered_field(A)
=> ! [C: A,A1: A,B: A] :
( ord_less(A,B,A1)
=> ( ord_less(A,C,zero_zero(A))
=> ord_less(A,inverse_divide(A,A1,C),inverse_divide(A,B,C)) ) ) ) ).
tff(fact_64_divide__strict__right__mono,axiom,
! [A: $tType] :
( linordered_field(A)
=> ! [C: A,B: A,A1: A] :
( ord_less(A,A1,B)
=> ( ord_less(A,zero_zero(A),C)
=> ord_less(A,inverse_divide(A,A1,C),inverse_divide(A,B,C)) ) ) ) ).
tff(fact_65_divide__neg__neg,axiom,
! [A: $tType] :
( linordered_field(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,zero_zero(A))
=> ( ord_less(A,Y,zero_zero(A))
=> ord_less(A,zero_zero(A),inverse_divide(A,X,Y)) ) ) ) ).
tff(fact_66_nat__number__of__Pls,axiom,
number_number_of(nat,pls) = zero_zero(nat) ).
tff(fact_67_number__of__is__id,axiom,
! [K: int] : number_number_of(int,K) = K ).
tff(fact_68_semiring__norm_I113_J,axiom,
zero_zero(nat) = number_number_of(nat,pls) ).
tff(fact_69_zero__less__divide__iff,axiom,
! [A: $tType] :
( linord1117847801e_zero(A)
=> ! [B1: A,A2: A] :
( ord_less(A,zero_zero(A),inverse_divide(A,A2,B1))
<=> ( ( ord_less(A,zero_zero(A),A2)
& ord_less(A,zero_zero(A),B1) )
| ( ord_less(A,A2,zero_zero(A))
& ord_less(A,B1,zero_zero(A)) ) ) ) ) ).
tff(fact_70_divide__less__0__iff,axiom,
! [A: $tType] :
( linord1117847801e_zero(A)
=> ! [B1: A,A2: A] :
( ord_less(A,inverse_divide(A,A2,B1),zero_zero(A))
<=> ( ( ord_less(A,zero_zero(A),A2)
& ord_less(A,B1,zero_zero(A)) )
| ( ord_less(A,A2,zero_zero(A))
& ord_less(A,zero_zero(A),B1) ) ) ) ) ).
tff(fact_71_divide__less__cancel,axiom,
! [A: $tType] :
( linord1117847801e_zero(A)
=> ! [B1: A,C1: A,A2: A] :
( ord_less(A,inverse_divide(A,A2,C1),inverse_divide(A,B1,C1))
<=> ( ( ord_less(A,zero_zero(A),C1)
=> ord_less(A,A2,B1) )
& ( ord_less(A,C1,zero_zero(A))
=> ord_less(A,B1,A2) )
& ( C1 != zero_zero(A) ) ) ) ) ).
tff(fact_72_divide__pos__pos,axiom,
! [A: $tType] :
( linordered_field(A)
=> ! [Y: A,X: A] :
( ord_less(A,zero_zero(A),X)
=> ( ord_less(A,zero_zero(A),Y)
=> ord_less(A,zero_zero(A),inverse_divide(A,X,Y)) ) ) ) ).
tff(fact_73_divide__pos__neg,axiom,
! [A: $tType] :
( linordered_field(A)
=> ! [Y: A,X: A] :
( ord_less(A,zero_zero(A),X)
=> ( ord_less(A,Y,zero_zero(A))
=> ord_less(A,inverse_divide(A,X,Y),zero_zero(A)) ) ) ) ).
tff(fact_74_divide__neg__pos,axiom,
! [A: $tType] :
( linordered_field(A)
=> ! [Y: A,X: A] :
( ord_less(A,X,zero_zero(A))
=> ( ord_less(A,zero_zero(A),Y)
=> ord_less(A,inverse_divide(A,X,Y),zero_zero(A)) ) ) ) ).
tff(fact_75_neq0__conv,axiom,
! [N1: nat] :
( ( N1 != zero_zero(nat) )
<=> ord_less(nat,zero_zero(nat),N1) ) ).
tff(fact_76_less__nat__zero__code,axiom,
! [N: nat] : ~ ord_less(nat,N,zero_zero(nat)) ).
tff(fact_77_less__zeroE,axiom,
! [N: nat] : ~ ord_less(nat,N,zero_zero(nat)) ).
tff(fact_78_min__0R,axiom,
! [N: nat] : ord_min(nat,N,zero_zero(nat)) = zero_zero(nat) ).
tff(fact_79_min__0L,axiom,
! [N: nat] : ord_min(nat,zero_zero(nat),N) = zero_zero(nat) ).
tff(fact_80_nat__less__cases,axiom,
! [P: fun(nat,fun(nat,bool)),N1: nat,M1: nat] :
( ( ord_less(nat,M1,N1)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N1),M1)) )
=> ( ( ( M1 = N1 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N1),M1)) )
=> ( ( ord_less(nat,N1,M1)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N1),M1)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),P,N1),M1)) ) ) ) ).
tff(fact_81_less__not__refl3,axiom,
! [T: nat,S: nat] :
( ord_less(nat,S,T)
=> ( S != T ) ) ).
tff(fact_82_less__not__refl2,axiom,
! [M: nat,N: nat] :
( ord_less(nat,N,M)
=> ( M != N ) ) ).
tff(fact_83_less__irrefl__nat,axiom,
! [N: nat] : ~ ord_less(nat,N,N) ).
tff(fact_84_linorder__neqE__nat,axiom,
! [Y: nat,X: nat] :
( ( X != Y )
=> ( ~ ord_less(nat,X,Y)
=> ord_less(nat,Y,X) ) ) ).
tff(fact_85_nat__neq__iff,axiom,
! [N1: nat,M1: nat] :
( ( M1 != N1 )
<=> ( ord_less(nat,M1,N1)
| ord_less(nat,N1,M1) ) ) ).
tff(fact_86_less__not__refl,axiom,
! [N: nat] : ~ ord_less(nat,N,N) ).
tff(fact_87_gr0I,axiom,
! [N: nat] :
( ( N != zero_zero(nat) )
=> ord_less(nat,zero_zero(nat),N) ) ).
tff(fact_88_gr__implies__not0,axiom,
! [N: nat,M: nat] :
( ord_less(nat,M,N)
=> ( N != zero_zero(nat) ) ) ).
tff(fact_89_not__less0,axiom,
! [N: nat] : ~ ord_less(nat,N,zero_zero(nat)) ).
tff(fact_90_min__max_Oinf__left__idem,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y: A,X: A] : ord_min(A,X,ord_min(A,X,Y)) = ord_min(A,X,Y) ) ).
tff(fact_91_min__max_Oinf_Oleft__idem,axiom,
! [A: $tType] :
( linorder(A)
=> ! [B: A,A1: A] : ord_min(A,A1,ord_min(A,A1,B)) = ord_min(A,A1,B) ) ).
tff(fact_92_min__max_Oinf_Oidem,axiom,
! [A: $tType] :
( linorder(A)
=> ! [A1: A] : ord_min(A,A1,A1) = A1 ) ).
tff(fact_93_min__max_Oinf_Ocommute,axiom,
! [A: $tType] :
( linorder(A)
=> ! [B: A,A1: A] : ord_min(A,A1,B) = ord_min(A,B,A1) ) ).
tff(fact_94_min__max_Oinf__commute,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Y: A,X: A] : ord_min(A,X,Y) = ord_min(A,Y,X) ) ).
tff(fact_95_min__max_Oinf_Oleft__commute,axiom,
! [A: $tType] :
( linorder(A)
=> ! [C: A,A1: A,B: A] : ord_min(A,B,ord_min(A,A1,C)) = ord_min(A,A1,ord_min(A,B,C)) ) ).
tff(fact_96_min__max_Oinf__left__commute,axiom,
! [A: $tType] :
( linorder(A)
=> ! [Z: A,Y: A,X: A] : ord_min(A,X,ord_min(A,Y,Z)) = ord_min(A,Y,ord_min(A,X,Z)) ) ).
tff(fact_97_min__max_Oinf_Oassoc,axiom,
! [A: $tType] :
( linorder(A)
=> ! [C: A,B: A,A1: A] : ord_min(A,ord_min(A,A1,B),C) = ord_min(A,A1,ord_min(A,B,C)) ) ).
%----Arities (34)
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___Orderings_Opreorder,axiom,
preorder(int) ).
tff(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int) ).
tff(arity_Int_Oint___Orderings_Oorder,axiom,
order(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___Orderings_Oord,axiom,
ord(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___Orderings_Opreorder,axiom,
preorder(nat) ).
tff(arity_Nat_Onat___Orderings_Olinorder,axiom,
linorder(nat) ).
tff(arity_Nat_Onat___Orderings_Oorder,axiom,
order(nat) ).
tff(arity_Nat_Onat___Orderings_Oord,axiom,
ord(nat) ).
tff(arity_Nat_Onat___Int_Onumber,axiom,
number(nat) ).
tff(arity_HOL_Obool___Orderings_Opreorder,axiom,
preorder(bool) ).
tff(arity_HOL_Obool___Orderings_Olinorder,axiom,
linorder(bool) ).
tff(arity_HOL_Obool___Orderings_Oorder,axiom,
order(bool) ).
tff(arity_HOL_Obool___Orderings_Oord,axiom,
ord(bool) ).
tff(arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero,axiom,
linord1117847801e_zero(real) ).
tff(arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero,axiom,
divisi14063676e_zero(real) ).
tff(arity_RealDef_Oreal___Fields_Ofield__inverse__zero,axiom,
field_inverse_zero(real) ).
tff(arity_RealDef_Oreal___Fields_Olinordered__field,axiom,
linordered_field(real) ).
tff(arity_RealDef_Oreal___Rings_Olinordered__idom,axiom,
linordered_idom(real) ).
tff(arity_RealDef_Oreal___Fields_Odivision__ring,axiom,
division_ring(real) ).
tff(arity_RealDef_Oreal___Int_Onumber__semiring,axiom,
number_semiring(real) ).
tff(arity_RealDef_Oreal___Orderings_Opreorder,axiom,
preorder(real) ).
tff(arity_RealDef_Oreal___Orderings_Olinorder,axiom,
linorder(real) ).
tff(arity_RealDef_Oreal___Orderings_Oorder,axiom,
order(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___Orderings_Oord,axiom,
ord(real) ).
tff(arity_RealDef_Oreal___Fields_Ofield,axiom,
field(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 (3)
tff(conj_0,hypothesis,
ord_less(real,zero_zero(real),d1) ).
tff(conj_1,hypothesis,
ord_less(real,zero_zero(real),d2) ).
tff(conj_2,conjecture,
( ord_less(real,zero_zero(real),inverse_divide(real,ord_min(real,d1,d2),number_number_of(real,bit0(bit1(pls)))))
& ord_less(real,inverse_divide(real,ord_min(real,d1,d2),number_number_of(real,bit0(bit1(pls)))),d1)
& ord_less(real,inverse_divide(real,ord_min(real,d1,d2),number_number_of(real,bit0(bit1(pls)))),d2) ) ).
%------------------------------------------------------------------------------