%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV629-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:58:24 AM UTC 2026
% Result : Unsatisfiable 37.31s 6.55s
% Output : CNFRefutation 37.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 390
% Syntax : Number of formulae : 2965 (1805 unt; 0 typ; 0 def)
% Number of atoms : 15465 (6958 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 34206 (3305 ~;4644 |; 0 &;26257 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 54 ( 51 usr; 5 con; 0-3 aty)
% Number of variables : 7452 ( 0 ^;7452 !; 0 ?;7452 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Complex_Ocnj,type,
c_Complex_Ocnj: $i > $i ).
thf(tp_c_Complex_Oii,type,
c_Complex_Oii: $i ).
thf(tp_c_Divides_Odiv__class_Odiv,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).
thf(tp_c_FFT__Mirabelle_Oroot,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
thf(tp_c_Fact_Ofact__class_Ofact,type,
c_Fact_Ofact__class_Ofact: $i > $i > $i ).
thf(tp_c_GCD_Ogcd__class_Ogcd,type,
c_GCD_Ogcd__class_Ogcd: $i > $i > $i > $i ).
thf(tp_c_GCD_Ogcd__class_Olcm,type,
c_GCD_Ogcd__class_Olcm: $i > $i > $i > $i ).
thf(tp_c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(tp_c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(tp_c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(tp_c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tp_c_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: $i > $i > $i ).
thf(tp_c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_Int_Oiszero,type,
c_Int_Oiszero: $i > $i > $o ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(tp_c_Parity_Oeven__odd__class_Oeven,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(tp_class_Divides_Osemiring__div,type,
class_Divides_Osemiring__div: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(tp_class_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra__1,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__div__algebra,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__vector,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Odvd,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(tp_class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Osgn__if,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_tc_Complex_Ocomplex,type,
tc_Complex_Ocomplex: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(1,axiom,
class_Power_Opower @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
thf(2,axiom,
class_Int_Onumber__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
thf(3,axiom,
class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
thf(4,axiom,
class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
thf(5,axiom,
class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
thf(6,axiom,
class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
thf(7,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
thf(8,axiom,
class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
thf(9,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
thf(10,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
thf(11,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
thf(12,axiom,
class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
thf(13,axiom,
class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
thf(14,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
thf(15,axiom,
class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
thf(16,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
thf(17,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
thf(18,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
thf(19,axiom,
class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
thf(20,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
thf(21,axiom,
class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
thf(22,axiom,
class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
thf(23,axiom,
class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
thf(24,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(25,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(26,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(27,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(28,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(29,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(30,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(31,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(32,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(33,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(34,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
thf(35,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(36,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(37,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(38,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
thf(39,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).
thf(40,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(41,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).
thf(42,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__one_0) ).
thf(43,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).
thf(44,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).
thf(45,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
thf(46,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
thf(47,axiom,
! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).
thf(48,axiom,
! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_n @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).
thf(49,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
thf(50,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
thf(51,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
thf(52,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
thf(53,axiom,
( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).
thf(54,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(55,axiom,
! [V_n: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ V_n ) @ V_n @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).
thf(56,axiom,
( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__1__nat_0) ).
thf(57,axiom,
! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Obot__least_0) ).
thf(58,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(59,axiom,
! [V_m: $i] :
( ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).
thf(60,axiom,
! [V_m: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__1__nat_0) ).
thf(61,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__bot__left_0) ).
thf(62,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__bot__right_0) ).
thf(63,axiom,
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__1__nat_0) ).
thf(64,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
thf(65,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(66,axiom,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root0_0) ).
thf(67,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(68,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(69,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(70,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_1) ).
thf(71,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_0) ).
thf(72,axiom,
! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq1_0) ).
thf(73,axiom,
! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__eq__bot__eq2_0) ).
thf(74,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__bot__left_0) ).
thf(75,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__bot__right_0) ).
thf(76,axiom,
( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
thf(77,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(78,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(79,axiom,
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__1__iff__nat_2) ).
thf(80,axiom,
( ( c_Complex_Ocnj @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
thf(81,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(82,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(83,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
thf(84,axiom,
! [V_n: $i] :
( ( c_FFT__Mirabelle_Oroot @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__nonzero_0) ).
thf(85,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).
thf(86,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).
thf(87,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
thf(88,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
thf(89,axiom,
! [T_a: $i,V_l: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_l @ T_a )
!= ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_l @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(90,axiom,
! [T_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) @ V_c @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
thf(91,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_0) ).
thf(92,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_0) ).
thf(93,axiom,
! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq2_0) ).
thf(94,axiom,
! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq1_0) ).
thf(95,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__zero__nat_0) ).
thf(96,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__zero__nat_1) ).
thf(97,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) @ ( c_HOL_Osgn__class_Osgn @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).
thf(98,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_x @ T_a ) @ ( c_HOL_Osgn__class_Osgn @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
thf(99,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).
thf(100,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_w: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a )
!= ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_w @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
thf(101,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
!= ( c_HOL_Oinverse__class_Odivide @ V_w @ V_z @ T_a ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
thf(102,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__left__idem_0) ).
thf(103,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(104,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__commute_0) ).
thf(105,axiom,
! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__commute__nat_0) ).
thf(106,axiom,
! [V_y: $i,V_x: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
thf(107,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(108,axiom,
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__zero__nat_2) ).
thf(109,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
!= V_x )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__iff__inf_1) ).
thf(110,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__proj1__if__dvd__nat_0) ).
thf(111,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__proj2__if__dvd__nat_0) ).
thf(112,axiom,
! [V_d: $i,V_b: $i,V_a: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_a @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__mult__nat_0) ).
thf(113,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_d @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(114,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(115,axiom,
( c_Complex_Oii
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
thf(116,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__0_0) ).
thf(117,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oinverse__class_Oinverse @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).
thf(118,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
thf(119,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Complex_Ocnj @ V_x )
!= ( c_Complex_Ocnj @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
thf(120,axiom,
! [V_z: $i] :
( ( ( c_Complex_Ocnj @ V_z )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
thf(121,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(122,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(123,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__assoc_0) ).
thf(124,axiom,
! [V_n: $i,V_m: $i,V_p: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ V_n @ V_m @ tc_nat ) @ V_p @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_n @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_p @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__assoc__nat_0) ).
thf(125,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_y @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__left__commute__nat_0) ).
thf(126,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
thf(127,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
thf(128,axiom,
! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
thf(129,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__mult__cancel__nat_0) ).
thf(130,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__left__idem_0) ).
thf(131,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(132,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(133,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(134,axiom,
! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(135,axiom,
! [T_a: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Int_Oiszero @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__def_0) ).
thf(136,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(137,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(138,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(139,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(140,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(141,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(142,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(143,axiom,
! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(144,axiom,
! [V_m: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(145,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(146,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(147,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(148,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(149,axiom,
! [T_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_c @ T_a )
= V_b )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).
thf(150,axiom,
! [T_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( V_b
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_c @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
thf(151,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(152,axiom,
! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
thf(153,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).
thf(154,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__assoc_0) ).
thf(155,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__assoc__nat_0) ).
thf(156,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__left__commute__nat_0) ).
thf(157,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(158,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(159,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(160,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ V_n @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
thf(161,axiom,
c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(162,axiom,
! [T_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).
thf(163,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(164,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(165,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(166,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
thf(167,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__commute_0) ).
thf(168,axiom,
! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__commute__nat_0) ).
thf(169,axiom,
! [V_z: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ V_z ) )
= V_z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
thf(170,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
thf(171,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
thf(172,axiom,
! [V_d: $i,V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_a @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__lmult__nat_0) ).
thf(173,axiom,
! [V_d: $i,V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_b @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__rmult__nat_0) ).
thf(174,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(175,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(176,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(177,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
thf(178,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_x @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__idem__nat_0) ).
thf(179,axiom,
! [V_m: $i,V_n: $i,V_k: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__dvd__prod__nat_0) ).
thf(180,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
thf(181,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(182,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__0__nat_0) ).
thf(183,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__0__left__nat_0) ).
thf(184,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prod__gcd__lcm__nat_0) ).
thf(185,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
thf(186,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
thf(187,axiom,
! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
thf(188,axiom,
! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
thf(189,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__greatest__iff__nat_2) ).
thf(190,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__greatest__nat_0) ).
thf(191,axiom,
! [V_e: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__unique__nat_5) ).
thf(192,axiom,
! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__unique__nat_4) ).
thf(193,axiom,
! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__unique__nat_3) ).
thf(194,axiom,
! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__dvd2__nat_0) ).
thf(195,axiom,
! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__dvd1__nat_0) ).
thf(196,axiom,
! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le1_0) ).
thf(197,axiom,
! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_y @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le2_0) ).
thf(198,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI_0) ).
thf(199,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_2) ).
thf(200,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_1) ).
thf(201,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_1) ).
thf(202,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__greatest_0) ).
thf(203,axiom,
! [V_x: $i,V_n: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ V_x ) @ V_n @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__power_0) ).
thf(204,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
thf(205,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(206,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(207,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ V_n @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__fact__not__zero_0) ).
thf(208,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_a @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
thf(209,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
thf(210,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
thf(211,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
thf(212,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
thf(213,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ V_x @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
thf(214,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__divide_0) ).
thf(216,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
thf(217,axiom,
! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(218,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
thf(219,axiom,
! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_x @ T_a ) @ V_n @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__even__abs_0) ).
thf(220,axiom,
( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__num__eq__if__nat_0) ).
thf(221,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ V_a @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
thf(222,axiom,
! [V_b: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ( V_b
!= ( c_HOL_Otimes__class_Otimes @ V_b_H @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
| ( V_a
!= ( c_HOL_Otimes__class_Otimes @ V_a_H @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_a_H @ V_b_H @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__coprime__nat_0) ).
thf(223,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(224,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(225,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(226,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(227,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_x @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__idem_0) ).
thf(228,axiom,
! [V_x: $i,V_y: $i,V_z: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Odistrib__inf__le_0) ).
thf(229,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(230,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(231,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_x @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(232,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(233,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(234,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(235,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(236,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(237,axiom,
( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
thf(238,axiom,
! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ V_q @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
thf(239,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(240,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(241,axiom,
! [T_a: $i,V_b: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_k @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(242,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(243,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(244,axiom,
! [V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__nat_2) ).
thf(245,axiom,
! [V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__nat_1) ).
thf(246,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(248,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__0__iff__nat_0) ).
thf(249,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__dvd__mult__nat_0) ).
thf(250,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__dvd__mult__iff__nat_1) ).
thf(251,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__lcm__I2__nat_0) ).
thf(252,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__lcm__I1__nat_0) ).
thf(253,axiom,
! [V_a: $i,V_x: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supE_0) ).
thf(254,axiom,
! [V_b: $i,V_x: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supE_1) ).
thf(255,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI1_0) ).
thf(256,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI2_0) ).
thf(257,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_0) ).
thf(258,axiom,
! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_1) ).
thf(259,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__proj2__if__dvd__nat_0) ).
thf(260,axiom,
! [V_y: $i,V_x: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_y @ V_x @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__proj1__if__dvd__nat_0) ).
thf(261,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= V_n )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__proj2__iff__nat_1) ).
thf(262,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= V_n )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__proj2__iff__nat_0) ).
thf(263,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= V_m )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__proj1__iff__nat_1) ).
thf(264,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= V_m )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__proj1__iff__nat_0) ).
thf(265,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
!= V_y )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__iff__sup_1) ).
thf(266,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__absorb1_0) ).
thf(267,axiom,
! [V_a: $i,V_b: $i,V_d: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_d
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__nat_0) ).
thf(268,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coprime__common__divisor__nat_0) ).
thf(269,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_x @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_x @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
thf(270,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(271,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(272,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
thf(273,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
thf(274,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(275,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(276,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(277,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(278,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
thf(279,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
thf(280,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(281,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(282,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(283,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a )
= V_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).
thf(284,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( V_a
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).
thf(285,axiom,
! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
thf(286,axiom,
! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).
thf(287,axiom,
! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
thf(288,axiom,
! [V_n: $i] :
( ( c_Fact_Ofact__class_Ofact @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fact__nonzero__nat_0) ).
thf(289,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(290,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(291,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(292,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
thf(293,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
thf(294,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI2_0) ).
thf(295,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI1_0) ).
thf(296,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(297,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
thf(298,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
thf(299,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
thf(300,axiom,
! [T_a: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_k @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Osgn__class_Osgn @ V_k @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
thf(301,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__mult__distrib__nat_0) ).
thf(302,axiom,
! [V_x: $i,V_y: $i,V_z: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_z @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Odistrib__sup__le_0) ).
thf(303,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) @ T_a )
= ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
thf(304,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
thf(305,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
thf(306,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).
thf(307,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).
thf(308,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
thf(309,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(310,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(311,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(312,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(313,axiom,
! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(314,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(315,axiom,
! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(316,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(317,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(318,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(319,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
thf(320,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
thf(321,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(322,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(323,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(324,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(325,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(326,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
thf(327,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(328,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(329,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(330,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__top__right_0) ).
thf(331,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Osup__top__left_0) ).
thf(332,axiom,
! [V_m: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__0__nat_0) ).
thf(333,axiom,
! [V_n: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__0__iff__nat_1) ).
thf(334,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(335,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(336,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(337,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(338,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI2_1) ).
thf(339,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Oless__supI1_1) ).
thf(340,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__sup__iff_2) ).
thf(341,axiom,
! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__least_0) ).
thf(342,axiom,
! [V_y: $i,V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__ge2_0) ).
thf(343,axiom,
! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Osup__ge1_0) ).
thf(344,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__semilattice__nat_Ole__supI_0) ).
thf(345,axiom,
! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__dvd1__nat_0) ).
thf(346,axiom,
! [V_n: $i,V_m: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__dvd2__nat_0) ).
thf(347,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_k @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__least__nat_0) ).
thf(348,axiom,
! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__unique__nat_3) ).
thf(349,axiom,
! [V_b: $i,V_a: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__unique__nat_4) ).
thf(350,axiom,
! [V_a: $i,V_b: $i,V_e: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_e @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_e @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_e @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lcm__unique__nat_5) ).
thf(351,axiom,
! [V_m: $i,V_n: $i,V_r: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_r @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_r @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_r @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divides__mult__nat_0) ).
thf(352,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
thf(353,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(354,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(355,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(356,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(357,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_w @ V_z @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_w @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_w @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
thf(358,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(359,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(360,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(361,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_z @ V_w @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_w @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
thf(362,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(363,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(364,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(365,axiom,
! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
thf(366,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(367,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(368,axiom,
! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
thf(369,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
thf(370,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
thf(371,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_1) ).
thf(372,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_0) ).
thf(373,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI2_0) ).
thf(374,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI1_0) ).
thf(375,axiom,
! [V_x: $i,V_b: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infE_1) ).
thf(376,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infE_0) ).
thf(377,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__gcd__D1__nat_0) ).
thf(378,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__gcd__D2__nat_0) ).
thf(379,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Oinf__sup__absorb_0) ).
thf(380,axiom,
! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
thf(381,axiom,
! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
thf(382,axiom,
! [V_y: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
thf(383,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
thf(384,axiom,
! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
thf(385,axiom,
! [V_b: $i,V_a: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_a @ tc_nat )
| ( V_a = V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
thf(386,axiom,
! [V_b: $i,V_a: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ tc_nat )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
thf(387,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(388,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__lattice__nat_Osup__inf__absorb_0) ).
thf(389,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(390,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[389]) ).
thf(391,negated_conjecture,
( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(392,plain,
$false = $false,
inference(unfold_def,[status(thm)],[390]) ).
thf(393,plain,
( ( class_Power_Opower @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(394,plain,
( ( class_Int_Onumber__ring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(395,plain,
( ( class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(396,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(397,plain,
( ( class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(398,plain,
( ( class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(399,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(400,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(401,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(402,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(403,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(404,plain,
( ( class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(405,plain,
( ( class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(406,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(407,plain,
( ( class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(408,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(409,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(410,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(411,plain,
( ( class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(412,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(413,plain,
( ( class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(414,plain,
( ( class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(415,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(416,plain,
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(417,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(418,plain,
( ( class_Ring__and__Field_Odvd @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(419,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(420,plain,
( ( class_Divides_Osemiring__div @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(421,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(422,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(423,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(424,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(425,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(426,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(427,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(428,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(429,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(430,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(431,plain,
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(432,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(433,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(434,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(435,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(436,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(437,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(438,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(439,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(440,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(441,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(442,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(443,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(444,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(445,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(446,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(447,plain,
( ( ! [V_n: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ V_n ) @ V_n @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(448,plain,
( ( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(449,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(450,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(451,plain,
( ( ! [V_m: $i] :
( ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(452,plain,
( ( ! [V_m: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(453,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(454,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(455,plain,
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(456,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(457,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(458,plain,
( ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(459,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(460,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(461,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(462,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(463,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(464,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(465,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(466,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(467,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(468,plain,
( ( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(469,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(470,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(471,plain,
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(472,plain,
( ( ( c_Complex_Ocnj @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(473,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(474,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(475,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(476,plain,
( ( ! [V_n: $i] :
( ( c_FFT__Mirabelle_Oroot @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(477,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(478,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(479,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(480,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(481,plain,
( ( ! [T_a: $i,V_l: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_l @ T_a )
!= ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_l @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(482,plain,
( ( ! [T_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) @ V_c @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(483,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(484,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(485,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(486,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(487,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(488,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(489,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) @ ( c_HOL_Osgn__class_Osgn @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(490,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_x @ T_a ) @ ( c_HOL_Osgn__class_Osgn @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(491,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(492,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_w: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a )
!= ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_w @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(493,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
!= ( c_HOL_Oinverse__class_Odivide @ V_w @ V_z @ T_a ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(494,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(495,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(496,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(497,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(498,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(499,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(500,plain,
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(501,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
!= V_x )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(502,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(503,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(504,plain,
( ( ! [V_d: $i,V_b: $i,V_a: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_a @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(505,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_d @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(506,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(507,plain,
( ( c_Complex_Oii
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(508,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(509,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oinverse__class_Oinverse @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(510,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(511,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Complex_Ocnj @ V_x )
!= ( c_Complex_Ocnj @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(512,plain,
( ( ! [V_z: $i] :
( ( ( c_Complex_Ocnj @ V_z )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(513,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(514,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(515,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(516,plain,
( ( ! [V_n: $i,V_m: $i,V_p: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ V_n @ V_m @ tc_nat ) @ V_p @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_n @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_p @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(517,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_y @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(518,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(519,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(520,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(521,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(522,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(523,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(524,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(525,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(526,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(527,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Int_Oiszero @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(528,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(529,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(530,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(531,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(532,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(533,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(534,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(535,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(536,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(537,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(538,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(539,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(540,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(541,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_c @ T_a )
= V_b )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(542,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( V_b
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_c @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(543,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(544,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(545,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(546,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(547,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(548,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(549,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(550,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(551,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(552,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ V_n @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(553,plain,
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(554,plain,
( ( ! [T_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(555,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(556,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(557,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(558,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(559,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(560,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(561,plain,
( ( ! [V_z: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ V_z ) )
= V_z ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(562,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(563,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(564,plain,
( ( ! [V_d: $i,V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_a @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(565,plain,
( ( ! [V_d: $i,V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_b @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(566,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(567,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(568,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(569,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(570,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(571,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(572,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(573,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(574,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(575,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(576,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(577,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(578,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(579,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(580,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(581,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(582,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(583,plain,
( ( ! [V_e: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(584,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(585,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(586,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(587,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(588,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(589,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_y @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(590,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(591,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(592,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(593,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(594,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(595,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ V_x ) @ V_n @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(596,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(597,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(598,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(599,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ V_n @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(600,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_a @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(601,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(602,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(603,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(604,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(605,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ V_x @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(606,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(607,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(608,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(609,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(610,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(611,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_x @ T_a ) @ V_n @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(612,plain,
( ( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(613,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ V_a @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(614,plain,
( ( ! [V_b: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ( V_b
!= ( c_HOL_Otimes__class_Otimes @ V_b_H @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
| ( V_a
!= ( c_HOL_Otimes__class_Otimes @ V_a_H @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_a_H @ V_b_H @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(615,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(616,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(617,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(618,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(619,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(620,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(621,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(622,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(623,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_x @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(624,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(625,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(626,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(627,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(628,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(629,plain,
( ( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(630,plain,
( ( ! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ V_q @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(631,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(632,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(633,plain,
( ( ! [T_a: $i,V_b: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(634,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(635,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(636,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(637,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(638,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(639,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(640,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(641,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(642,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(643,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(644,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(645,plain,
( ( ! [V_a: $i,V_x: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(646,plain,
( ( ! [V_b: $i,V_x: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(647,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(648,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(649,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(650,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(651,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(652,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_y @ V_x @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(653,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= V_n )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(654,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= V_n )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(655,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= V_m )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(656,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= V_m )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(657,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
!= V_y )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(658,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(659,plain,
( ( ! [V_a: $i,V_b: $i,V_d: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_d
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(660,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(661,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_x @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_x @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(662,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(663,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(664,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(665,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(666,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(667,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(668,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(669,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(670,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(671,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(672,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(673,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(674,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(675,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a )
= V_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(676,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( V_a
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(677,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(678,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(679,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(680,plain,
( ( ! [V_n: $i] :
( ( c_Fact_Ofact__class_Ofact @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(681,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(682,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(683,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(684,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(685,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(686,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(687,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(688,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(689,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(690,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(691,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(692,plain,
( ( ! [T_a: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_k @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Osgn__class_Osgn @ V_k @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(693,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(694,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_z @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(695,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) @ T_a )
= ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(696,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(697,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(698,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(699,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(700,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(701,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(702,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(703,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(704,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(705,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(706,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(707,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(708,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(709,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(710,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(711,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(712,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(713,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(714,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(715,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(716,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(717,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(718,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(719,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(720,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(721,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(722,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(723,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(724,plain,
( ( ! [V_m: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(725,plain,
( ( ! [V_n: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(726,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(727,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(728,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(729,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(730,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(731,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(732,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(733,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(734,plain,
( ( ! [V_y: $i,V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(735,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(736,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(737,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(738,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(739,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_k @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(740,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(741,plain,
( ( ! [V_b: $i,V_a: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(742,plain,
( ( ! [V_a: $i,V_b: $i,V_e: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_e @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_e @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_e @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(743,plain,
( ( ! [V_m: $i,V_n: $i,V_r: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_r @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_r @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_r @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(744,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(745,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(746,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(747,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(748,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(749,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_w @ V_z @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_w @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_w @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(750,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(751,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(752,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(753,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_z @ V_w @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_w @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(754,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(755,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(756,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(757,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(758,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(759,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(760,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(761,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(762,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(763,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(764,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(765,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(766,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(767,plain,
( ( ! [V_x: $i,V_b: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(768,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(769,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(770,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(771,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(772,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(773,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(774,plain,
( ( ! [V_y: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(775,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(776,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(777,plain,
( ( ! [V_b: $i,V_a: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_a @ tc_nat )
| ( V_a = V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(778,plain,
( ( ! [V_b: $i,V_a: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ tc_nat )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(779,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(780,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(781,plain,
( ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(782,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[392]) ).
thf(783,plain,
( ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(784,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(785,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(786,plain,
( ( ! [V_b: $i,V_a: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ tc_nat )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(787,plain,
( ( ! [V_b: $i,V_a: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_a @ tc_nat )
| ( V_a = V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(788,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(789,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(790,plain,
( ( ! [V_y: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(791,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(792,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(793,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(794,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(795,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(796,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(797,plain,
( ( ! [V_x: $i,V_b: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(798,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(799,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(800,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(801,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(802,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(803,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(804,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(805,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(806,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(807,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(808,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(809,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(810,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(811,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_z @ V_w @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_w @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(812,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(813,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(814,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(815,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_w @ V_z @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_w @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_w @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(816,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(817,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(818,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(819,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(820,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(821,plain,
( ( ! [V_m: $i,V_n: $i,V_r: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_r @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_r @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_r @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(822,plain,
( ( ! [V_a: $i,V_b: $i,V_e: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_e @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_e @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_e @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(823,plain,
( ( ! [V_b: $i,V_a: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(824,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(825,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_k @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(826,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(827,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(828,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(829,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(830,plain,
( ( ! [V_y: $i,V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(831,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(832,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(833,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(834,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(835,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(836,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(837,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(838,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(839,plain,
( ( ! [V_n: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(840,plain,
( ( ! [V_m: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(841,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(842,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(843,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(844,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(845,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(846,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(847,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(848,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(849,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(850,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(851,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(852,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_q @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_x @ V_q @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_q @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(853,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(854,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(855,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(856,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(857,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ly @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(858,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_rx @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_rx @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(859,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ V_ry @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(860,plain,
( ( ! [T_a: $i,V_lx: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(861,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(862,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(863,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(864,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(865,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(866,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(867,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(868,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_Divides_Odiv__class_Odiv @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(869,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) @ T_a )
= ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(870,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_z @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(871,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(872,plain,
( ( ! [T_a: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_k @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Osgn__class_Osgn @ V_k @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(873,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(874,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ ( c_Divides_Odiv__class_Odiv @ V_c @ V_a @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_c @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(875,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(876,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(877,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(878,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(879,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(880,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(881,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(882,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(883,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(884,plain,
( ( ! [V_n: $i] :
( ( c_Fact_Ofact__class_Ofact @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(885,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(886,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(887,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(888,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( V_a
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(889,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ V_c @ T_a )
= V_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(890,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_rx @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(891,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_lx @ ( c_HOL_Otimes__class_Otimes @ V_ly @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(892,plain,
( ( ! [T_a: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_ly @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_rx @ V_ry @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ V_lx @ V_rx @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_ly @ V_ry @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(893,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(894,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= V_a )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(895,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(896,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(897,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(898,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(899,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(900,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(901,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(902,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(903,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_x @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_x @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[661]) ).
thf(904,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(905,plain,
( ( ! [V_a: $i,V_b: $i,V_d: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_d
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(906,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(907,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
!= V_y )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(908,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= V_m )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(909,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= V_m )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[655]) ).
thf(910,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= V_n )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(911,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= V_n )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[653]) ).
thf(912,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_y @ V_x @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(913,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(914,plain,
( ( ! [V_y: $i,V_z: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(915,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(916,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(917,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(918,plain,
( ( ! [V_b: $i,V_x: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(919,plain,
( ( ! [V_a: $i,V_x: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(920,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[644]) ).
thf(921,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[643]) ).
thf(922,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[642]) ).
thf(923,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(924,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[640]) ).
thf(925,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(926,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(927,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(928,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(929,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(930,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(931,plain,
( ( ! [T_a: $i,V_b: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(932,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(933,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[631]) ).
thf(934,plain,
( ( ! [T_a: $i,V_x: $i,V_p: $i,V_q: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_x @ V_p @ T_a ) @ V_q @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(935,plain,
( ( ( c_Complex_Ocnj @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(936,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(937,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(938,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(939,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(940,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(941,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_x @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(942,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[622]) ).
thf(943,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[621]) ).
thf(944,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(945,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(946,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(947,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(948,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(949,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(950,plain,
( ( ! [V_b: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ( V_b
!= ( c_HOL_Otimes__class_Otimes @ V_b_H @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
| ( V_a
!= ( c_HOL_Otimes__class_Otimes @ V_a_H @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_a_H @ V_b_H @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(951,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ V_a @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[613]) ).
thf(952,plain,
( ( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[612]) ).
thf(953,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_x @ T_a ) @ V_n @ T_a )
= ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(954,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(955,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(956,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(957,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[607]) ).
thf(958,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[606]) ).
thf(959,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ V_x @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(960,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(961,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(962,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(963,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(964,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ V_b @ V_a @ T_a ) @ V_a @ T_a )
= V_b )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[600]) ).
thf(965,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ V_n @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(966,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(967,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(968,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(969,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ V_x ) @ V_n @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(970,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[594]) ).
thf(971,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(972,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(973,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(974,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(975,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_y @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(976,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(977,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(978,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(979,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(980,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(981,plain,
( ( ! [V_e: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(982,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[582]) ).
thf(983,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(984,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(985,plain,
( ( ! [V_z: $i,V_x: $i,V_y: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(986,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(987,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(988,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(989,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(990,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(991,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(992,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(993,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(994,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(995,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(996,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_a @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(997,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(998,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(999,plain,
( ( ! [V_d: $i,V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_b @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(1000,plain,
( ( ! [V_d: $i,V_a: $i,V_b: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_a @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1001,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1002,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1003,plain,
( ( ! [V_z: $i] :
( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ V_z ) )
= V_z ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1004,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1005,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_a @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1007,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1008,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1009,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n )
| ( V_k
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1010,plain,
( ( ! [T_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1011,plain,
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ V_x @ V_y @ T_a ) @ V_n @ T_a )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1013,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[551]) ).
thf(1014,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(1016,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(1017,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(1018,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(1019,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(1020,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(1021,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(1022,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( V_b
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_c @ T_a ) )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_c @ T_a )
= V_b )
| ( V_c
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1026,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1027,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(1028,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1029,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1030,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1031,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1032,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1033,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1034,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1035,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1036,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1037,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Int_Oiszero @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1038,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1039,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ V_m @ T_a ) @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(1040,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[524]) ).
thf(1041,plain,
( ( ! [T_a: $i,V_m: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(1042,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(1043,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(1044,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1045,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osgn__if @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(1046,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(1047,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_y @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(1048,plain,
( ( ! [V_n: $i,V_m: $i,V_p: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ V_n @ V_m @ tc_nat ) @ V_p @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_n @ ( c_GCD_Ogcd__class_Olcm @ V_m @ V_p @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(1049,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_GCD_Ogcd__class_Olcm @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(1050,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(1051,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(1052,plain,
( ( ! [V_z: $i] :
( ( ( c_Complex_Ocnj @ V_z )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1053,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Complex_Ocnj @ V_x )
!= ( c_Complex_Ocnj @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(1055,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_x @ ( c_HOL_Oinverse__class_Oinverse @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1056,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(1057,plain,
( ( c_Complex_Oii
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[507]) ).
thf(1058,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[506]) ).
thf(1059,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_d @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(1060,plain,
( ( ! [V_d: $i,V_b: $i,V_a: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_b @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ V_a @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ V_d @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1061,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[503]) ).
thf(1062,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(1063,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
!= V_x )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(1064,plain,
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1065,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(1066,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(1067,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(1068,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(1069,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(1070,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(1071,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_w: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
!= ( c_HOL_Oinverse__class_Odivide @ V_w @ V_z @ T_a ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a )
= ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(1072,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_w: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a )
!= ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) )
| ( V_z
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_w @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1073,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1074,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_x @ T_a ) @ ( c_HOL_Osgn__class_Osgn @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(1075,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ V_a @ T_a ) @ ( c_HOL_Osgn__class_Osgn @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(1076,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1077,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(1078,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(1079,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(1080,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(1081,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(1082,plain,
( ( ! [T_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) @ V_c @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_l: $i,V_k: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_l @ T_a )
!= ( c_HOL_Oabs__class_Oabs @ V_k @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_l @ V_k @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1084,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(1085,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_z @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(1086,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(1087,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(1088,plain,
( ( ! [V_n: $i] :
( ( c_FFT__Mirabelle_Oroot @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(1089,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(1090,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(1091,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(1092,plain,
( ( ( c_Complex_Ocnj @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(1093,plain,
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(1096,plain,
( ( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(1097,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(1098,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(1099,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_B
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(1100,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_A
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(1101,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(1102,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(1104,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(1105,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(1106,plain,
( ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(1107,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(1108,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[456]) ).
thf(1109,plain,
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(1110,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(1111,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(1112,plain,
( ( ! [V_m: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(1113,plain,
( ( ! [V_m: $i] :
( ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[451]) ).
thf(1114,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[450]) ).
thf(1115,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[449]) ).
thf(1116,plain,
( ( ( c_Fact_Ofact__class_Ofact @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(1117,plain,
( ( ! [V_n: $i] :
( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ V_n ) @ V_n @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(1118,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(1119,plain,
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(1122,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(1123,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(1124,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(1125,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_n @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[439]) ).
thf(1126,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[438]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(1128,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_m
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(1129,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( V_n
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(1130,plain,
( ( ! [T_a: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra__1 @ T_a )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(1131,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(1133,plain,
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(1134,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Odiv @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(1135,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(1136,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(1137,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(1138,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(1139,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(1140,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(1141,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(1142,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[422]) ).
thf(1143,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[421]) ).
thf(1144,plain,
( ( class_Divides_Osemiring__div @ tc_nat )
= $true ),
inference(copy,[status(thm)],[420]) ).
thf(1145,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[419]) ).
thf(1146,plain,
( ( class_Ring__and__Field_Odvd @ tc_nat )
= $true ),
inference(copy,[status(thm)],[418]) ).
thf(1147,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[417]) ).
thf(1148,plain,
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[416]) ).
thf(1149,plain,
( ( class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[415]) ).
thf(1150,plain,
( ( class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[414]) ).
thf(1151,plain,
( ( class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[413]) ).
thf(1152,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[412]) ).
thf(1153,plain,
( ( class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[411]) ).
thf(1154,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[410]) ).
thf(1155,plain,
( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[409]) ).
thf(1156,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[408]) ).
thf(1157,plain,
( ( class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[407]) ).
thf(1158,plain,
( ( class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[406]) ).
thf(1159,plain,
( ( class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[405]) ).
thf(1160,plain,
( ( class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[404]) ).
thf(1161,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[403]) ).
thf(1162,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[402]) ).
thf(1163,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[401]) ).
thf(1164,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[400]) ).
thf(1165,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[399]) ).
thf(1166,plain,
( ( class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[398]) ).
thf(1167,plain,
( ( class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[397]) ).
thf(1168,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[396]) ).
thf(1169,plain,
( ( class_Ring__and__Field_Odvd @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[395]) ).
thf(1170,plain,
( ( class_Int_Onumber__ring @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[394]) ).
thf(1171,plain,
( ( class_Power_Opower @ tc_Complex_Ocomplex )
= $true ),
inference(copy,[status(thm)],[393]) ).
thf(1172,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[782]) ).
thf(1173,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1078]) ).
thf(1175,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1105]) ).
thf(1176,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1102]) ).
thf(1177,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1178,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX2 @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1008]) ).
thf(1179,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Oinverse__class_Oinverse @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[848]) ).
thf(1180,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= SX1 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[910]) ).
thf(1181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(1182,plain,
( ( c_Complex_Oii
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(1183,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1051]) ).
thf(1184,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1079]) ).
thf(1185,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX2 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1060]) ).
thf(1186,plain,
( ( ! [SX0: $i] :
( ( c_FFT__Mirabelle_Oroot @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1088]) ).
thf(1187,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1019]) ).
thf(1188,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1099]) ).
thf(1189,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SX0 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ SX1 @ tc_nat ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1087]) ).
thf(1191,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SX0 )
| ( ( c_HOL_Oabs__class_Oabs @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1065]) ).
thf(1192,plain,
( ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
!= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(1193,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Oone__class_Oone @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1118]) ).
thf(1194,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[813]) ).
thf(1195,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= SX0 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1063]) ).
thf(1196,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX2 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1197,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX0
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1128]) ).
thf(1198,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Oinverse__class_Oinverse @ SX2 @ SX0 ) )
| ( SX1 = SX2 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[849]) ).
thf(1199,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX2 @ tc_nat ) )
| ( SX1 = SX2 )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1009]) ).
thf(1200,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ( ( c_HOL_Oinverse__class_Odivide @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[855]) ).
thf(1201,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX2 @ tc_nat ) @ SX1 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SX2 @ SX1 @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1043]) ).
thf(1202,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SX0 )
| ( ( c_HOL_Osgn__class_Osgn @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[959]) ).
thf(1203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Complex_Ocnj @ SX0 )
!= ( c_Complex_Ocnj @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1053]) ).
thf(1204,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= SX1 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[907]) ).
thf(1205,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( c_HOL_Otimes__class_Otimes @ SX1 @ ( c_GCD_Ogcd__class_Ogcd @ SX2 @ SX0 @ tc_nat ) @ tc_nat ) )
| ( SX2
!= ( c_HOL_Otimes__class_Otimes @ SX3 @ ( c_GCD_Ogcd__class_Ogcd @ SX2 @ SX0 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SX2 @ SX0 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SX3 @ SX1 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1206,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[846]) ).
thf(1207,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX2 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[923]) ).
thf(1208,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1077]) ).
thf(1209,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SX0 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SX1 @ SX0 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(1210,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX4
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SX1 @ SX4 @ SX0 )
= ( c_HOL_Oinverse__class_Odivide @ SX3 @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1072]) ).
thf(1211,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[927]) ).
thf(1212,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SX0 )
| ( ( c_HOL_Oabs__class_Oabs @ SX1 @ SX0 )
!= ( c_HOL_Oabs__class_Oabs @ SX2 @ SX0 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1083]) ).
thf(1213,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX2
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX2 @ SX1 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX2 @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[904]) ).
thf(1214,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1050]) ).
thf(1215,plain,
( ( ! [SX0: $i] :
( ( c_Fact_Ofact__class_Ofact @ SX0 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[884]) ).
thf(1216,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) )
| ( SX0
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1086]) ).
thf(1217,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1129]) ).
thf(1218,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX0
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1101]) ).
thf(1219,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(1220,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX2
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX2 @ SX1 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX2 @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1221,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ( ( c_HOL_Oinverse__class_Odivide @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oinverse__class_Odivide @ SX3 @ SX4 @ SX0 ) )
| ( SX4
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 )
= ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1071]) ).
thf(1222,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1223,plain,
( ( c_Complex_Oii
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ),
inference(unfold_def,[status(thm)],[1057]) ).
thf(1224,plain,
( ( ! [SX0: $i] :
( ( ( c_Complex_Ocnj @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1052]) ).
thf(1225,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SX0
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1100]) ).
thf(1226,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SX0 @ SX1 @ tc_nat )
!= SX0 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX1 @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[908]) ).
thf(1227,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[814]) ).
thf(1228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[928]) ).
thf(1229,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ( ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(1230,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1231,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1232,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX1 @ SX2 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX2 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) @ SX2 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[821]) ).
thf(1233,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1076]) ).
thf(1234,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX2 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[922]) ).
thf(1235,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SX0 )
| ( ( c_HOL_Osgn__class_Osgn @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(1236,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1132]) ).
thf(1237,plain,
! [SV1: $i] :
( ( ! [SY836: $i] :
( ( c_GCD_Ogcd__class_Olcm @ SV1 @ ( c_GCD_Ogcd__class_Ogcd @ SV1 @ SY836 @ tc_nat ) @ tc_nat )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1238,plain,
! [SV2: $i] :
( ( ! [SY837: $i,SY838: $i,SY839: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV2 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SY837 @ SY838 @ SV2 ) @ SY839 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SY837 @ SY839 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SY838 @ SY839 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1239,plain,
! [SV3: $i] :
( ( ! [SY840: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV3 @ SY840 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY840 @ SV3 @ tc_nat )
| ( SY840 = SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1240,plain,
! [SV4: $i] :
( ( ! [SY841: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV4 @ SY841 @ tc_nat )
| ( SY841 = SV4 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY841 @ SV4 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1241,plain,
! [SV5: $i] :
( ( ! [SY842: $i] :
( ( SV5 = SY842 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV5 @ SY842 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY842 @ SV5 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1242,plain,
! [SV6: $i] :
( ( ! [SY843: $i] :
( ( SV6 = SY843 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY843 @ SV6 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV6 @ SY843 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1243,plain,
! [SV7: $i] :
( ( ! [SY844: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV7 @ SY844 @ tc_nat )
| ( SY844 = SV7 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY844 @ SV7 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1244,plain,
! [SV8: $i] :
( ( ! [SY845: $i] :
( ( SV8 = SY845 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY845 @ SV8 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV8 @ SY845 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1245,plain,
! [SV9: $i] :
( ( ! [SY846: $i] :
( ( SV9 = SY846 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY846 @ SV9 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV9 @ SY846 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1246,plain,
! [SV10: $i] :
( ( ! [SY847: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV10 @ ( c_GCD_Ogcd__class_Olcm @ SV10 @ SY847 @ tc_nat ) @ tc_nat )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1247,plain,
! [SV11: $i] :
( ( ! [SY848: $i,SY849: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ SY848 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ ( c_GCD_Ogcd__class_Ogcd @ SY849 @ SY848 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1248,plain,
! [SV12: $i] :
( ( ! [SY850: $i,SY851: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ SY850 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ ( c_GCD_Ogcd__class_Ogcd @ SY850 @ SY851 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1249,plain,
! [SV13: $i] :
( ( ! [SY852: $i,SY853: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ SY852 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ ( c_GCD_Ogcd__class_Ogcd @ SY852 @ SY853 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1250,plain,
! [SV14: $i] :
( ( ! [SY854: $i,SY855: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ SY854 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ ( c_GCD_Ogcd__class_Ogcd @ SY855 @ SY854 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1251,plain,
! [SV15: $i] :
( ( ! [SY856: $i,SY857: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV15 @ SY856 @ tc_nat ) @ SY857 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV15 @ SY857 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1252,plain,
! [SV16: $i] :
( ( ! [SY858: $i,SY859: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV16 @ SY858 @ tc_nat ) @ SY859 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY858 @ SY859 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1253,plain,
! [SV17: $i] :
( ( ! [SY860: $i,SY861: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ SY860 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ ( c_GCD_Ogcd__class_Ogcd @ SY860 @ SY861 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1254,plain,
! [SV18: $i] :
( ( ! [SY862: $i,SY863: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ SY862 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ ( c_GCD_Ogcd__class_Ogcd @ SY863 @ SY862 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1255,plain,
! [SV19: $i] :
( ( ! [SY864: $i,SY865: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SY864 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY865 @ SY864 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SY865 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1256,plain,
! [SV20: $i] :
( ( ! [SY866: $i,SY867: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SY866 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY866 @ SY867 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY867 @ SY866 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY867 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SY867 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1257,plain,
! [SV21: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SV21 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1258,plain,
! [SV22: $i] :
( ( ! [SY868: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV22 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY868 @ SY868 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1259,plain,
! [SV23: $i] :
( ( ! [SY869: $i,SY870: $i,SY871: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY869 @ SY870 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY871 @ SY870 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY869 @ SY871 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1260,plain,
! [SV24: $i] :
( ( ! [SY872: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV24 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY872 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1261,plain,
! [SV25: $i] :
( ( ! [SY873: $i,SY874: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV25 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SY873 @ SV25 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SY874 @ SV25 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1262,plain,
! [SV26: $i] :
( ( ! [SY875: $i,SY876: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV26 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY875 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ ( c_HOL_Otimes__class_Otimes @ SY876 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1263,plain,
! [SV27: $i] :
( ( ! [SY877: $i,SY878: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV27 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY877 @ SY878 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY877 @ SV27 ) @ ( c_HOL_Oabs__class_Oabs @ SY878 @ SV27 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1264,plain,
! [SV28: $i] :
( ( ! [SY879: $i,SY880: $i,SY881: $i,SY882: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SY879 @ SY880 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SY881 @ SY882 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY879 @ SY881 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SY880 @ SY882 @ SV28 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1265,plain,
! [SV29: $i] :
( ( ! [SY883: $i,SY884: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
| ( ( c_HOL_Otimes__class_Otimes @ SY883 @ ( c_HOL_Otimes__class_Otimes @ SY883 @ SY884 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SY883 @ SY884 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1266,plain,
! [SV30: $i] :
( ( ! [SY885: $i,SY886: $i,SY887: $i,SY888: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY885 @ SY886 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SY887 @ SY888 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY885 @ SY887 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SY886 @ SY888 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY888 @ SY887 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY886 @ SY885 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1267,plain,
! [SV31: $i] :
( ( ! [SY889: $i] :
( ~ ( class_Power_Opower @ SV31 )
| ( ( c_Power_Opower__class_Opower @ SY889 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV31 )
= ( c_HOL_Oone__class_Oone @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1268,plain,
! [SV32: $i] :
( ( ! [SY890: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 )
| ( ( c_Power_Opower__class_Opower @ SY890 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 )
= ( c_HOL_Oone__class_Oone @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1269,plain,
! [SV33: $i] :
( ( ! [SY891: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV33 )
| ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SY891 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SY891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1270,plain,
! [SV34: $i] :
( ( ! [SY892: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV34 )
| ~ ( class_Power_Opower @ SV34 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SY892 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
| ( SY892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1271,plain,
! [SV35: $i] :
( ( ! [SY893: $i,SY894: $i] :
( ~ ( class_Divides_Osemiring__div @ SV35 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SY893 @ SV35 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SY894 @ SV35 ) @ SV35 )
= ( c_HOL_Ozero__class_Ozero @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1272,plain,
! [SV36: $i] :
( ( ! [SY895: $i,SY896: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SY895 @ tc_nat ) @ SY896 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY895 @ SY896 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SY896 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1273,plain,
! [SV37: $i] :
( ( ! [SY897: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ SV37 @ ( c_GCD_Ogcd__class_Olcm @ SY897 @ SV37 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1274,plain,
! [SV38: $i] :
( ( ! [SY898: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ SV38 @ ( c_GCD_Ogcd__class_Olcm @ SV38 @ SY898 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1275,plain,
! [SV39: $i] :
( ( ! [SY899: $i,SY900: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SY899 @ tc_nat ) @ SY900 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY899 @ SY900 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SY900 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1276,plain,
! [SV40: $i] :
( ( ! [SY901: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ SV40 @ ( c_GCD_Ogcd__class_Olcm @ SY901 @ SV40 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1277,plain,
! [SV41: $i] :
( ( ! [SY902: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ SV41 @ ( c_GCD_Ogcd__class_Olcm @ SV41 @ SY902 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1278,plain,
! [SV42: $i] :
( ( ! [SY903: $i,SY904: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SY903 @ tc_nat ) @ SY904 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY903 @ SY904 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SY904 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1279,plain,
! [SV43: $i] :
( ( ! [SY905: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ SV43 @ ( c_GCD_Ogcd__class_Olcm @ SV43 @ SY905 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1280,plain,
! [SV44: $i] :
( ( ! [SY906: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ SV44 @ ( c_GCD_Ogcd__class_Olcm @ SY906 @ SV44 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1281,plain,
! [SV45: $i] :
( ( ! [SY907: $i,SY908: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SY907 @ tc_nat ) @ SY908 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY907 @ SY908 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SY908 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1282,plain,
! [SV46: $i] :
( ( ! [SY909: $i,SY910: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SY909 @ tc_nat ) @ SY910 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY909 @ SY910 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SY910 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1283,plain,
! [SV47: $i] :
( ( ! [SY911: $i,SY912: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SY911 @ tc_nat ) @ SY912 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SY912 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY912 @ SV47 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1284,plain,
! [SV48: $i] :
( ( ! [SY913: $i,SY914: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SY913 @ tc_nat ) @ SY914 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY913 @ SY914 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY914 @ SY913 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1285,plain,
! [SV49: $i] :
( ( ! [SY915: $i,SY916: $i,SY917: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY915 @ ( c_HOL_Otimes__class_Otimes @ SY916 @ SY917 @ SV49 ) @ SV49 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY915 @ SY917 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1286,plain,
! [SV50: $i] :
( ( ! [SY918: $i,SY919: $i,SY920: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY918 @ ( c_HOL_Otimes__class_Otimes @ SY919 @ SY920 @ SV50 ) @ SV50 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY918 @ SY919 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1287,plain,
! [SV51: $i] :
( ( ! [SY921: $i,SY922: $i,SY923: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY921 @ SY922 @ SV51 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY921 @ SY923 @ SV51 ) @ SY922 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1288,plain,
! [SV52: $i] :
( ( ! [SY924: $i,SY925: $i,SY926: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY924 @ SY925 @ SV52 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY926 @ SY924 @ SV52 ) @ SY925 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1289,plain,
! [SV53: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV53 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1290,plain,
! [SV54: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV54 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1291,plain,
! [SV55: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV55 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1292,plain,
! [SV56: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV56 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1293,plain,
! [SV57: $i] :
( ( ! [SY927: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV57 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SY927 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1294,plain,
! [SV58: $i] :
( ( ! [SY928: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV58 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY928 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1295,plain,
! [SV59: $i] :
( ( ! [SY929: $i,SY930: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV59 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SY929 @ SY930 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SY930 @ SY929 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1296,plain,
! [SV60: $i] :
( ( ! [SY931: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ SY931 @ SY931 @ SV60 )
= SY931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1297,plain,
! [SV61: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV61 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV61 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= ( c_HOL_Ozero__class_Ozero @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1298,plain,
! [SV62: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV62 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= ( c_HOL_Ozero__class_Ozero @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1299,plain,
! [SV63: $i] :
( ( ! [SY932: $i,SY933: $i,SY934: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SY932 @ SY933 @ SV63 ) @ SY934 @ SV63 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY932 @ SY934 @ SV63 ) @ ( c_Power_Opower__class_Opower @ SY933 @ SY934 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1300,plain,
! [SV64: $i] :
( ( ! [SY935: $i,SY936: $i,SY937: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV64 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SY935 @ SY936 @ SV64 ) @ SY937 @ SV64 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY935 @ SY937 @ SV64 ) @ ( c_Power_Opower__class_Opower @ SY936 @ SY937 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1301,plain,
! [SV65: $i] :
( ( ! [SY938: $i,SY939: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV65 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV65 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SY938 @ SY939 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SY938 @ SV65 ) @ SY939 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1302,plain,
! [SV66: $i] :
( ( ! [SY940: $i,SY941: $i,SY942: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY940 @ SY941 @ SV66 ) @ SY942 @ SV66 )
= ( c_HOL_Otimes__class_Otimes @ SY940 @ ( c_HOL_Otimes__class_Otimes @ SY941 @ SY942 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1303,plain,
! [SV67: $i] :
( ( ! [SY943: $i,SY944: $i,SY945: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY943 @ SY944 @ SV67 ) @ SY945 @ SV67 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY943 @ SY945 @ SV67 ) @ SY944 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1304,plain,
! [SV68: $i] :
( ( ! [SY946: $i,SY947: $i,SY948: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY946 @ SY947 @ SV68 ) @ SY948 @ SV68 )
= ( c_HOL_Otimes__class_Otimes @ SY946 @ ( c_HOL_Otimes__class_Otimes @ SY947 @ SY948 @ SV68 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1305,plain,
! [SV69: $i] :
( ( ! [SY949: $i,SY950: $i,SY951: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV69 )
| ( ( c_HOL_Otimes__class_Otimes @ SY949 @ ( c_HOL_Otimes__class_Otimes @ SY950 @ SY951 @ SV69 ) @ SV69 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY949 @ SY950 @ SV69 ) @ SY951 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1306,plain,
! [SV70: $i] :
( ( ! [SY952: $i,SY953: $i,SY954: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( c_HOL_Otimes__class_Otimes @ SY952 @ ( c_HOL_Otimes__class_Otimes @ SY953 @ SY954 @ SV70 ) @ SV70 )
= ( c_HOL_Otimes__class_Otimes @ SY953 @ ( c_HOL_Otimes__class_Otimes @ SY952 @ SY954 @ SV70 ) @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1307,plain,
! [SV71: $i] :
( ( ! [SY955: $i,SY956: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV71 @ SY955 @ tc_nat ) @ SY956 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV71 @ ( c_HOL_Otimes__class_Otimes @ SY955 @ SY956 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1308,plain,
! [SV72: $i] :
( ( ! [SY957: $i,SY958: $i,SY959: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Otimes__class_Otimes @ SY957 @ ( c_HOL_Otimes__class_Otimes @ SY958 @ SY959 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY957 @ SY958 @ SV72 ) @ SY959 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1309,plain,
! [SV73: $i] :
( ( ! [SY960: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV73 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY960 @ SV73 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV73 ) @ SY960 @ SV73 ) )
| ( SY960
= ( c_HOL_Ozero__class_Ozero @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1310,plain,
! [SV74: $i] :
( ( ! [SY961: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV74 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SY961 @ SV74 ) @ SY961 @ SV74 )
= ( c_HOL_Oone__class_Oone @ SV74 ) )
| ( SY961
= ( c_HOL_Ozero__class_Ozero @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1311,plain,
! [SV75: $i] :
( ( ! [SY962: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV75 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SY962 @ SV75 ) @ SY962 @ SV75 )
= ( c_HOL_Oone__class_Oone @ SV75 ) )
| ( SY962
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1312,plain,
! [SV76: $i] :
( ( ! [SY963: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV76 )
| ( ( c_HOL_Otimes__class_Otimes @ SY963 @ ( c_HOL_Oinverse__class_Oinverse @ SY963 @ SV76 ) @ SV76 )
= ( c_HOL_Oone__class_Oone @ SV76 ) )
| ( SY963
= ( c_HOL_Ozero__class_Ozero @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1313,plain,
! [SV77: $i] :
( ( ! [SY964: $i,SY965: $i,SY966: $i] :
( ~ ( class_Divides_Osemiring__div @ SV77 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY964 @ SY965 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SY964 @ SY966 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SY965 @ SY966 @ SV77 ) )
| ( SY964
= ( c_HOL_Ozero__class_Ozero @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1314,plain,
! [SV78: $i] :
( ( ! [SY967: $i,SY968: $i,SY969: $i] :
( ~ ( class_Divides_Osemiring__div @ SV78 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY967 @ SY968 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SY969 @ SY968 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SY967 @ SY969 @ SV78 ) )
| ( SY968
= ( c_HOL_Ozero__class_Ozero @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1315,plain,
! [SV79: $i] :
( ( ! [SY970: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV79 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ SY970 @ SV79 ) @ SV79 )
= ( c_HOL_Osgn__class_Osgn @ SY970 @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1316,plain,
! [SV80: $i] :
( ( ! [SY971: $i,SY972: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ ( c_GCD_Ogcd__class_Ogcd @ SY971 @ SY972 @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ SY971 @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ SY972 @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1317,plain,
! [SV81: $i] :
( ( ! [SY973: $i,SY974: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV81 @ ( c_GCD_Ogcd__class_Ogcd @ SY973 @ SY974 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV81 @ SY973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV81 @ SY974 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1318,plain,
! [SV82: $i] :
( ( ! [SY975: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 )
| ( ( c_HOL_Oabs__class_Oabs @ SY975 @ SV82 )
= ( c_HOL_Otimes__class_Otimes @ SY975 @ ( c_HOL_Osgn__class_Osgn @ SY975 @ SV82 ) @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1319,plain,
! [SV83: $i] :
( ( ! [SY976: $i,SY977: $i,SY978: $i] :
( ~ ( class_Divides_Osemiring__div @ SV83 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY976 @ SY977 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SY976 @ SY978 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SY977 @ SY978 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY978 @ SY977 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY978 @ SY976 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1320,plain,
! [SV84: $i] :
( ( ! [SY979: $i,SY980: $i,SY981: $i] :
( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SY979 @ SY980 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SY981 @ SY980 @ SV84 ) @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY979 @ SY981 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY980 @ SY981 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY980 @ SY979 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1321,plain,
! [SV85: $i] :
( ( ! [SY982: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV85 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY982 @ SV85 ) @ SV85 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SY982 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1322,plain,
! [SV86: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV86 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV86 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1323,plain,
! [SV87: $i] :
( ( ! [SY983: $i,SY984: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ ( c_GCD_Ogcd__class_Olcm @ SY983 @ SY984 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY983 @ SV87 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ SY983 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1324,plain,
! [SV88: $i] :
( ( ! [SY985: $i,SY986: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ ( c_GCD_Ogcd__class_Olcm @ SY985 @ SY986 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY986 @ SV88 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ SY986 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1325,plain,
! [SV89: $i] :
( ( ! [SY987: $i,SY988: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV89 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV89 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SY987 @ SY988 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SY987 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY988 @ SV89 ) @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1326,plain,
! [SV90: $i] :
( ( ! [SY989: $i,SY990: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SY989 @ SY990 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SY990 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY989 @ SV90 ) @ SV90 ) )
| ( SY990
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SY989
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1327,plain,
! [SV91: $i] :
( ( ! [SY991: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV91 )
| ( SY991
= ( c_HOL_Ozero__class_Ozero @ SV91 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SY991 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1328,plain,
! [SV92: $i] :
( ( ! [SY992: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV92 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SY992 @ SV92 ) @ SV92 )
= SY992 )
| ( SY992
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1329,plain,
! [SV93: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV93 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1330,plain,
! [SV94: $i] :
( ( ! [SY993: $i,SY994: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SY993 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SY994 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY994 @ SV94 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY994 @ SY993 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY993 @ SY994 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1331,plain,
! [SV95: $i] :
( ( ! [SY995: $i,SY996: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SY995
= ( c_HOL_Ozero__class_Ozero @ SV95 ) )
| ( SY996
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY996 @ SY995 @ SV95 ) @ SY995 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1332,plain,
! [SV96: $i] :
( ( ! [SY997: $i,SY998: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV96 )
| ( SY997
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY998 @ SY997 @ SV96 ) @ SY997 @ SV96 )
= SY998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1333,plain,
! [SV97: $i] :
( ( ! [SY999: $i,SY1000: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV97 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
| ( SY999
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY999 @ SY1000 @ SV97 ) @ SY1000 @ SV97 ) )
| ( SY1000
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1334,plain,
! [SV98: $i] :
( ( ! [SY1001: $i,SY1002: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV98 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY1001 @ SY1002 @ SV98 ) @ SY1002 @ SV98 )
= SY1001 )
| ( SY1002
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1335,plain,
! [SV99: $i] :
( ( ! [SY1003: $i,SY1004: $i,SY1005: $i,SY1006: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1003 @ SY1004 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SY1005 @ SY1006 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SY1005 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1003 @ SY1004 @ SV99 ) @ SY1006 @ SV99 ) @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1336,plain,
! [SV100: $i] :
( ( ! [SY1007: $i,SY1008: $i,SY1009: $i,SY1010: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1007 @ SY1008 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SY1009 @ SY1010 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SY1007 @ ( c_HOL_Otimes__class_Otimes @ SY1008 @ ( c_HOL_Otimes__class_Otimes @ SY1009 @ SY1010 @ SV100 ) @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1337,plain,
! [SV101: $i] :
( ( ! [SY1011: $i,SY1012: $i,SY1013: $i,SY1014: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1011 @ SY1012 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SY1013 @ SY1014 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY1011 @ SY1013 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SY1012 @ SY1014 @ SV101 ) @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1338,plain,
! [SV102: $i] :
( ( ! [SY1015: $i,SY1016: $i] :
( ~ ( class_Divides_Osemiring__div @ SV102 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1015 @ SY1016 @ SV102 ) @ SY1016 @ SV102 )
= SY1015 )
| ( SY1016
= ( c_HOL_Ozero__class_Ozero @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1339,plain,
! [SV103: $i] :
( ( ! [SY1017: $i,SY1018: $i] :
( ~ ( class_Divides_Osemiring__div @ SV103 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1017 @ SY1018 @ SV103 ) @ SY1017 @ SV103 )
= SY1018 )
| ( SY1017
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1340,plain,
! [SV104: $i] :
( ( ! [SY1019: $i] :
( ~ ( class_Divides_Osemiring__div @ SV104 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1019 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= ( c_HOL_Ozero__class_Ozero @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1341,plain,
! [SV105: $i] :
( ( ! [SY1020: $i] :
( ~ ( class_Divides_Osemiring__div @ SV105 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SY1020 @ SV105 )
= ( c_HOL_Ozero__class_Ozero @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1342,plain,
! [SV106: $i] :
( ( ! [SY1021: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV106 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV106 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV106 ) @ SY1021 @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1343,plain,
! [SV107: $i] :
( ( ! [SY1022: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV107 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SY1022 @ SV107 ) @ ( c_HOL_Oabs__class_Oabs @ SY1022 @ SV107 ) @ SV107 )
= SY1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1344,plain,
! [SV108: $i] :
( ( ! [SY1023: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV108 @ SY1023 @ tc_nat )
= SV108 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1023 @ SV108 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1345,plain,
! [SV109: $i] :
( ( ! [SY1024: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV109 @ SY1024 @ tc_nat )
= SV109 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1024 @ SV109 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1346,plain,
! [SV110: $i] :
( ( ! [SY1025: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV110 @ SY1025 @ tc_nat )
= SY1025 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV110 @ SY1025 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1347,plain,
! [SV111: $i] :
( ( ! [SY1026: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV111 @ SY1026 @ tc_nat )
= SV111 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1026 @ SV111 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1348,plain,
! [SV112: $i] :
( ( ! [SY1027: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV112 @ SY1027 @ tc_nat )
= SY1027 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV112 @ SY1027 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1349,plain,
! [SV113: $i] :
( ( ! [SY1028: $i,SY1029: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV113 @ SY1028 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SY1029 @ SV113 @ tc_nat ) @ SY1028 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1350,plain,
! [SV114: $i] :
( ( ! [SY1030: $i,SY1031: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV114 @ SY1030 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV114 @ SY1031 @ tc_nat ) @ SY1030 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1351,plain,
! [SV115: $i] :
( ( ! [SY1032: $i,SY1033: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ ( c_GCD_Ogcd__class_Olcm @ SY1032 @ SY1033 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ SY1033 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1352,plain,
! [SV116: $i] :
( ( ! [SY1034: $i,SY1035: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ ( c_GCD_Ogcd__class_Olcm @ SY1034 @ SY1035 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ SY1034 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1353,plain,
! [SV117: $i] :
( ( ! [SY1036: $i,SY1037: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV117 @ SY1036 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SY1037 @ SV117 @ tc_nat ) @ SY1036 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1354,plain,
! [SV118: $i] :
( ( ! [SY1038: $i,SY1039: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV118 @ SY1038 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV118 @ SY1039 @ tc_nat ) @ SY1038 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1355,plain,
! [SV119: $i] :
( ( ! [SY1040: $i,SY1041: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ ( c_GCD_Ogcd__class_Olcm @ SY1040 @ SY1041 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ SY1040 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1356,plain,
! [SV120: $i] :
( ( ! [SY1042: $i,SY1043: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ ( c_GCD_Ogcd__class_Olcm @ SY1042 @ SY1043 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ SY1043 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1357,plain,
! [SV121: $i] :
( ( ! [SY1044: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV121 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1044 @ SV121 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV121 ) @ SY1044 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1358,plain,
! [SV122: $i] :
( ( ! [SY1045: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV122 )
| ~ ( class_Int_Onumber__ring @ SV122 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1045 @ SV122 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV122 ) @ SY1045 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1359,plain,
! [SV123: $i] :
( ( ! [SY1046: $i,SY1047: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1046 @ ( c_HOL_Otimes__class_Otimes @ SY1047 @ SY1046 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1360,plain,
! [SV124: $i] :
( ( ! [SY1048: $i,SY1049: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1048 @ ( c_HOL_Otimes__class_Otimes @ SY1048 @ SY1049 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1361,plain,
! [SV125: $i] :
( ( ! [SY1050: $i,SY1051: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV125 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1050 @ ( c_HOL_Otimes__class_Otimes @ SY1050 @ SY1051 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1362,plain,
! [SV126: $i] :
( ( ! [SY1052: $i,SY1053: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV126 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV126 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SY1052 @ SY1053 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SY1052 @ SV126 ) @ SY1053 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1363,plain,
! [SV127: $i] :
( ( ! [SY1054: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV127 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV127 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SY1054 @ SV127 ) @ SV127 )
= SY1054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1364,plain,
! [SV128: $i] :
( ( ! [SY1055: $i,SY1056: $i,SY1057: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SY1055 @ SY1056 @ SV128 ) @ SY1057 @ SV128 )
= ( c_Power_Opower__class_Opower @ SY1055 @ ( c_HOL_Otimes__class_Otimes @ SY1056 @ SY1057 @ tc_nat ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1365,plain,
! [SV129: $i] :
( ( ! [SY1058: $i,SY1059: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1058 @ SY1059 @ SV129 )
= ( c_HOL_Otimes__class_Otimes @ SY1059 @ SY1058 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1366,plain,
! [SV130: $i] :
( ( ! [SY1060: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV130 @ SY1060 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SY1060 @ SV130 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1367,plain,
! [SV131: $i] :
( ( ! [SY1061: $i,SY1062: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV131 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1061 @ SY1062 @ SV131 )
= ( c_HOL_Otimes__class_Otimes @ SY1062 @ SY1061 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1368,plain,
! [SV132: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV132 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 )
= ( c_HOL_Ozero__class_Ozero @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1369,plain,
! [SV133: $i] :
( ( ! [SY1063: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( SY1063
= ( c_HOL_Ozero__class_Ozero @ SV133 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1063 @ SY1063 @ SV133 )
= ( c_HOL_Oone__class_Oone @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1370,plain,
! [SV134: $i] :
( ( ! [SY1064: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV134 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1064 @ SY1064 @ SV134 )
= ( c_HOL_Oone__class_Oone @ SV134 ) )
| ( SY1064
= ( c_HOL_Ozero__class_Ozero @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1371,plain,
! [SV135: $i] :
( ( ! [SY1065: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV135 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV135 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1065 @ SY1065 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
| ( SY1065
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1372,plain,
! [SV136: $i] :
( ( ! [SY1066: $i,SY1067: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ SY1066 @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ SY1067 @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ ( c_GCD_Ogcd__class_Olcm @ SY1066 @ SY1067 @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1373,plain,
! [SV137: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV137 @ SV137 @ tc_nat )
= SV137 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1374,plain,
! [SV138: $i] :
( ( ! [SY1068: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV138 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV138 ) @ SY1068 @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1375,plain,
! [SV139: $i] :
( ( ! [SY1069: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV139 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV139 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1069 @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1376,plain,
! [SV140: $i] :
( ( ! [SY1070: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV140 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV140 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1070 @ ( c_HOL_Ozero__class_Ozero @ SV140 ) @ SV140 )
= ( c_HOL_Ozero__class_Ozero @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1377,plain,
! [SV141: $i] :
( ( ! [SY1071: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV141 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SY1071 @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1378,plain,
! [SV142: $i] :
( ( ! [SY1072: $i,SY1073: $i,SY1074: $i] :
( ~ ( class_Divides_Osemiring__div @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1072 @ SY1073 @ SV142 ) @ SY1074 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SY1072 @ SY1074 @ SV142 ) @ SY1073 @ SV142 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1073 @ SY1072 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1379,plain,
! [SV143: $i] :
( ( ! [SY1075: $i,SY1076: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV143 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SY1075 @ SV143 ) @ SY1076 @ SV143 )
= ( c_Power_Opower__class_Opower @ SY1075 @ SY1076 @ SV143 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY1076 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1380,plain,
! [SV144: $i] :
( ( ! [SY1077: $i,SY1078: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV144 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SY1077 @ SY1078 @ SV144 ) @ SV144 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SY1077 @ SV144 ) @ SY1078 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1381,plain,
! [SV145: $i] :
( ( ! [SY1079: $i,SY1080: $i,SY1081: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY1079 @ SY1080 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SY1081 @ SY1080 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1079 @ SY1081 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1382,plain,
! [SV146: $i] :
( ( ! [SY1082: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV146 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SY1082 @ SV146 ) @ SV146 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SY1082 @ SV146 ) @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1383,plain,
! [SV147: $i] :
( ( ! [SY1083: $i,SY1084: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV147 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV147 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SY1083 @ SY1084 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SY1083 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SY1084 @ SV147 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1384,plain,
! [SV148: $i] :
( ( ! [SY1085: $i,SY1086: $i,SY1087: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV148 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY1085 @ SY1086 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SY1087 @ SY1086 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SY1085 @ SY1087 @ SV148 ) )
| ( SY1086
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1385,plain,
! [SV149: $i] :
( ( ! [SY1088: $i,SY1089: $i,SY1090: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY1088 @ SY1089 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SY1088 @ SY1090 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SY1089 @ SY1090 @ SV149 ) )
| ( SY1088
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1386,plain,
! [SV150: $i] :
( ( ! [SY1091: $i,SY1092: $i,SY1093: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV150 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SY1091 @ SY1092 @ SV150 ) @ SY1093 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY1091 @ SY1093 @ SV150 ) @ SY1092 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1387,plain,
! [SV151: $i] :
( ( ! [SY1094: $i,SY1095: $i] :
( ~ ( class_Divides_Osemiring__div @ SV151 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1094 @ ( c_Divides_Odiv__class_Odiv @ SY1095 @ SY1094 @ SV151 ) @ SV151 )
= SY1095 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1094 @ SY1095 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1388,plain,
! [SV152: $i] :
( ( ! [SY1096: $i,SY1097: $i] :
( ~ ( class_Divides_Osemiring__div @ SV152 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SY1096 @ SY1097 @ SV152 ) @ SY1097 @ SV152 )
= SY1096 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1097 @ SY1096 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1389,plain,
! [SV153: $i] :
( ( ! [SY1098: $i,SY1099: $i,SY1100: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV153 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1098 @ SY1099 @ SV153 )
| ( SY1100
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1098 @ SY1100 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SY1099 @ SY1100 @ SV153 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1390,plain,
! [SV154: $i] :
( ( ! [SY1101: $i,SY1102: $i,SY1103: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV154 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1101 @ SY1102 @ SV154 )
| ( SY1103
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1103 @ SY1101 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SY1103 @ SY1102 @ SV154 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1391,plain,
! [SV155: $i] :
( ( ! [SY1104: $i,SY1105: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV155 @ SY1104 @ tc_nat )
| ( SY1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1105 @ SV155 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY1105 @ SY1104 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1392,plain,
! [SV156: $i] :
( ( ! [SY1106: $i] :
( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ SV156 @ SY1106 @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ SV156 ) @ SY1106 @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1393,plain,
! [SV157: $i] :
( ( ! [SY1107: $i,SY1108: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SY1107 @ SY1108 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SY1108 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SY1107 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1394,plain,
! [SV158: $i] :
( ( ! [SY1109: $i,SY1110: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SY1109 @ SY1110 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SY1110 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1110 @ SV158 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1395,plain,
! [SV159: $i] :
( ( ! [SY1111: $i,SY1112: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SY1111 @ SY1112 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SY1111 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1111 @ SV159 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1396,plain,
! [SV160: $i] :
( ( ! [SY1113: $i,SY1114: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SY1113 @ SY1114 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SY1114 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SY1113 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1397,plain,
! [SV161: $i] :
( ( ! [SY1115: $i,SY1116: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SY1115 @ SY1116 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SY1116 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SY1115 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1398,plain,
! [SV162: $i] :
( ( ! [SY1117: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV162 @ SY1117 @ tc_nat ) @ SY1117 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1399,plain,
! [SV163: $i] :
( ( ! [SY1118: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV163 @ SY1118 @ tc_nat ) @ SV163 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1400,plain,
! [SV164: $i] :
( ( ! [SY1119: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV164 @ SY1119 @ tc_nat ) @ SV164 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1401,plain,
! [SV165: $i] :
( ( ! [SY1120: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV165 @ SY1120 @ tc_nat ) @ SY1120 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1402,plain,
! [SV166: $i] :
( ( ! [SY1121: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV166 @ SY1121 @ tc_nat ) @ SV166 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1403,plain,
! [SV167: $i] :
( ( ! [SY1122: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV167 @ SY1122 @ tc_nat ) @ SY1122 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1404,plain,
! [SV168: $i] :
( ( ! [SY1123: $i,SY1124: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SY1123 @ SY1124 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SY1124 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SY1123 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1405,plain,
! [SV169: $i] :
( ( ! [SY1125: $i,SY1126: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SY1125 @ SY1126 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SY1126 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SY1125 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1406,plain,
! [SV170: $i] :
( ( ! [SY1127: $i,SY1128: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SY1127 @ SY1128 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SY1128 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SY1127 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1407,plain,
! [SV171: $i] :
( ( ! [SY1129: $i,SY1130: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SY1129 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SY1130 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1130 @ SV171 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1129 @ SY1130 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1408,plain,
! [SV172: $i] :
( ( ! [SY1131: $i,SY1132: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SY1131 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1132 @ SV172 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1132 @ SY1131 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1131 @ SY1132 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1409,plain,
! [SV173: $i] :
( ( ! [SY1133: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV173 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SY1133 @ SV173 ) @ SV173 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SY1133 @ SV173 ) @ SV173 ) )
| ( SY1133
= ( c_HOL_Ozero__class_Ozero @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1410,plain,
! [SV174: $i] :
( ( ! [SY1134: $i,SY1135: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV174 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SY1134 @ SY1135 @ SV174 ) @ SV174 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SY1134 @ SV174 ) @ ( c_HOL_Oabs__class_Oabs @ SY1135 @ SV174 ) @ SV174 ) )
| ( SY1135
= ( c_HOL_Ozero__class_Ozero @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1411,plain,
! [SV175: $i] :
( ( ! [SY1136: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV175 @ SY1136 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ SV175 @ SY1136 @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ SV175 @ SY1136 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1412,plain,
! [SV176: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV176 @ tc_nat )
= SV176 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1413,plain,
! [SV177: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV177 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV177 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1414,plain,
! [SV178: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV178 )
| ~ ( class_Power_Opower @ SV178 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV178 )
= ( c_HOL_Oone__class_Oone @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1415,plain,
! [SV179: $i] :
( ( ! [SY1137: $i] :
( ~ ( class_Divides_Osemiring__div @ SV179 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1137 @ SY1137 @ SV179 )
= ( c_HOL_Oone__class_Oone @ SV179 ) )
| ( SY1137
= ( c_HOL_Ozero__class_Ozero @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1416,plain,
! [SV180: $i] :
( ( ! [SY1138: $i,SY1139: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV180 @ SY1138 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY1139 @ SY1138 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1417,plain,
! [SV181: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV181 @ SV181 @ tc_nat )
= SV181 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1418,plain,
! [SV182: $i] :
( ( ! [SY1140: $i,SY1141: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SY1140 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SY1141 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1140 @ SY1141 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1419,plain,
! [SV183: $i] :
( ( ! [SY1142: $i,SY1143: $i,SY1144: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV183 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1142 @ SY1143 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SY1142 @ SY1144 @ SV183 ) @ SV183 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1143 @ SY1144 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1420,plain,
! [SV184: $i] :
( ( ! [SY1145: $i,SY1146: $i,SY1147: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV184 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1145 @ SY1146 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY1147 @ SY1146 @ SV184 ) @ SV184 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1145 @ SY1147 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1421,plain,
! [SV185: $i] :
( ( ! [SY1148: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV185 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SY1148 @ SV185 ) @ SV185 )
= ( c_HOL_Oabs__class_Oabs @ SY1148 @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1422,plain,
! [SV186: $i] :
( ( ! [SY1149: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV186 @ SY1149 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY1149 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1423,plain,
! [SV187: $i] :
( ( ! [SY1150: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV187 @ SY1150 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV187 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1424,plain,
! [SV188: $i] :
( ( ( c_Complex_Ocnj @ ( c_Complex_Ocnj @ SV188 ) )
= SV188 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1425,plain,
! [SV189: $i] :
( ( ! [SY1151: $i] :
( ( c_GCD_Ogcd__class_Olcm @ SV189 @ SY1151 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SY1151 @ SV189 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1426,plain,
! [SV190: $i] :
( ( ! [SY1152: $i] :
( ( c_GCD_Ogcd__class_Olcm @ SV190 @ SY1152 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SY1152 @ SV190 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1427,plain,
! [SV191: $i] :
( ( ! [SY1153: $i,SY1154: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SY1153 @ SY1154 @ SV191 ) @ SY1153 @ SV191 )
= ( c_HOL_Otimes__class_Otimes @ SY1153 @ ( c_Power_Opower__class_Opower @ SY1153 @ SY1154 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1428,plain,
! [SV192: $i] :
( ( ! [SY1155: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV192 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV192 )
| ( ( c_HOL_Ozero__class_Ozero @ SV192 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SY1155 @ SV192 ) @ SY1155 @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1429,plain,
! [SV193: $i] :
( ( ! [SY1156: $i,SY1157: $i,SY1158: $i] :
( ~ ( class_Divides_Osemiring__div @ SV193 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SY1156 @ SY1157 @ SV193 ) @ SY1158 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SY1156 @ SY1158 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SY1157 @ SY1158 @ SV193 ) @ SV193 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1157 @ SY1156 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1430,plain,
! [SV194: $i] :
( ( ! [SY1159: $i,SY1160: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV194 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SY1159 @ SY1160 @ tc_nat ) @ SV194 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1159 @ SV194 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1160 @ SV194 ) @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1431,plain,
! [SV195: $i] :
( ( ! [SY1161: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV195 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY1161 @ SV195 ) @ ( c_HOL_Oabs__class_Oabs @ SY1161 @ SV195 ) @ SV195 )
= ( c_HOL_Otimes__class_Otimes @ SY1161 @ SY1161 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1432,plain,
! [SV196: $i] :
( ( ! [SY1162: $i,SY1163: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV196 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SY1162 @ SY1163 @ SV196 ) @ SV196 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SY1162 @ SV196 ) @ SY1163 @ SV196 ) )
| ( SY1162
= ( c_HOL_Ozero__class_Ozero @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1433,plain,
! [SV197: $i] :
( ( ! [SY1164: $i,SY1165: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV197 @ ( c_GCD_Ogcd__class_Ogcd @ SY1164 @ SY1165 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY1164 @ ( c_GCD_Ogcd__class_Ogcd @ SV197 @ SY1165 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1434,plain,
! [SV198: $i] :
( ( ! [SY1166: $i,SY1167: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV198 @ SY1166 @ tc_nat ) @ SY1167 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV198 @ ( c_GCD_Ogcd__class_Ogcd @ SY1166 @ SY1167 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1435,plain,
! [SV199: $i] :
( ( ! [SY1168: $i,SY1169: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV199 @ SY1168 @ tc_nat ) @ SY1169 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV199 @ ( c_GCD_Ogcd__class_Ogcd @ SY1168 @ SY1169 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1436,plain,
! [SV200: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV200 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1437,plain,
! [SV201: $i] :
( ( ! [SY1170: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1170 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1438,plain,
! [SV202: $i] :
( ( ! [SY1171: $i,SY1172: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( SY1171
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SY1171 @ SY1172 @ SV202 ) @ SY1172 @ SV202 ) )
| ( SY1172
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1439,plain,
! [SV203: $i] :
( ( ! [SY1173: $i,SY1174: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SY1173 @ SY1174 @ SV203 ) @ SY1174 @ SV203 )
= SY1173 )
| ( SY1174
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1440,plain,
! [SV204: $i] :
( ( ! [SY1175: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV204 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY1175 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1441,plain,
! [SV205: $i] :
( ( ! [SY1176: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV205 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1176 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= ( c_HOL_Ozero__class_Ozero @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1442,plain,
! [SV206: $i] :
( ( ! [SY1177: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV206 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SY1177 @ SV206 )
= ( c_HOL_Ozero__class_Ozero @ SV206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1443,plain,
! [SV207: $i] :
( ( ! [SY1178: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV207 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SY1178 @ SV207 )
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1444,plain,
! [SV208: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV208 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1445,plain,
! [SV209: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV209 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1446,plain,
! [SV210: $i] :
( ( ! [SY1179: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV210 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1179 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 )
= ( c_HOL_Ozero__class_Ozero @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1447,plain,
! [SV211: $i] :
( ( ! [SY1180: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV211 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1180 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1448,plain,
! [SV212: $i] :
( ( ! [SY1181: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV212 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SY1181 @ SV212 )
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1449,plain,
! [SV213: $i] :
( ( ! [SY1182: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SY1182 @ SV213 )
= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1450,plain,
! [SV214: $i] :
( ( ! [SY1183: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV214 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1183 @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1451,plain,
! [SV215: $i] :
( ( ! [SY1184: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV215 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SY1184 @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1452,plain,
! [SV216: $i] :
( ( ! [SY1185: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV216 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1185 @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1453,plain,
! [SV217: $i] :
( ( ! [SY1186: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV217 )
| ( SY1186
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
| ~ ( c_Int_Oiszero @ SY1186 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1454,plain,
! [SV218: $i] :
( ( ! [SY1187: $i,SY1188: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV218 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1187 @ SY1188 @ SV218 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SY1187 @ SV218 ) @ SY1188 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1455,plain,
! [SV219: $i] :
( ( ! [SY1189: $i,SY1190: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV219 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SY1189 @ SV219 ) @ SY1190 @ SV219 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1189 @ SY1190 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1456,plain,
! [SV220: $i] :
( ( ! [SY1191: $i,SY1192: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV220 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1191 @ SY1192 @ SV220 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1191 @ ( c_HOL_Oabs__class_Oabs @ SY1192 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1457,plain,
! [SV221: $i] :
( ( ! [SY1193: $i,SY1194: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1193 @ ( c_HOL_Oabs__class_Oabs @ SY1194 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1193 @ SY1194 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1458,plain,
! [SV222: $i] :
( ( ! [SY1195: $i] :
( ( c_GCD_Ogcd__class_Olcm @ SV222 @ ( c_GCD_Ogcd__class_Olcm @ SV222 @ SY1195 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV222 @ SY1195 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1459,plain,
! [SV223: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV223 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1460,plain,
! [SV224: $i] :
( ( ~ ( class_Ring__and__Field_Osgn__if @ SV224 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1461,plain,
! [SV225: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV225 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1462,plain,
! [SV226: $i] :
( ( ! [SY1196: $i,SY1197: $i] :
( ( c_GCD_Ogcd__class_Olcm @ SV226 @ ( c_GCD_Ogcd__class_Olcm @ SY1196 @ SY1197 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SY1196 @ ( c_GCD_Ogcd__class_Olcm @ SV226 @ SY1197 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1463,plain,
! [SV227: $i] :
( ( ! [SY1198: $i,SY1199: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ SV227 @ SY1198 @ tc_nat ) @ SY1199 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV227 @ ( c_GCD_Ogcd__class_Olcm @ SY1198 @ SY1199 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1464,plain,
! [SV228: $i] :
( ( ! [SY1200: $i,SY1201: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ SV228 @ SY1200 @ tc_nat ) @ SY1201 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV228 @ ( c_GCD_Ogcd__class_Olcm @ SY1200 @ SY1201 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1465,plain,
! [SV229: $i] :
( ( ! [SY1202: $i,SY1203: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV229 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1202 @ SY1203 @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ SY1202 @ ( c_HOL_Oinverse__class_Oinverse @ SY1203 @ SV229 ) @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1466,plain,
! [SV230: $i] :
( ( ! [SY1204: $i,SY1205: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV230 )
| ~ ( class_Int_Onumber__ring @ SV230 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1204 @ SY1205 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SY1204 @ ( c_HOL_Oinverse__class_Oinverse @ SY1205 @ SV230 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1467,plain,
! [SV231: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV231 )
| ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1468,plain,
! [SV232: $i] :
( ( ! [SY1206: $i,SY1207: $i,SY1208: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV232 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SY1206 @ SY1207 @ SV232 ) @ SY1208 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SY1206 @ SY1208 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SY1207 @ SY1208 @ SV232 ) @ SV232 ) )
| ( SY1207
= ( c_HOL_Ozero__class_Ozero @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1469,plain,
! [SV233: $i] :
( ( ! [SY1209: $i,SY1210: $i,SY1211: $i,SY1212: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1209 @ SY1210 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SY1211 @ SY1212 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1210 @ SY1212 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1209 @ SY1211 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1470,plain,
! [SV234: $i] :
( ( ! [SY1213: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV234 @ SY1213 @ tc_nat )
= SY1213 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1213 @ SV234 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1471,plain,
! [SV235: $i] :
( ( ! [SY1214: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SY1214 @ tc_nat )
= SV235 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV235 @ SY1214 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1472,plain,
! [SV236: $i] :
( ( ! [SY1215: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ SV236 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY1215 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SY1215 @ SV236 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1473,plain,
! [SV237: $i] :
( ( ! [SY1216: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV237 @ SY1216 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY1216 @ SV237 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1474,plain,
! [SV238: $i] :
( ( ! [SY1217: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV238 @ SY1217 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY1217 @ SV238 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1475,plain,
! [SV239: $i] :
( ( ! [SY1218: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV239 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV239 )
| ( ( c_HOL_Ozero__class_Ozero @ SV239 )
= ( c_HOL_Oinverse__class_Odivide @ SY1218 @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1476,plain,
! [SV240: $i] :
( ( ! [SY1219: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV240 @ ( c_GCD_Ogcd__class_Ogcd @ SV240 @ SY1219 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV240 @ SY1219 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1477,plain,
! [SV241: $i] :
( ( ! [SY1220: $i,SY1221: $i,SY1222: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV241 )
| ( ( c_Power_Opower__class_Opower @ SY1220 @ ( c_HOL_Otimes__class_Otimes @ SY1221 @ SY1222 @ tc_nat ) @ SV241 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SY1220 @ SY1221 @ SV241 ) @ SY1222 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1478,plain,
! [SV242: $i] :
( ( ! [SY1223: $i,SY1224: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV242 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SY1223 @ SY1224 @ SV242 ) @ SV242 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SY1223 @ SV242 ) @ ( c_HOL_Osgn__class_Osgn @ SY1224 @ SV242 ) @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1479,plain,
! [SV243: $i] :
( ( ! [SY1225: $i,SY1226: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV243 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SY1225 @ SY1226 @ SV243 ) @ SV243 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SY1225 @ SV243 ) @ ( c_HOL_Osgn__class_Osgn @ SY1226 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1480,plain,
! [SV244: $i] :
( ( ! [SY1227: $i,SY1228: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV244 @ SY1227 @ tc_nat ) @ SY1228 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1228 @ SV244 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV244 @ SY1228 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1481,plain,
! [SV245: $i] :
( ( ! [SY1229: $i,SY1230: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV245 @ SY1229 @ tc_nat ) @ SY1230 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1230 @ SY1229 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1229 @ SY1230 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1482,plain,
! [SV246: $i] :
( ( ! [SY1231: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV246 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV246 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SY1231 @ SV246 ) @ SY1231 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1483,plain,
! [SV247: $i] :
( ( ! [SY1232: $i,SY1233: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SY1232 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1233 @ SY1232 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1233 @ SV247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SY1233 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1484,plain,
! [SV248: $i] :
( ( ! [SY1234: $i,SY1235: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SY1234 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1234 @ SY1235 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1235 @ SY1234 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SY1235 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1485,plain,
! [SV249: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV249 )
| ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ SV249 ) @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1486,plain,
! [SV250: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV250 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV250 ) @ SV250 )
= ( c_HOL_Oone__class_Oone @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1487,plain,
! [SV251: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV251 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV251 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV251 ) @ SV251 )
= ( c_HOL_Oone__class_Oone @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1488,plain,
! [SV252: $i] :
( ( ! [SY1236: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV252 )
| ( ( c_Power_Opower__class_Opower @ SY1236 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV252 )
= SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1489,plain,
! [SV253: $i] :
( ( ! [SY1237: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
| ( ( c_Power_Opower__class_Opower @ SY1237 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV253 )
= SY1237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1490,plain,
! [SV254: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV254 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= SV254 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1491,plain,
! [SV255: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV255 @ tc_nat )
= SV255 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1492,plain,
! [SV256: $i] :
( ( ! [SY1238: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV256 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SY1238 @ SV256 )
= ( c_HOL_Oone__class_Oone @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1493,plain,
! [SV257: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV257 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV257 )
= ( c_HOL_Oone__class_Oone @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1494,plain,
! [SV258: $i] :
( ( ! [SY1239: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV258 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1239 @ ( c_HOL_Oone__class_Oone @ SV258 ) @ SV258 )
= SY1239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1495,plain,
! [SV259: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV259 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ SV259 ) @ SV259 )
= ( c_HOL_Oone__class_Oone @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1496,plain,
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1497,plain,
! [SV260: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV260 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1498,plain,
! [SV261: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV261 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1499,plain,
! [SV262: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV262 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1500,plain,
! [SV263: $i] :
( ( ( SV263
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1501,plain,
! [SV264: $i] :
( ( ! [SY1240: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV264 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV264 ) @ SY1240 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1502,plain,
! [SV265: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV265 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1503,plain,
! [SV266: $i] :
( ( ( c_Power_Opower__class_Opower @ ( c_FFT__Mirabelle_Oroot @ SV266 ) @ SV266 @ tc_Complex_Ocomplex )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1504,plain,
! [SV267: $i] :
( ( ! [SY1241: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV267 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1241 @ ( c_HOL_Oone__class_Oone @ SV267 ) @ SV267 )
= SY1241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1505,plain,
! [SV268: $i] :
( ( ! [SY1242: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV268 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV268 ) @ SY1242 @ SV268 )
= SY1242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1506,plain,
! [SV269: $i] :
( ( ! [SY1243: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV269 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV269 ) @ SY1243 @ SV269 )
= SY1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1507,plain,
! [SV270: $i] :
( ( ! [SY1244: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV270 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV270 ) @ SY1244 @ SV270 )
= SY1244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1508,plain,
! [SV271: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV271 @ tc_nat )
= SV271 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1509,plain,
! [SV272: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV272 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= SV272 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1510,plain,
! [SV273: $i] :
( ( ! [SY1245: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1245 @ ( c_HOL_Oone__class_Oone @ SV273 ) @ SV273 )
= SY1245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1511,plain,
! [SV274: $i] :
( ( ! [SY1246: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV274 ) @ SY1246 @ SV274 )
= SY1246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1512,plain,
! [SV275: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV275 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ SV275 ) @ SV275 )
= ( c_HOL_Oone__class_Oone @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1513,plain,
! [SV276: $i] :
( ( ! [SY1247: $i] :
( ~ ( class_Divides_Osemiring__div @ SV276 )
| ( ( c_Divides_Odiv__class_Odiv @ SY1247 @ ( c_HOL_Oone__class_Oone @ SV276 ) @ SV276 )
= SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1514,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1515,plain,
! [SV277: $i] :
( ( ! [SY1248: $i,SY1249: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1248 @ SY1249 @ SV277 )
!= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SY1249
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SY1248
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1516,plain,
! [SV278: $i] :
( ( ! [SY1250: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV278 @ SY1250 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV278
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1517,plain,
! [SV279: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV279 )
| ( ( c_HOL_Ozero__class_Ozero @ SV279 )
!= ( c_HOL_Oone__class_Oone @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1518,plain,
! [SV280: $i] :
( ( ! [SY1251: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV280 @ SY1251 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1251
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1519,plain,
! [SV281: $i] :
( ( ! [SY1252: $i,SY1253: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ ( c_HOL_Otimes__class_Otimes @ SY1252 @ SY1253 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ SY1252 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1520,plain,
! [SV282: $i] :
( ( ! [SY1254: $i,SY1255: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV282 @ SY1254 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV282 @ SY1255 @ tc_nat ) )
| ( SV282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1254 = SY1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1521,plain,
! [SV283: $i] :
( ( ! [SY1256: $i,SY1257: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV283 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1256 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY1257 @ SV283 ) )
| ( SY1256 = SY1257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1522,plain,
! [SV284: $i] :
( ( ! [SY1258: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV284 @ SY1258 @ tc_nat )
!= SY1258 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV284 @ SY1258 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1523,plain,
! [SV285: $i] :
( ( ! [SY1259: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV285 @ SY1259 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1259
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1524,plain,
( ( c_Complex_Oii
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1182]) ).
thf(1525,plain,
! [SV286: $i] :
( ( ! [SY1260: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV286 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1260 @ SV286 )
!= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ( SY1260
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1526,plain,
! [SV287: $i] :
( ( ! [SY1261: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV287 @ SY1261 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1261
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1527,plain,
! [SV288: $i] :
( ( ! [SY1262: $i,SY1263: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SY1262 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SY1263 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SY1263 @ SY1262 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1528,plain,
! [SV289: $i] :
( ( ( c_FFT__Mirabelle_Oroot @ SV289 )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1529,plain,
! [SV290: $i] :
( ( ! [SY1264: $i] :
( ( SV290
!= ( c_HOL_Otimes__class_Otimes @ SV290 @ SY1264 @ tc_nat ) )
| ( SV290
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1264
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1530,plain,
! [SV291: $i] :
( ( ! [SY1265: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV291 @ SY1265 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1265
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1531,plain,
! [SV292: $i] :
( ( ! [SY1266: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV292 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ SY1266 @ tc_nat ) @ SV292 )
!= ( c_HOL_Ozero__class_Ozero @ SV292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1532,plain,
! [SV293: $i] :
( ( ! [SY1267: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV293 @ SY1267 @ tc_nat ) )
| ( SY1267
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1533,plain,
! [SV294: $i] :
( ( ! [SY1268: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV294 )
| ( ( c_HOL_Oabs__class_Oabs @ SY1268 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SY1268
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1534,plain,
( ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1535,plain,
! [SV295: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV295 )
| ( ( c_HOL_Oone__class_Oone @ SV295 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1536,plain,
! [SV296: $i] :
( ( ! [SY1269: $i,SY1270: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SY1269 @ SY1270 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SY1269
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1537,plain,
! [SV297: $i] :
( ( ! [SY1271: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV297 @ SY1271 @ tc_nat )
!= SV297 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV297 @ SY1271 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1538,plain,
! [SV298: $i] :
( ( ! [SY1272: $i,SY1273: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ ( c_HOL_Otimes__class_Otimes @ SY1272 @ SY1273 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ SY1273 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1539,plain,
! [SV299: $i] :
( ( ! [SY1274: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV299 @ SY1274 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV299
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1540,plain,
! [SV300: $i] :
( ( ! [SY1275: $i,SY1276: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV300 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1275 @ SV300 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY1276 @ SV300 ) )
| ( SY1275 = SY1276 )
| ( SY1276
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SY1275
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1541,plain,
! [SV301: $i] :
( ( ! [SY1277: $i,SY1278: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV301 @ SY1277 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV301 @ SY1278 @ tc_nat ) )
| ( SY1277 = SY1278 )
| ( SV301
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1542,plain,
! [SV302: $i] :
( ( ! [SY1279: $i,SY1280: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV302 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1279 @ SY1280 @ SV302 )
!= ( c_HOL_Oone__class_Oone @ SV302 ) )
| ( SY1280
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SY1279 = SY1280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1543,plain,
! [SV303: $i] :
( ( ! [SY1281: $i,SY1282: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV303 @ SY1281 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV303 @ SY1282 @ tc_nat ) @ SY1281 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY1282 @ SY1281 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1544,plain,
! [SV304: $i] :
( ( ! [SY1283: $i] :
( ~ ( class_RealVector_Oreal__normed__vector @ SV304 )
| ( ( c_HOL_Osgn__class_Osgn @ SY1283 @ SV304 )
!= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
| ( SY1283
= ( c_HOL_Ozero__class_Ozero @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1545,plain,
! [SV305: $i] :
( ( ! [SY1284: $i] :
( ( ( c_Complex_Ocnj @ SV305 )
!= ( c_Complex_Ocnj @ SY1284 ) )
| ( SV305 = SY1284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1546,plain,
! [SV306: $i] :
( ( ! [SY1285: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV306 @ SY1285 @ tc_nat )
!= SY1285 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV306 @ SY1285 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1547,plain,
! [SV307: $i] :
( ( ! [SY1286: $i,SY1287: $i,SY1288: $i] :
( ( SV307
!= ( c_HOL_Otimes__class_Otimes @ SY1286 @ ( c_GCD_Ogcd__class_Ogcd @ SY1287 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( SY1287
!= ( c_HOL_Otimes__class_Otimes @ SY1288 @ ( c_GCD_Ogcd__class_Ogcd @ SY1287 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SY1287 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SY1288 @ SY1286 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1548,plain,
! [SV308: $i] :
( ( ! [SY1289: $i,SY1290: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV308 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1289 @ SY1290 @ SV308 )
!= ( c_HOL_Oone__class_Oone @ SV308 ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1289 @ SV308 )
= SY1290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1549,plain,
! [SV309: $i] :
( ( ! [SY1291: $i,SY1292: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SY1291 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SY1292 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SY1292 @ SY1291 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1550,plain,
! [SV310: $i] :
( ( ! [SY1293: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV310 @ SY1293 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV310
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1551,plain,
! [SV311: $i] :
( ( ! [SY1294: $i,SY1295: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV311 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY1294 @ SV311 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1295 @ SV311 ) )
| ( SY1294 = SY1295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1552,plain,
! [SV312: $i] :
( ( ! [SY1296: $i,SY1297: $i,SY1298: $i,SY1299: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV312 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1296 @ SY1297 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SY1298 @ SY1299 @ SV312 ) )
| ( SY1297
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SY1299
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1296 @ SY1299 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SY1298 @ SY1297 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1553,plain,
! [SV313: $i] :
( ( ! [SY1300: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV313 @ SY1300 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV313 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1554,plain,
! [SV314: $i] :
( ( ! [SY1301: $i,SY1302: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV314 )
| ( ( c_HOL_Oabs__class_Oabs @ SY1301 @ SV314 )
!= ( c_HOL_Oabs__class_Oabs @ SY1302 @ SV314 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1301 @ SY1302 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1555,plain,
! [SV315: $i] :
( ( ! [SY1303: $i,SY1304: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SY1303 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1304
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1304 @ SY1303 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1304 @ SV315 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1556,plain,
! [SV316: $i] :
( ( ! [SY1305: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV316 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1305 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SY1305
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1557,plain,
! [SV317: $i] :
( ( ( c_Fact_Ofact__class_Ofact @ SV317 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1558,plain,
! [SV318: $i] :
( ( ! [SY1306: $i] :
( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV318 @ SY1306 @ tc_nat ) )
| ( SV318
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1559,plain,
! [SV319: $i] :
( ( ! [SY1307: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV319 @ SY1307 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1307
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1560,plain,
! [SV320: $i] :
( ( ! [SY1308: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV320 @ SY1308 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV320
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1561,plain,
! [SV321: $i] :
( ( ! [SY1309: $i,SY1310: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1309 @ SY1310 @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SY1309
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SY1310
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1562,plain,
! [SV322: $i] :
( ( ! [SY1311: $i,SY1312: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SY1311 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1312
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1312 @ SY1311 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1312 @ SV322 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1563,plain,
! [SV323: $i] :
( ( ! [SY1313: $i,SY1314: $i,SY1315: $i,SY1316: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY1313 @ SY1314 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SY1315 @ SY1316 @ SV323 ) )
| ( SY1316
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SY1314
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SY1313 @ SY1316 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SY1315 @ SY1314 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1564,plain,
! [SV324: $i] :
( ( ! [SY1317: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV324 @ SY1317 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1317
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV324
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1565,plain,
( ( c_Complex_Oii
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1566,plain,
! [SV325: $i] :
( ( ( ( c_Complex_Ocnj @ SV325 )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( SV325
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1567,plain,
! [SV326: $i] :
( ( ! [SY1318: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV326 @ SY1318 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV326
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1568,plain,
! [SV327: $i] :
( ( ! [SY1319: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV327 @ SY1319 @ tc_nat )
!= SV327 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1319 @ SV327 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1569,plain,
! [SV328: $i] :
( ( ! [SY1320: $i,SY1321: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 )
| ( ( c_Power_Opower__class_Opower @ SY1320 @ SY1321 @ SV328 )
!= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
| ( SY1320
= ( c_HOL_Ozero__class_Ozero @ SV328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1570,plain,
! [SV329: $i] :
( ( ! [SY1322: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV329 @ SY1322 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SY1322 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1571,plain,
! [SV330: $i] :
( ( ! [SY1323: $i,SY1324: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
| ( ( c_HOL_Otimes__class_Otimes @ SY1323 @ SY1324 @ SV330 )
!= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SY1324
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SY1323
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1572,plain,
! [SV331: $i] :
( ( ! [SY1325: $i,SY1326: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV331 @ SY1325 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SY1326 @ SY1325 @ tc_nat ) )
| ( SY1325
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV331 = SY1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1573,plain,
! [SV332: $i] :
( ( ! [SY1327: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV332 )
| ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SY1327 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1574,plain,
! [SV333: $i] :
( ( ! [SY1328: $i,SY1329: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SY1328 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1328 @ SY1329 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SY1329 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SY1328 @ tc_nat ) @ SY1329 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1575,plain,
! [SV334: $i] :
( ( ! [SY1330: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV334 @ SY1330 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY1330
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1576,plain,
! [SV335: $i] :
( ( ! [SY1331: $i,SY1332: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SY1331 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SY1332 @ SY1331 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SY1332 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1577,plain,
! [SV336: $i] :
( ( ! [SY1333: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV336 )
| ( ( c_HOL_Osgn__class_Osgn @ SY1333 @ SV336 )
!= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
| ( SY1333
= ( c_HOL_Ozero__class_Ozero @ SV336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1578,plain,
! [SV337: $i] :
( ( ! [SY1334: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV337 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY1334 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
| ( SY1334
= ( c_HOL_Oone__class_Oone @ SV337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1579,plain,
! [SV338: $i,SV1: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV1 @ ( c_GCD_Ogcd__class_Ogcd @ SV1 @ SV338 @ tc_nat ) @ tc_nat )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1580,plain,
! [SV339: $i,SV2: $i] :
( ( ! [SY1335: $i,SY1336: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV2 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SY1335 @ SV2 ) @ SY1336 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SY1336 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SY1335 @ SY1336 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1581,plain,
! [SV340: $i,SV3: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV3 @ SV340 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV3 @ tc_nat )
| ( SV340 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1582,plain,
! [SV341: $i,SV4: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV4 @ SV341 @ tc_nat )
| ( SV341 = SV4 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV341 @ SV4 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1583,plain,
! [SV342: $i,SV5: $i] :
( ( ( SV5 = SV342 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV5 @ SV342 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV342 @ SV5 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1584,plain,
! [SV343: $i,SV6: $i] :
( ( ( SV6 = SV343 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV343 @ SV6 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV6 @ SV343 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1585,plain,
! [SV344: $i,SV7: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV7 @ SV344 @ tc_nat )
| ( SV344 = SV7 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV344 @ SV7 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1586,plain,
! [SV345: $i,SV8: $i] :
( ( ( SV8 = SV345 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV345 @ SV8 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV8 @ SV345 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1587,plain,
! [SV346: $i,SV9: $i] :
( ( ( SV9 = SV346 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV346 @ SV9 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV9 @ SV346 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1588,plain,
! [SV347: $i,SV10: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV10 @ ( c_GCD_Ogcd__class_Olcm @ SV10 @ SV347 @ tc_nat ) @ tc_nat )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1589,plain,
! [SV348: $i,SV11: $i] :
( ( ! [SY1337: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ SV348 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ ( c_GCD_Ogcd__class_Ogcd @ SY1337 @ SV348 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1590,plain,
! [SV349: $i,SV12: $i] :
( ( ! [SY1338: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ SV349 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ ( c_GCD_Ogcd__class_Ogcd @ SV349 @ SY1338 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1591,plain,
! [SV350: $i,SV13: $i] :
( ( ! [SY1339: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ SV350 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ ( c_GCD_Ogcd__class_Ogcd @ SV350 @ SY1339 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1592,plain,
! [SV351: $i,SV14: $i] :
( ( ! [SY1340: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ SV351 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ ( c_GCD_Ogcd__class_Ogcd @ SY1340 @ SV351 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1593,plain,
! [SV352: $i,SV15: $i] :
( ( ! [SY1341: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV15 @ SV352 @ tc_nat ) @ SY1341 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV15 @ SY1341 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1594,plain,
! [SV353: $i,SV16: $i] :
( ( ! [SY1342: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV16 @ SV353 @ tc_nat ) @ SY1342 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV353 @ SY1342 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1595,plain,
! [SV354: $i,SV17: $i] :
( ( ! [SY1343: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ SV354 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ ( c_GCD_Ogcd__class_Ogcd @ SV354 @ SY1343 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1596,plain,
! [SV355: $i,SV18: $i] :
( ( ! [SY1344: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ SV355 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ ( c_GCD_Ogcd__class_Ogcd @ SY1344 @ SV355 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1597,plain,
! [SV356: $i,SV19: $i] :
( ( ! [SY1345: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV356 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1345 @ SV356 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SY1345 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1598,plain,
! [SV357: $i,SV20: $i] :
( ( ! [SY1346: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SY1346 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1346 @ SV357 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1346 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SY1346 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1599,plain,
! [SV358: $i,SV22: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV22 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV358 @ SV358 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1600,plain,
! [SV359: $i,SV23: $i] :
( ( ! [SY1347: $i,SY1348: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SY1347 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1348 @ SY1347 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SY1348 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1601,plain,
! [SV360: $i,SV24: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV24 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV360 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1602,plain,
! [SV361: $i,SV25: $i] :
( ( ! [SY1349: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV25 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV361 @ SV25 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SY1349 @ SV25 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1603,plain,
! [SV362: $i,SV26: $i] :
( ( ! [SY1350: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV26 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV362 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ ( c_HOL_Otimes__class_Otimes @ SY1350 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1604,plain,
! [SV363: $i,SV27: $i] :
( ( ! [SY1351: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV27 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SY1351 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV363 @ SV27 ) @ ( c_HOL_Oabs__class_Oabs @ SY1351 @ SV27 ) @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1605,plain,
! [SV364: $i,SV28: $i] :
( ( ! [SY1352: $i,SY1353: $i,SY1354: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SY1352 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SY1353 @ SY1354 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SY1353 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SY1352 @ SY1354 @ SV28 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1606,plain,
! [SV365: $i,SV29: $i] :
( ( ! [SY1355: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
| ( ( c_HOL_Otimes__class_Otimes @ SV365 @ ( c_HOL_Otimes__class_Otimes @ SV365 @ SY1355 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV365 @ SY1355 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1607,plain,
! [SV366: $i,SV30: $i] :
( ( ! [SY1356: $i,SY1357: $i,SY1358: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SY1356 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SY1357 @ SY1358 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SY1357 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SY1356 @ SY1358 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1358 @ SY1357 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1356 @ SV366 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1608,plain,
! [SV367: $i,SV31: $i] :
( ( ~ ( class_Power_Opower @ SV31 )
| ( ( c_Power_Opower__class_Opower @ SV367 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV31 )
= ( c_HOL_Oone__class_Oone @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1609,plain,
! [SV368: $i,SV32: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 )
| ( ( c_Power_Opower__class_Opower @ SV368 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 )
= ( c_HOL_Oone__class_Oone @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1610,plain,
! [SV369: $i,SV33: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV33 )
| ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1611,plain,
! [SV370: $i,SV34: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV34 )
| ~ ( class_Power_Opower @ SV34 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV370 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
| ( SV370
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1612,plain,
! [SV371: $i,SV35: $i] :
( ( ! [SY1359: $i] :
( ~ ( class_Divides_Osemiring__div @ SV35 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV371 @ SV35 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SY1359 @ SV35 ) @ SV35 )
= ( c_HOL_Ozero__class_Ozero @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1613,plain,
! [SV372: $i,SV36: $i] :
( ( ! [SY1360: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SV372 @ tc_nat ) @ SY1360 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV372 @ SY1360 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SY1360 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1614,plain,
! [SV373: $i,SV37: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV37 @ ( c_GCD_Ogcd__class_Olcm @ SV373 @ SV37 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1615,plain,
! [SV374: $i,SV38: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV38 @ ( c_GCD_Ogcd__class_Olcm @ SV38 @ SV374 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1616,plain,
! [SV375: $i,SV39: $i] :
( ( ! [SY1361: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SV375 @ tc_nat ) @ SY1361 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV375 @ SY1361 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SY1361 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1617,plain,
! [SV376: $i,SV40: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV40 @ ( c_GCD_Ogcd__class_Olcm @ SV376 @ SV40 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1618,plain,
! [SV377: $i,SV41: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV41 @ ( c_GCD_Ogcd__class_Olcm @ SV41 @ SV377 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1619,plain,
! [SV378: $i,SV42: $i] :
( ( ! [SY1362: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SV378 @ tc_nat ) @ SY1362 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV378 @ SY1362 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SY1362 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1620,plain,
! [SV379: $i,SV43: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV43 @ ( c_GCD_Ogcd__class_Olcm @ SV43 @ SV379 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1621,plain,
! [SV380: $i,SV44: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV44 @ ( c_GCD_Ogcd__class_Olcm @ SV380 @ SV44 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1622,plain,
! [SV381: $i,SV45: $i] :
( ( ! [SY1363: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SV381 @ tc_nat ) @ SY1363 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV381 @ SY1363 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SY1363 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1623,plain,
! [SV382: $i,SV46: $i] :
( ( ! [SY1364: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SV382 @ tc_nat ) @ SY1364 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV382 @ SY1364 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SY1364 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1624,plain,
! [SV383: $i,SV47: $i] :
( ( ! [SY1365: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SV383 @ tc_nat ) @ SY1365 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SY1365 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1365 @ SV47 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1625,plain,
! [SV384: $i,SV48: $i] :
( ( ! [SY1366: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SV384 @ tc_nat ) @ SY1366 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV384 @ SY1366 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1366 @ SV384 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1626,plain,
! [SV385: $i,SV49: $i] :
( ( ! [SY1367: $i,SY1368: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SY1367 @ SY1368 @ SV49 ) @ SV49 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SY1368 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1627,plain,
! [SV386: $i,SV50: $i] :
( ( ! [SY1369: $i,SY1370: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SY1369 @ SY1370 @ SV50 ) @ SV50 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SY1369 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1628,plain,
! [SV387: $i,SV51: $i] :
( ( ! [SY1371: $i,SY1372: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SY1371 @ SV51 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SY1372 @ SV51 ) @ SY1371 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1629,plain,
! [SV388: $i,SV52: $i] :
( ( ! [SY1373: $i,SY1374: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SY1373 @ SV52 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1374 @ SV388 @ SV52 ) @ SY1373 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1630,plain,
! [SV389: $i,SV57: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV57 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV389 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1631,plain,
! [SV390: $i,SV58: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV58 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV390 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1632,plain,
! [SV391: $i,SV59: $i] :
( ( ! [SY1375: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV59 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV391 @ SY1375 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SY1375 @ SV391 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1633,plain,
! [SV392: $i,SV60: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV60 )
| ( ( c_HOL_Otimes__class_Otimes @ SV392 @ SV392 @ SV60 )
= SV392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1634,plain,
! [SV61: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV61 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV61 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= ( c_HOL_Ozero__class_Ozero @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1297]) ).
thf(1635,plain,
! [SV62: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV62 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1636,plain,
! [SV393: $i,SV63: $i] :
( ( ! [SY1376: $i,SY1377: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SY1376 @ SV63 ) @ SY1377 @ SV63 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV393 @ SY1377 @ SV63 ) @ ( c_Power_Opower__class_Opower @ SY1376 @ SY1377 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1637,plain,
! [SV394: $i,SV64: $i] :
( ( ! [SY1378: $i,SY1379: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV64 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV394 @ SY1378 @ SV64 ) @ SY1379 @ SV64 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV394 @ SY1379 @ SV64 ) @ ( c_Power_Opower__class_Opower @ SY1378 @ SY1379 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1638,plain,
! [SV395: $i,SV65: $i] :
( ( ! [SY1380: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV65 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV65 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV395 @ SY1380 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV395 @ SV65 ) @ SY1380 @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1639,plain,
! [SV396: $i,SV66: $i] :
( ( ! [SY1381: $i,SY1382: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV396 @ SY1381 @ SV66 ) @ SY1382 @ SV66 )
= ( c_HOL_Otimes__class_Otimes @ SV396 @ ( c_HOL_Otimes__class_Otimes @ SY1381 @ SY1382 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1640,plain,
! [SV397: $i,SV67: $i] :
( ( ! [SY1383: $i,SY1384: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SY1383 @ SV67 ) @ SY1384 @ SV67 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SY1384 @ SV67 ) @ SY1383 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1641,plain,
! [SV398: $i,SV68: $i] :
( ( ! [SY1385: $i,SY1386: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV398 @ SY1385 @ SV68 ) @ SY1386 @ SV68 )
= ( c_HOL_Otimes__class_Otimes @ SV398 @ ( c_HOL_Otimes__class_Otimes @ SY1385 @ SY1386 @ SV68 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1642,plain,
! [SV399: $i,SV69: $i] :
( ( ! [SY1387: $i,SY1388: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV69 )
| ( ( c_HOL_Otimes__class_Otimes @ SV399 @ ( c_HOL_Otimes__class_Otimes @ SY1387 @ SY1388 @ SV69 ) @ SV69 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV399 @ SY1387 @ SV69 ) @ SY1388 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1643,plain,
! [SV400: $i,SV70: $i] :
( ( ! [SY1389: $i,SY1390: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( c_HOL_Otimes__class_Otimes @ SV400 @ ( c_HOL_Otimes__class_Otimes @ SY1389 @ SY1390 @ SV70 ) @ SV70 )
= ( c_HOL_Otimes__class_Otimes @ SY1389 @ ( c_HOL_Otimes__class_Otimes @ SV400 @ SY1390 @ SV70 ) @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1644,plain,
! [SV401: $i,SV71: $i] :
( ( ! [SY1391: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV71 @ SV401 @ tc_nat ) @ SY1391 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV71 @ ( c_HOL_Otimes__class_Otimes @ SV401 @ SY1391 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1645,plain,
! [SV402: $i,SV72: $i] :
( ( ! [SY1392: $i,SY1393: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Otimes__class_Otimes @ SV402 @ ( c_HOL_Otimes__class_Otimes @ SY1392 @ SY1393 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV402 @ SY1392 @ SV72 ) @ SY1393 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1646,plain,
! [SV403: $i,SV73: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV73 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV403 @ SV73 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV73 ) @ SV403 @ SV73 ) )
| ( SV403
= ( c_HOL_Ozero__class_Ozero @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1647,plain,
! [SV404: $i,SV74: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV74 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV404 @ SV74 ) @ SV404 @ SV74 )
= ( c_HOL_Oone__class_Oone @ SV74 ) )
| ( SV404
= ( c_HOL_Ozero__class_Ozero @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1648,plain,
! [SV405: $i,SV75: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV75 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV405 @ SV75 ) @ SV405 @ SV75 )
= ( c_HOL_Oone__class_Oone @ SV75 ) )
| ( SV405
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1649,plain,
! [SV406: $i,SV76: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV76 )
| ( ( c_HOL_Otimes__class_Otimes @ SV406 @ ( c_HOL_Oinverse__class_Oinverse @ SV406 @ SV76 ) @ SV76 )
= ( c_HOL_Oone__class_Oone @ SV76 ) )
| ( SV406
= ( c_HOL_Ozero__class_Ozero @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1650,plain,
! [SV407: $i,SV77: $i] :
( ( ! [SY1394: $i,SY1395: $i] :
( ~ ( class_Divides_Osemiring__div @ SV77 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SY1394 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SY1395 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SY1394 @ SY1395 @ SV77 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1651,plain,
! [SV408: $i,SV78: $i] :
( ( ! [SY1396: $i,SY1397: $i] :
( ~ ( class_Divides_Osemiring__div @ SV78 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV408 @ SY1396 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SY1397 @ SY1396 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SV408 @ SY1397 @ SV78 ) )
| ( SY1396
= ( c_HOL_Ozero__class_Ozero @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1652,plain,
! [SV409: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV79 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ SV409 @ SV79 ) @ SV79 )
= ( c_HOL_Osgn__class_Osgn @ SV409 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1653,plain,
! [SV410: $i,SV80: $i] :
( ( ! [SY1398: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ ( c_GCD_Ogcd__class_Ogcd @ SV410 @ SY1398 @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ SV410 @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ SY1398 @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1654,plain,
! [SV411: $i,SV81: $i] :
( ( ! [SY1399: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV81 @ ( c_GCD_Ogcd__class_Ogcd @ SV411 @ SY1399 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV81 @ SV411 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV81 @ SY1399 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1655,plain,
! [SV412: $i,SV82: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 )
| ( ( c_HOL_Oabs__class_Oabs @ SV412 @ SV82 )
= ( c_HOL_Otimes__class_Otimes @ SV412 @ ( c_HOL_Osgn__class_Osgn @ SV412 @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1656,plain,
! [SV413: $i,SV83: $i] :
( ( ! [SY1400: $i,SY1401: $i] :
( ~ ( class_Divides_Osemiring__div @ SV83 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SY1400 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SY1401 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SY1400 @ SY1401 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1401 @ SY1400 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1401 @ SV413 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1657,plain,
! [SV414: $i,SV84: $i] :
( ( ! [SY1402: $i,SY1403: $i] :
( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SY1402 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SY1403 @ SY1402 @ SV84 ) @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SY1403 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1402 @ SY1403 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1402 @ SV414 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1658,plain,
! [SV415: $i,SV85: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV85 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV415 @ SV85 ) @ SV85 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV415 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1659,plain,
! [SV86: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV86 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV86 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1660,plain,
! [SV416: $i,SV87: $i] :
( ( ! [SY1404: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ ( c_GCD_Ogcd__class_Olcm @ SV416 @ SY1404 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV416 @ SV87 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ SV416 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1661,plain,
! [SV417: $i,SV88: $i] :
( ( ! [SY1405: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ ( c_GCD_Ogcd__class_Olcm @ SV417 @ SY1405 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1405 @ SV88 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ SY1405 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1662,plain,
! [SV418: $i,SV89: $i] :
( ( ! [SY1406: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV89 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV89 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SY1406 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV418 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY1406 @ SV89 ) @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1663,plain,
! [SV419: $i,SV90: $i] :
( ( ! [SY1407: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV419 @ SY1407 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SY1407 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV419 @ SV90 ) @ SV90 ) )
| ( SY1407
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV419
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1664,plain,
! [SV420: $i,SV91: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV91 )
| ( SV420
= ( c_HOL_Ozero__class_Ozero @ SV91 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV420 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1665,plain,
! [SV421: $i,SV92: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV92 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV421 @ SV92 ) @ SV92 )
= SV421 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1666,plain,
! [SV93: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV93 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1667,plain,
! [SV422: $i,SV94: $i] :
( ( ! [SY1408: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SY1408 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1408 @ SV94 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1408 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SY1408 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1668,plain,
! [SV423: $i,SV95: $i] :
( ( ! [SY1409: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SV423
= ( c_HOL_Ozero__class_Ozero @ SV95 ) )
| ( SY1409
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY1409 @ SV423 @ SV95 ) @ SV423 @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1669,plain,
! [SV424: $i,SV96: $i] :
( ( ! [SY1410: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV96 )
| ( SV424
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SY1410 @ SV424 @ SV96 ) @ SV424 @ SV96 )
= SY1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1670,plain,
! [SV425: $i,SV97: $i] :
( ( ! [SY1411: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV97 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
| ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SY1411 @ SV97 ) @ SY1411 @ SV97 ) )
| ( SY1411
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1671,plain,
! [SV426: $i,SV98: $i] :
( ( ! [SY1412: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV98 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SY1412 @ SV98 ) @ SY1412 @ SV98 )
= SV426 )
| ( SY1412
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1672,plain,
! [SV427: $i,SV99: $i] :
( ( ! [SY1413: $i,SY1414: $i,SY1415: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SY1413 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SY1414 @ SY1415 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SY1414 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SY1413 @ SV99 ) @ SY1415 @ SV99 ) @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1673,plain,
! [SV428: $i,SV100: $i] :
( ( ! [SY1416: $i,SY1417: $i,SY1418: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV428 @ SY1416 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SY1417 @ SY1418 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SV428 @ ( c_HOL_Otimes__class_Otimes @ SY1416 @ ( c_HOL_Otimes__class_Otimes @ SY1417 @ SY1418 @ SV100 ) @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1674,plain,
! [SV429: $i,SV101: $i] :
( ( ! [SY1419: $i,SY1420: $i,SY1421: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SY1419 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SY1420 @ SY1421 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SY1420 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SY1419 @ SY1421 @ SV101 ) @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1675,plain,
! [SV430: $i,SV102: $i] :
( ( ! [SY1422: $i] :
( ~ ( class_Divides_Osemiring__div @ SV102 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SY1422 @ SV102 ) @ SY1422 @ SV102 )
= SV430 )
| ( SY1422
= ( c_HOL_Ozero__class_Ozero @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1676,plain,
! [SV431: $i,SV103: $i] :
( ( ! [SY1423: $i] :
( ~ ( class_Divides_Osemiring__div @ SV103 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SY1423 @ SV103 ) @ SV431 @ SV103 )
= SY1423 )
| ( SV431
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1677,plain,
! [SV432: $i,SV104: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV104 )
| ( ( c_Divides_Odiv__class_Odiv @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= ( c_HOL_Ozero__class_Ozero @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1678,plain,
! [SV433: $i,SV105: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV105 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV433 @ SV105 )
= ( c_HOL_Ozero__class_Ozero @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1679,plain,
! [SV434: $i,SV106: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV106 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV106 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV106 ) @ SV434 @ SV106 ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1680,plain,
! [SV435: $i,SV107: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV107 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV435 @ SV107 ) @ ( c_HOL_Oabs__class_Oabs @ SV435 @ SV107 ) @ SV107 )
= SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1681,plain,
! [SV436: $i,SV108: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV108 @ SV436 @ tc_nat )
= SV108 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV436 @ SV108 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1682,plain,
! [SV437: $i,SV109: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV109 @ SV437 @ tc_nat )
= SV109 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV437 @ SV109 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1683,plain,
! [SV438: $i,SV110: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV110 @ SV438 @ tc_nat )
= SV438 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV110 @ SV438 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1684,plain,
! [SV439: $i,SV111: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV111 @ SV439 @ tc_nat )
= SV111 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV439 @ SV111 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1685,plain,
! [SV440: $i,SV112: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV112 @ SV440 @ tc_nat )
= SV440 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV112 @ SV440 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1686,plain,
! [SV441: $i,SV113: $i] :
( ( ! [SY1424: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV113 @ SV441 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SY1424 @ SV113 @ tc_nat ) @ SV441 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1687,plain,
! [SV442: $i,SV114: $i] :
( ( ! [SY1425: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV114 @ SV442 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV114 @ SY1425 @ tc_nat ) @ SV442 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1688,plain,
! [SV443: $i,SV115: $i] :
( ( ! [SY1426: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ ( c_GCD_Ogcd__class_Olcm @ SV443 @ SY1426 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ SY1426 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1689,plain,
! [SV444: $i,SV116: $i] :
( ( ! [SY1427: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ ( c_GCD_Ogcd__class_Olcm @ SV444 @ SY1427 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ SV444 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1690,plain,
! [SV445: $i,SV117: $i] :
( ( ! [SY1428: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV117 @ SV445 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SY1428 @ SV117 @ tc_nat ) @ SV445 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1691,plain,
! [SV446: $i,SV118: $i] :
( ( ! [SY1429: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV118 @ SV446 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV118 @ SY1429 @ tc_nat ) @ SV446 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1692,plain,
! [SV447: $i,SV119: $i] :
( ( ! [SY1430: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ ( c_GCD_Ogcd__class_Olcm @ SV447 @ SY1430 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ SV447 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1693,plain,
! [SV448: $i,SV120: $i] :
( ( ! [SY1431: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ ( c_GCD_Ogcd__class_Olcm @ SV448 @ SY1431 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ SY1431 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1694,plain,
! [SV449: $i,SV121: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV121 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV449 @ SV121 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV121 ) @ SV449 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1695,plain,
! [SV450: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV122 )
| ~ ( class_Int_Onumber__ring @ SV122 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV450 @ SV122 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV122 ) @ SV450 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1696,plain,
! [SV451: $i,SV123: $i] :
( ( ! [SY1432: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Otimes__class_Otimes @ SY1432 @ SV451 @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1697,plain,
! [SV452: $i,SV124: $i] :
( ( ! [SY1433: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV452 @ ( c_HOL_Otimes__class_Otimes @ SV452 @ SY1433 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1698,plain,
! [SV453: $i,SV125: $i] :
( ( ! [SY1434: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV125 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV453 @ ( c_HOL_Otimes__class_Otimes @ SV453 @ SY1434 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1699,plain,
! [SV454: $i,SV126: $i] :
( ( ! [SY1435: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV126 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV126 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SV454 @ SY1435 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SV454 @ SV126 ) @ SY1435 @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1700,plain,
! [SV455: $i,SV127: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV127 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV127 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV455 @ SV127 ) @ SV127 )
= SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1701,plain,
! [SV456: $i,SV128: $i] :
( ( ! [SY1436: $i,SY1437: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV456 @ SY1436 @ SV128 ) @ SY1437 @ SV128 )
= ( c_Power_Opower__class_Opower @ SV456 @ ( c_HOL_Otimes__class_Otimes @ SY1436 @ SY1437 @ tc_nat ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1702,plain,
! [SV457: $i,SV129: $i] :
( ( ! [SY1438: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SV457 @ SY1438 @ SV129 )
= ( c_HOL_Otimes__class_Otimes @ SY1438 @ SV457 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1703,plain,
! [SV458: $i,SV130: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV130 @ SV458 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV458 @ SV130 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1704,plain,
! [SV459: $i,SV131: $i] :
( ( ! [SY1439: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV131 )
| ( ( c_HOL_Otimes__class_Otimes @ SV459 @ SY1439 @ SV131 )
= ( c_HOL_Otimes__class_Otimes @ SY1439 @ SV459 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1705,plain,
! [SV132: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV132 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 )
= ( c_HOL_Ozero__class_Ozero @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1706,plain,
! [SV460: $i,SV133: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV133 )
| ( SV460
= ( c_HOL_Ozero__class_Ozero @ SV133 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV460 @ SV460 @ SV133 )
= ( c_HOL_Oone__class_Oone @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1707,plain,
! [SV461: $i,SV134: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV134 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV461 @ SV461 @ SV134 )
= ( c_HOL_Oone__class_Oone @ SV134 ) )
| ( SV461
= ( c_HOL_Ozero__class_Ozero @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1708,plain,
! [SV462: $i,SV135: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV135 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV135 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV462 @ SV462 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
| ( SV462
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1709,plain,
! [SV463: $i,SV136: $i] :
( ( ! [SY1440: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ SV463 @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ SY1440 @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ ( c_GCD_Ogcd__class_Olcm @ SV463 @ SY1440 @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1710,plain,
! [SV464: $i,SV138: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV138 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV138 ) @ SV464 @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1711,plain,
! [SV465: $i,SV139: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV139 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV139 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV465 @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1712,plain,
! [SV466: $i,SV140: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV140 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV140 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV466 @ ( c_HOL_Ozero__class_Ozero @ SV140 ) @ SV140 )
= ( c_HOL_Ozero__class_Ozero @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1713,plain,
! [SV467: $i,SV141: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV141 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SV467 @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1714,plain,
! [SV468: $i,SV142: $i] :
( ( ! [SY1441: $i,SY1442: $i] :
( ~ ( class_Divides_Osemiring__div @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SY1441 @ SV142 ) @ SY1442 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SY1442 @ SV142 ) @ SY1441 @ SV142 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1441 @ SV468 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1715,plain,
! [SV469: $i,SV143: $i] :
( ( ! [SY1443: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV143 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV469 @ SV143 ) @ SY1443 @ SV143 )
= ( c_Power_Opower__class_Opower @ SV469 @ SY1443 @ SV143 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY1443 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1716,plain,
! [SV470: $i,SV144: $i] :
( ( ! [SY1444: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV144 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV470 @ SY1444 @ SV144 ) @ SV144 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV470 @ SV144 ) @ SY1444 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1717,plain,
! [SV471: $i,SV145: $i] :
( ( ! [SY1445: $i,SY1446: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SY1445 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SY1446 @ SY1445 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SY1446 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1718,plain,
! [SV472: $i,SV146: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV146 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV472 @ SV146 ) @ SV146 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV472 @ SV146 ) @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1719,plain,
! [SV473: $i,SV147: $i] :
( ( ! [SY1447: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV147 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV147 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV473 @ SY1447 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV473 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SY1447 @ SV147 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1720,plain,
! [SV474: $i,SV148: $i] :
( ( ! [SY1448: $i,SY1449: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV148 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SY1448 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SY1449 @ SY1448 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SY1449 @ SV148 ) )
| ( SY1448
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1721,plain,
! [SV475: $i,SV149: $i] :
( ( ! [SY1450: $i,SY1451: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SY1450 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SY1451 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SY1450 @ SY1451 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1722,plain,
! [SV476: $i,SV150: $i] :
( ( ! [SY1452: $i,SY1453: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV150 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SY1452 @ SV150 ) @ SY1453 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SY1453 @ SV150 ) @ SY1452 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1723,plain,
! [SV477: $i,SV151: $i] :
( ( ! [SY1454: $i] :
( ~ ( class_Divides_Osemiring__div @ SV151 )
| ( ( c_HOL_Otimes__class_Otimes @ SV477 @ ( c_Divides_Odiv__class_Odiv @ SY1454 @ SV477 @ SV151 ) @ SV151 )
= SY1454 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV477 @ SY1454 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1724,plain,
! [SV478: $i,SV152: $i] :
( ( ! [SY1455: $i] :
( ~ ( class_Divides_Osemiring__div @ SV152 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV478 @ SY1455 @ SV152 ) @ SY1455 @ SV152 )
= SV478 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1455 @ SV478 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1725,plain,
! [SV479: $i,SV153: $i] :
( ( ! [SY1456: $i,SY1457: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV153 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SY1456 @ SV153 )
| ( SY1457
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SY1457 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SY1456 @ SY1457 @ SV153 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1726,plain,
! [SV480: $i,SV154: $i] :
( ( ! [SY1458: $i,SY1459: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV154 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SY1458 @ SV154 )
| ( SY1459
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1459 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SY1459 @ SY1458 @ SV154 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1727,plain,
! [SV481: $i,SV155: $i] :
( ( ! [SY1460: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV155 @ SV481 @ tc_nat )
| ( SY1460
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1460 @ SV155 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY1460 @ SV481 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1728,plain,
! [SV482: $i,SV156: $i] :
( ( ( c_Complex_Ocnj @ ( c_Power_Opower__class_Opower @ SV156 @ SV482 @ tc_Complex_Ocomplex ) )
= ( c_Power_Opower__class_Opower @ ( c_Complex_Ocnj @ SV156 ) @ SV482 @ tc_Complex_Ocomplex ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1729,plain,
! [SV483: $i,SV157: $i] :
( ( ! [SY1461: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SV483 @ SY1461 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SY1461 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV483 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1730,plain,
! [SV484: $i,SV158: $i] :
( ( ! [SY1462: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SV484 @ SY1462 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SY1462 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1462 @ SV158 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1731,plain,
! [SV485: $i,SV159: $i] :
( ( ! [SY1463: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SV485 @ SY1463 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SV485 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV485 @ SV159 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1732,plain,
! [SV486: $i,SV160: $i] :
( ( ! [SY1464: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SV486 @ SY1464 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SY1464 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV486 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1733,plain,
! [SV487: $i,SV161: $i] :
( ( ! [SY1465: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SV487 @ SY1465 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SY1465 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV487 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1734,plain,
! [SV488: $i,SV162: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV162 @ SV488 @ tc_nat ) @ SV488 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1735,plain,
! [SV489: $i,SV163: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV163 @ SV489 @ tc_nat ) @ SV163 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1736,plain,
! [SV490: $i,SV164: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV164 @ SV490 @ tc_nat ) @ SV164 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1737,plain,
! [SV491: $i,SV165: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV165 @ SV491 @ tc_nat ) @ SV491 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1738,plain,
! [SV492: $i,SV166: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV166 @ SV492 @ tc_nat ) @ SV166 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1739,plain,
! [SV493: $i,SV167: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV167 @ SV493 @ tc_nat ) @ SV493 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1740,plain,
! [SV494: $i,SV168: $i] :
( ( ! [SY1466: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SV494 @ SY1466 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SY1466 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV494 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1741,plain,
! [SV495: $i,SV169: $i] :
( ( ! [SY1467: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SV495 @ SY1467 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SY1467 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV495 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1742,plain,
! [SV496: $i,SV170: $i] :
( ( ! [SY1468: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SV496 @ SY1468 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SY1468 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV496 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1743,plain,
! [SV497: $i,SV171: $i] :
( ( ! [SY1469: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SY1469 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1469 @ SV171 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SY1469 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1744,plain,
! [SV498: $i,SV172: $i] :
( ( ! [SY1470: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1470 @ SV172 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1470 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SY1470 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1745,plain,
! [SV499: $i,SV173: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV173 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV499 @ SV173 ) @ SV173 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV499 @ SV173 ) @ SV173 ) )
| ( SV499
= ( c_HOL_Ozero__class_Ozero @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1746,plain,
! [SV500: $i,SV174: $i] :
( ( ! [SY1471: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV174 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV500 @ SY1471 @ SV174 ) @ SV174 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV500 @ SV174 ) @ ( c_HOL_Oabs__class_Oabs @ SY1471 @ SV174 ) @ SV174 ) )
| ( SY1471
= ( c_HOL_Ozero__class_Ozero @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1747,plain,
! [SV501: $i,SV175: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV175 @ SV501 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_GCD_Ogcd__class_Ogcd @ SV175 @ SV501 @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ SV175 @ SV501 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1748,plain,
! [SV178: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV178 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV178 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV178 )
= ( c_HOL_Oone__class_Oone @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1749,plain,
! [SV502: $i,SV179: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV179 )
| ( ( c_Divides_Odiv__class_Odiv @ SV502 @ SV502 @ SV179 )
= ( c_HOL_Oone__class_Oone @ SV179 ) )
| ( SV502
= ( c_HOL_Ozero__class_Ozero @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1750,plain,
! [SV503: $i,SV180: $i] :
( ( ! [SY1472: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV180 @ SV503 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY1472 @ SV503 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1751,plain,
! [SV504: $i,SV182: $i] :
( ( ! [SY1473: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV504 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SY1473 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SY1473 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1752,plain,
! [SV505: $i,SV183: $i] :
( ( ! [SY1474: $i,SY1475: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV183 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY1474 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY1475 @ SV183 ) @ SV183 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1474 @ SY1475 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1753,plain,
! [SV506: $i,SV184: $i] :
( ( ! [SY1476: $i,SY1477: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV184 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SY1476 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY1477 @ SY1476 @ SV184 ) @ SV184 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SY1477 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1754,plain,
! [SV507: $i,SV185: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV185 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV507 @ SV185 ) @ SV185 )
= ( c_HOL_Oabs__class_Oabs @ SV507 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1755,plain,
! [SV508: $i,SV186: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV186 @ SV508 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV508 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1756,plain,
! [SV509: $i,SV187: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV187 @ SV509 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV187 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1757,plain,
! [SV510: $i,SV189: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV189 @ SV510 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV510 @ SV189 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1758,plain,
! [SV511: $i,SV190: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV190 @ SV511 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV511 @ SV190 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1759,plain,
! [SV512: $i,SV191: $i] :
( ( ! [SY1478: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV512 @ SY1478 @ SV191 ) @ SV512 @ SV191 )
= ( c_HOL_Otimes__class_Otimes @ SV512 @ ( c_Power_Opower__class_Opower @ SV512 @ SY1478 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1760,plain,
! [SV513: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV192 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV192 )
| ( ( c_HOL_Ozero__class_Ozero @ SV192 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV513 @ SV192 ) @ SV513 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1761,plain,
! [SV514: $i,SV193: $i] :
( ( ! [SY1479: $i,SY1480: $i] :
( ~ ( class_Divides_Osemiring__div @ SV193 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SY1479 @ SV193 ) @ SY1480 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SY1480 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SY1479 @ SY1480 @ SV193 ) @ SV193 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1479 @ SV514 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1762,plain,
! [SV515: $i,SV194: $i] :
( ( ! [SY1481: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV194 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV515 @ SY1481 @ tc_nat ) @ SV194 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV515 @ SV194 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1481 @ SV194 ) @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1763,plain,
! [SV516: $i,SV195: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV195 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV516 @ SV195 ) @ ( c_HOL_Oabs__class_Oabs @ SV516 @ SV195 ) @ SV195 )
= ( c_HOL_Otimes__class_Otimes @ SV516 @ SV516 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1764,plain,
! [SV517: $i,SV196: $i] :
( ( ! [SY1482: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV196 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV517 @ SY1482 @ SV196 ) @ SV196 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV517 @ SV196 ) @ SY1482 @ SV196 ) )
| ( SV517
= ( c_HOL_Ozero__class_Ozero @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1765,plain,
! [SV518: $i,SV197: $i] :
( ( ! [SY1483: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV197 @ ( c_GCD_Ogcd__class_Ogcd @ SV518 @ SY1483 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV518 @ ( c_GCD_Ogcd__class_Ogcd @ SV197 @ SY1483 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1766,plain,
! [SV519: $i,SV198: $i] :
( ( ! [SY1484: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV198 @ SV519 @ tc_nat ) @ SY1484 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV198 @ ( c_GCD_Ogcd__class_Ogcd @ SV519 @ SY1484 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1767,plain,
! [SV520: $i,SV199: $i] :
( ( ! [SY1485: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV199 @ SV520 @ tc_nat ) @ SY1485 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV199 @ ( c_GCD_Ogcd__class_Ogcd @ SV520 @ SY1485 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1768,plain,
! [SV521: $i,SV201: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV521 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1769,plain,
! [SV522: $i,SV202: $i] :
( ( ! [SY1486: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SY1486 @ SV202 ) @ SY1486 @ SV202 ) )
| ( SY1486
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1770,plain,
! [SV523: $i,SV203: $i] :
( ( ! [SY1487: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SY1487 @ SV203 ) @ SY1487 @ SV203 )
= SV523 )
| ( SY1487
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1771,plain,
! [SV524: $i,SV204: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV204 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV524 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1772,plain,
! [SV525: $i,SV205: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV205 )
| ( ( c_HOL_Otimes__class_Otimes @ SV525 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= ( c_HOL_Ozero__class_Ozero @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1773,plain,
! [SV526: $i,SV206: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV206 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV526 @ SV206 )
= ( c_HOL_Ozero__class_Ozero @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1774,plain,
! [SV527: $i,SV207: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV207 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SV527 @ SV207 )
= ( c_HOL_Ozero__class_Ozero @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1775,plain,
! [SV528: $i,SV210: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV210 )
| ( ( c_HOL_Otimes__class_Otimes @ SV528 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 )
= ( c_HOL_Ozero__class_Ozero @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1776,plain,
! [SV529: $i,SV211: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV211 )
| ( ( c_HOL_Otimes__class_Otimes @ SV529 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1777,plain,
! [SV530: $i,SV212: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV212 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV530 @ SV212 )
= ( c_HOL_Ozero__class_Ozero @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1778,plain,
! [SV531: $i,SV213: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV213 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV531 @ SV213 )
= ( c_HOL_Ozero__class_Ozero @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1779,plain,
! [SV532: $i,SV214: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV214 )
| ( ( c_HOL_Otimes__class_Otimes @ SV532 @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1780,plain,
! [SV533: $i,SV215: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV215 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV533 @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1781,plain,
! [SV534: $i,SV216: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV216 )
| ( ( c_HOL_Otimes__class_Otimes @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1782,plain,
! [SV535: $i,SV217: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV217 )
| ( SV535
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
| ~ ( c_Int_Oiszero @ SV535 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1783,plain,
! [SV536: $i,SV218: $i] :
( ( ! [SY1488: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV218 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV536 @ SY1488 @ SV218 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV536 @ SV218 ) @ SY1488 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1784,plain,
! [SV537: $i,SV219: $i] :
( ( ! [SY1489: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV219 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV537 @ SV219 ) @ SY1489 @ SV219 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV537 @ SY1489 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1785,plain,
! [SV538: $i,SV220: $i] :
( ( ! [SY1490: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV220 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ SY1490 @ SV220 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ ( c_HOL_Oabs__class_Oabs @ SY1490 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1786,plain,
! [SV539: $i,SV221: $i] :
( ( ! [SY1491: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ ( c_HOL_Oabs__class_Oabs @ SY1491 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ SY1491 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1787,plain,
! [SV540: $i,SV222: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV222 @ ( c_GCD_Ogcd__class_Olcm @ SV222 @ SV540 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV222 @ SV540 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1788,plain,
! [SV223: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV223 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1789,plain,
! [SV224: $i] :
( ( ( ~ ( class_Ring__and__Field_Osgn__if @ SV224 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1460]) ).
thf(1790,plain,
! [SV225: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV225 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1791,plain,
! [SV541: $i,SV226: $i] :
( ( ! [SY1492: $i] :
( ( c_GCD_Ogcd__class_Olcm @ SV226 @ ( c_GCD_Ogcd__class_Olcm @ SV541 @ SY1492 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV541 @ ( c_GCD_Ogcd__class_Olcm @ SV226 @ SY1492 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1792,plain,
! [SV542: $i,SV227: $i] :
( ( ! [SY1493: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ SV227 @ SV542 @ tc_nat ) @ SY1493 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV227 @ ( c_GCD_Ogcd__class_Olcm @ SV542 @ SY1493 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1793,plain,
! [SV543: $i,SV228: $i] :
( ( ! [SY1494: $i] :
( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ SV228 @ SV543 @ tc_nat ) @ SY1494 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV228 @ ( c_GCD_Ogcd__class_Olcm @ SV543 @ SY1494 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1794,plain,
! [SV544: $i,SV229: $i] :
( ( ! [SY1495: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV229 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV544 @ SY1495 @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ SV544 @ ( c_HOL_Oinverse__class_Oinverse @ SY1495 @ SV229 ) @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1795,plain,
! [SV545: $i,SV230: $i] :
( ( ! [SY1496: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV230 )
| ~ ( class_Int_Onumber__ring @ SV230 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV545 @ SY1496 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SV545 @ ( c_HOL_Oinverse__class_Oinverse @ SY1496 @ SV230 ) @ SV230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1796,plain,
! [SV231: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV231 ) )
= $true )
| ( ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1797,plain,
! [SV546: $i,SV232: $i] :
( ( ! [SY1497: $i,SY1498: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV232 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV546 @ SY1497 @ SV232 ) @ SY1498 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV546 @ SY1498 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SY1497 @ SY1498 @ SV232 ) @ SV232 ) )
| ( SY1497
= ( c_HOL_Ozero__class_Ozero @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1798,plain,
! [SV547: $i,SV233: $i] :
( ( ! [SY1499: $i,SY1500: $i,SY1501: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SY1499 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SY1500 @ SY1501 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1499 @ SY1501 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SY1500 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1799,plain,
! [SV548: $i,SV234: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV234 @ SV548 @ tc_nat )
= SV548 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV548 @ SV234 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1800,plain,
! [SV549: $i,SV235: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SV549 @ tc_nat )
= SV235 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV235 @ SV549 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1801,plain,
! [SV550: $i,SV236: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV236 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV550 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV550 @ SV236 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1802,plain,
! [SV551: $i,SV237: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV237 @ SV551 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV551 @ SV237 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1803,plain,
! [SV552: $i,SV238: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV238 @ SV552 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV552 @ SV238 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1804,plain,
! [SV553: $i,SV239: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV239 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV239 )
| ( ( c_HOL_Ozero__class_Ozero @ SV239 )
= ( c_HOL_Oinverse__class_Odivide @ SV553 @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1805,plain,
! [SV554: $i,SV240: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV240 @ ( c_GCD_Ogcd__class_Ogcd @ SV240 @ SV554 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV240 @ SV554 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1806,plain,
! [SV555: $i,SV241: $i] :
( ( ! [SY1502: $i,SY1503: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV241 )
| ( ( c_Power_Opower__class_Opower @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SY1502 @ SY1503 @ tc_nat ) @ SV241 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV555 @ SY1502 @ SV241 ) @ SY1503 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1807,plain,
! [SV556: $i,SV242: $i] :
( ( ! [SY1504: $i] :
( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV242 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SY1504 @ SV242 ) @ SV242 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV556 @ SV242 ) @ ( c_HOL_Osgn__class_Osgn @ SY1504 @ SV242 ) @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1808,plain,
! [SV557: $i,SV243: $i] :
( ( ! [SY1505: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV243 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV557 @ SY1505 @ SV243 ) @ SV243 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV557 @ SV243 ) @ ( c_HOL_Osgn__class_Osgn @ SY1505 @ SV243 ) @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1809,plain,
! [SV558: $i,SV244: $i] :
( ( ! [SY1506: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV244 @ SV558 @ tc_nat ) @ SY1506 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1506 @ SV244 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV244 @ SY1506 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1810,plain,
! [SV559: $i,SV245: $i] :
( ( ! [SY1507: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV245 @ SV559 @ tc_nat ) @ SY1507 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1507 @ SV559 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV559 @ SY1507 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1811,plain,
! [SV560: $i,SV246: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV246 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV246 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV560 @ SV246 ) @ SV560 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1812,plain,
! [SV561: $i,SV247: $i] :
( ( ! [SY1508: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1508 @ SV561 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1508 @ SV247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SY1508 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1813,plain,
! [SV562: $i,SV248: $i] :
( ( ! [SY1509: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SY1509 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1509 @ SV562 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SY1509 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1814,plain,
! [SV249: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV249 ) )
= $true )
| ( ( ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ SV249 ) @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1815,plain,
! [SV250: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV250 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV250 ) @ SV250 )
= ( c_HOL_Oone__class_Oone @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1486]) ).
thf(1816,plain,
! [SV251: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV251 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV251 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV251 ) @ SV251 )
= ( c_HOL_Oone__class_Oone @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1487]) ).
thf(1817,plain,
! [SV563: $i,SV252: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV252 )
| ( ( c_Power_Opower__class_Opower @ SV563 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV252 )
= SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1818,plain,
! [SV564: $i,SV253: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
| ( ( c_Power_Opower__class_Opower @ SV564 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV253 )
= SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1819,plain,
! [SV565: $i,SV256: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV256 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV565 @ SV256 )
= ( c_HOL_Oone__class_Oone @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1820,plain,
! [SV257: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV257 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV257 )
= ( c_HOL_Oone__class_Oone @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1821,plain,
! [SV566: $i,SV258: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV258 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV566 @ ( c_HOL_Oone__class_Oone @ SV258 ) @ SV258 )
= SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1822,plain,
! [SV259: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV259 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ SV259 ) @ SV259 )
= ( c_HOL_Oone__class_Oone @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1823,plain,
! [SV263: $i] :
( ( ( SV263
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1824,plain,
! [SV567: $i,SV264: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV264 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV264 ) @ SV567 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1825,plain,
! [SV568: $i,SV267: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV267 )
| ( ( c_HOL_Otimes__class_Otimes @ SV568 @ ( c_HOL_Oone__class_Oone @ SV267 ) @ SV267 )
= SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1826,plain,
! [SV569: $i,SV268: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV268 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV268 ) @ SV569 @ SV268 )
= SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1827,plain,
! [SV570: $i,SV269: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV269 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV269 ) @ SV570 @ SV269 )
= SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1828,plain,
! [SV571: $i,SV270: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV270 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV270 ) @ SV571 @ SV270 )
= SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1829,plain,
! [SV572: $i,SV273: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
| ( ( c_HOL_Otimes__class_Otimes @ SV572 @ ( c_HOL_Oone__class_Oone @ SV273 ) @ SV273 )
= SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1830,plain,
! [SV573: $i,SV274: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV274 ) @ SV573 @ SV274 )
= SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1831,plain,
! [SV275: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ SV275 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ SV275 ) @ SV275 )
= ( c_HOL_Oone__class_Oone @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1512]) ).
thf(1832,plain,
! [SV574: $i,SV276: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV276 )
| ( ( c_Divides_Odiv__class_Odiv @ SV574 @ ( c_HOL_Oone__class_Oone @ SV276 ) @ SV276 )
= SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1833,plain,
! [SV575: $i,SV277: $i] :
( ( ! [SY1510: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
| ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SY1510 @ SV277 )
!= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SY1510
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1834,plain,
! [SV576: $i,SV278: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV278 @ SV576 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV278
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1835,plain,
! [SV279: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV279 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV279 )
!= ( c_HOL_Oone__class_Oone @ SV279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1836,plain,
! [SV577: $i,SV280: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV280 @ SV577 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV577
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1837,plain,
! [SV578: $i,SV281: $i] :
( ( ! [SY1511: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ ( c_HOL_Otimes__class_Otimes @ SV578 @ SY1511 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ SV578 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1838,plain,
! [SV579: $i,SV282: $i] :
( ( ! [SY1512: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV282 @ SV579 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV282 @ SY1512 @ tc_nat ) )
| ( SV282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV579 = SY1512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1839,plain,
! [SV580: $i,SV283: $i] :
( ( ! [SY1513: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV283 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY1513 @ SV283 ) )
| ( SV580 = SY1513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1840,plain,
! [SV581: $i,SV284: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV284 @ SV581 @ tc_nat )
!= SV581 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV284 @ SV581 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1841,plain,
! [SV582: $i,SV285: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV285 @ SV582 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1842,plain,
! [SV583: $i,SV286: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV286 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV583 @ SV286 )
!= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ( SV583
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1843,plain,
! [SV584: $i,SV287: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV287 @ SV584 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV584
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1844,plain,
! [SV585: $i,SV288: $i] :
( ( ! [SY1514: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV585 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SY1514 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SY1514 @ SV585 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1845,plain,
! [SV289: $i] :
( ( ( c_FFT__Mirabelle_Oroot @ SV289 )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1846,plain,
! [SV586: $i,SV290: $i] :
( ( ( SV290
!= ( c_HOL_Otimes__class_Otimes @ SV290 @ SV586 @ tc_nat ) )
| ( SV290
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV586
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1847,plain,
! [SV587: $i,SV291: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV291 @ SV587 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV587
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1848,plain,
! [SV588: $i,SV292: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV292 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ SV588 @ tc_nat ) @ SV292 )
!= ( c_HOL_Ozero__class_Ozero @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1849,plain,
! [SV589: $i,SV293: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV293 @ SV589 @ tc_nat ) )
| ( SV589
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1850,plain,
! [SV590: $i,SV294: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV294 )
| ( ( c_HOL_Oabs__class_Oabs @ SV590 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV590
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1851,plain,
! [SV295: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV295 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV295 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1852,plain,
! [SV591: $i,SV296: $i] :
( ( ! [SY1515: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SY1515 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1853,plain,
! [SV592: $i,SV297: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV297 @ SV592 @ tc_nat )
!= SV297 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV297 @ SV592 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1854,plain,
! [SV593: $i,SV298: $i] :
( ( ! [SY1516: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ ( c_HOL_Otimes__class_Otimes @ SV593 @ SY1516 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ SY1516 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1855,plain,
! [SV594: $i,SV299: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV299 @ SV594 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV299
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1856,plain,
! [SV595: $i,SV300: $i] :
( ( ! [SY1517: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV300 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY1517 @ SV300 ) )
| ( SV595 = SY1517 )
| ( SY1517
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1857,plain,
! [SV596: $i,SV301: $i] :
( ( ! [SY1518: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV301 @ SV596 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV301 @ SY1518 @ tc_nat ) )
| ( SV596 = SY1518 )
| ( SV301
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1858,plain,
! [SV597: $i,SV302: $i] :
( ( ! [SY1519: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV302 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SY1519 @ SV302 )
!= ( c_HOL_Oone__class_Oone @ SV302 ) )
| ( SY1519
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SV597 = SY1519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1859,plain,
! [SV598: $i,SV303: $i] :
( ( ! [SY1520: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV303 @ SV598 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV303 @ SY1520 @ tc_nat ) @ SV598 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY1520 @ SV598 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1860,plain,
! [SV599: $i,SV304: $i] :
( ( ~ ( class_RealVector_Oreal__normed__vector @ SV304 )
| ( ( c_HOL_Osgn__class_Osgn @ SV599 @ SV304 )
!= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
| ( SV599
= ( c_HOL_Ozero__class_Ozero @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1861,plain,
! [SV600: $i,SV305: $i] :
( ( ( ( c_Complex_Ocnj @ SV305 )
!= ( c_Complex_Ocnj @ SV600 ) )
| ( SV305 = SV600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1862,plain,
! [SV601: $i,SV306: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV306 @ SV601 @ tc_nat )
!= SV601 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV306 @ SV601 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1863,plain,
! [SV602: $i,SV307: $i] :
( ( ! [SY1521: $i,SY1522: $i] :
( ( SV307
!= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SY1521 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( SY1521
!= ( c_HOL_Otimes__class_Otimes @ SY1522 @ ( c_GCD_Ogcd__class_Ogcd @ SY1521 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SY1521 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SY1522 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1864,plain,
! [SV603: $i,SV308: $i] :
( ( ! [SY1523: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV308 )
| ( ( c_HOL_Otimes__class_Otimes @ SV603 @ SY1523 @ SV308 )
!= ( c_HOL_Oone__class_Oone @ SV308 ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV603 @ SV308 )
= SY1523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1865,plain,
! [SV604: $i,SV309: $i] :
( ( ! [SY1524: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SV604 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SY1524 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SY1524 @ SV604 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1866,plain,
! [SV605: $i,SV310: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV310 @ SV605 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV310
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1867,plain,
! [SV606: $i,SV311: $i] :
( ( ! [SY1525: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV311 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV606 @ SV311 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY1525 @ SV311 ) )
| ( SV606 = SY1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1868,plain,
! [SV607: $i,SV312: $i] :
( ( ! [SY1526: $i,SY1527: $i,SY1528: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV312 )
| ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SY1526 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SY1527 @ SY1528 @ SV312 ) )
| ( SY1526
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SY1528
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SY1528 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SY1527 @ SY1526 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1869,plain,
! [SV608: $i,SV313: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV313 @ SV608 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV313 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1870,plain,
! [SV609: $i,SV314: $i] :
( ( ! [SY1529: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV314 )
| ( ( c_HOL_Oabs__class_Oabs @ SV609 @ SV314 )
!= ( c_HOL_Oabs__class_Oabs @ SY1529 @ SV314 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV609 @ SY1529 @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1871,plain,
! [SV610: $i,SV315: $i] :
( ( ! [SY1530: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1530
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1530 @ SV610 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1530 @ SV315 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1872,plain,
! [SV611: $i,SV316: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV316 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1873,plain,
! [SV317: $i] :
( ( ( c_Fact_Ofact__class_Ofact @ SV317 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1874,plain,
! [SV612: $i,SV318: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV318 @ SV612 @ tc_nat ) )
| ( SV318
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1875,plain,
! [SV613: $i,SV319: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV319 @ SV613 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV613
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1876,plain,
! [SV614: $i,SV320: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV320 @ SV614 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV320
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1877,plain,
! [SV615: $i,SV321: $i] :
( ( ! [SY1531: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
| ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SY1531 @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SY1531
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1878,plain,
! [SV616: $i,SV322: $i] :
( ( ! [SY1532: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SY1532
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1532 @ SV616 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1532 @ SV322 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1879,plain,
! [SV617: $i,SV323: $i] :
( ( ! [SY1533: $i,SY1534: $i,SY1535: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SY1533 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SY1534 @ SY1535 @ SV323 ) )
| ( SY1535
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SY1533
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SY1535 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SY1534 @ SY1533 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1880,plain,
! [SV618: $i,SV324: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV324 @ SV618 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV324
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1881,plain,
! [SV325: $i] :
( ( ( ( c_Complex_Ocnj @ SV325 )
!= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true )
| ( ( SV325
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1882,plain,
! [SV619: $i,SV326: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV326 @ SV619 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV326
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1883,plain,
! [SV620: $i,SV327: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV327 @ SV620 @ tc_nat )
!= SV327 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV620 @ SV327 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1884,plain,
! [SV621: $i,SV328: $i] :
( ( ! [SY1536: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 )
| ( ( c_Power_Opower__class_Opower @ SV621 @ SY1536 @ SV328 )
!= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
| ( SV621
= ( c_HOL_Ozero__class_Ozero @ SV328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(1885,plain,
! [SV622: $i,SV329: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV329 @ SV622 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV622 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1886,plain,
! [SV623: $i,SV330: $i] :
( ( ! [SY1537: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
| ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SY1537 @ SV330 )
!= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SY1537
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1887,plain,
! [SV624: $i,SV331: $i] :
( ( ! [SY1538: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV331 @ SV624 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SY1538 @ SV624 @ tc_nat ) )
| ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV331 = SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(1888,plain,
! [SV625: $i,SV332: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV332 )
| ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(1889,plain,
! [SV626: $i,SV333: $i] :
( ( ! [SY1539: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SY1539 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SY1539 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SY1539 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1890,plain,
! [SV627: $i,SV334: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV334 @ SV627 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1891,plain,
! [SV628: $i,SV335: $i] :
( ( ! [SY1540: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SV628 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SY1540 @ SV628 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SY1540 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1892,plain,
! [SV629: $i,SV336: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV336 )
| ( ( c_HOL_Osgn__class_Osgn @ SV629 @ SV336 )
!= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
| ( SV629
= ( c_HOL_Ozero__class_Ozero @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1893,plain,
! [SV630: $i,SV337: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV337 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
| ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1894,plain,
! [SV631: $i,SV339: $i,SV2: $i] :
( ( ! [SY1541: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV2 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SV631 @ SV2 ) @ SY1541 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SY1541 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SV631 @ SY1541 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1895,plain,
! [SV340: $i,SV3: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV3 @ SV340 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV3 @ tc_nat )
| ( SV340 = SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1896,plain,
! [SV341: $i,SV4: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV4 @ SV341 @ tc_nat ) )
= $true )
| ( ( ( SV341 = SV4 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV341 @ SV4 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1897,plain,
! [SV342: $i,SV5: $i] :
( ( ( SV5 = SV342 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV5 @ SV342 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV342 @ SV5 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1583]) ).
thf(1898,plain,
! [SV343: $i,SV6: $i] :
( ( ( SV6 = SV343 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV343 @ SV6 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV6 @ SV343 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1899,plain,
! [SV344: $i,SV7: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV7 @ SV344 @ tc_nat ) )
= $true )
| ( ( ( SV344 = SV7 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV344 @ SV7 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1900,plain,
! [SV345: $i,SV8: $i] :
( ( ( SV8 = SV345 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV345 @ SV8 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV8 @ SV345 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1901,plain,
! [SV346: $i,SV9: $i] :
( ( ( SV9 = SV346 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV346 @ SV9 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV9 @ SV346 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1902,plain,
! [SV632: $i,SV348: $i,SV11: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ SV348 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ ( c_GCD_Ogcd__class_Ogcd @ SV632 @ SV348 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(1903,plain,
! [SV633: $i,SV349: $i,SV12: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ SV349 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ ( c_GCD_Ogcd__class_Ogcd @ SV349 @ SV633 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1904,plain,
! [SV634: $i,SV350: $i,SV13: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ SV350 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ ( c_GCD_Ogcd__class_Ogcd @ SV350 @ SV634 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(1905,plain,
! [SV635: $i,SV351: $i,SV14: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ SV351 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ ( c_GCD_Ogcd__class_Ogcd @ SV635 @ SV351 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1906,plain,
! [SV636: $i,SV352: $i,SV15: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV15 @ SV352 @ tc_nat ) @ SV636 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV15 @ SV636 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1907,plain,
! [SV637: $i,SV353: $i,SV16: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV16 @ SV353 @ tc_nat ) @ SV637 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV353 @ SV637 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1908,plain,
! [SV638: $i,SV354: $i,SV17: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ SV354 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ ( c_GCD_Ogcd__class_Ogcd @ SV354 @ SV638 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(1909,plain,
! [SV639: $i,SV355: $i,SV18: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ SV355 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ ( c_GCD_Ogcd__class_Ogcd @ SV639 @ SV355 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1910,plain,
! [SV640: $i,SV356: $i,SV19: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV356 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV640 @ SV356 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV640 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(1911,plain,
! [SV641: $i,SV357: $i,SV20: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(1912,plain,
! [SV358: $i,SV22: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV22 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV358 @ SV358 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1913,plain,
! [SV642: $i,SV359: $i,SV23: $i] :
( ( ! [SY1542: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1542 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SY1542 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1914,plain,
! [SV643: $i,SV361: $i,SV25: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV25 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV361 @ SV25 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV643 @ SV25 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1915,plain,
! [SV644: $i,SV362: $i,SV26: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV26 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV362 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ ( c_HOL_Otimes__class_Otimes @ SV644 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1916,plain,
! [SV645: $i,SV363: $i,SV27: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV27 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV645 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV363 @ SV27 ) @ ( c_HOL_Oabs__class_Oabs @ SV645 @ SV27 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(1917,plain,
! [SV646: $i,SV364: $i,SV28: $i] :
( ( ! [SY1543: $i,SY1544: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SY1543 @ SY1544 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SY1543 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SY1544 @ SV28 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1918,plain,
! [SV647: $i,SV365: $i,SV29: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
| ( ( c_HOL_Otimes__class_Otimes @ SV365 @ ( c_HOL_Otimes__class_Otimes @ SV365 @ SV647 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV365 @ SV647 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(1919,plain,
! [SV648: $i,SV366: $i,SV30: $i] :
( ( ! [SY1545: $i,SY1546: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SY1545 @ SY1546 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SY1545 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SY1546 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1546 @ SY1545 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1920,plain,
! [SV367: $i,SV31: $i] :
( ( ( ~ ( class_Power_Opower @ SV31 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV367 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV31 )
= ( c_HOL_Oone__class_Oone @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1921,plain,
! [SV368: $i,SV32: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV368 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 )
= ( c_HOL_Oone__class_Oone @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1922,plain,
! [SV369: $i,SV33: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV33 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV33 )
| ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1923,plain,
! [SV370: $i,SV34: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV34 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV34 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV370 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
| ( SV370
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1611]) ).
thf(1924,plain,
! [SV649: $i,SV371: $i,SV35: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV35 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV371 @ SV35 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV649 @ SV35 ) @ SV35 )
= ( c_HOL_Ozero__class_Ozero @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1925,plain,
! [SV650: $i,SV372: $i,SV36: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SV372 @ tc_nat ) @ SV650 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV372 @ SV650 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SV650 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1926,plain,
! [SV651: $i,SV375: $i,SV39: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SV375 @ tc_nat ) @ SV651 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV375 @ SV651 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SV651 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1927,plain,
! [SV652: $i,SV378: $i,SV42: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SV378 @ tc_nat ) @ SV652 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV378 @ SV652 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SV652 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1928,plain,
! [SV653: $i,SV381: $i,SV45: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SV381 @ tc_nat ) @ SV653 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV381 @ SV653 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SV653 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1929,plain,
! [SV654: $i,SV382: $i,SV46: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SV382 @ tc_nat ) @ SV654 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV382 @ SV654 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SV654 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1930,plain,
! [SV655: $i,SV383: $i,SV47: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SV383 @ tc_nat ) @ SV655 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SV655 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV655 @ SV47 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1931,plain,
! [SV656: $i,SV384: $i,SV48: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SV384 @ tc_nat ) @ SV656 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV384 @ SV656 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV384 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1932,plain,
! [SV657: $i,SV385: $i,SV49: $i] :
( ( ! [SY1547: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SY1547 @ SV49 ) @ SV49 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SY1547 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1933,plain,
! [SV658: $i,SV386: $i,SV50: $i] :
( ( ! [SY1548: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SY1548 @ SV50 ) @ SV50 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SV658 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1934,plain,
! [SV659: $i,SV387: $i,SV51: $i] :
( ( ! [SY1549: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SV659 @ SV51 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SY1549 @ SV51 ) @ SV659 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1935,plain,
! [SV660: $i,SV388: $i,SV52: $i] :
( ( ! [SY1550: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SV660 @ SV52 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1550 @ SV388 @ SV52 ) @ SV660 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1936,plain,
! [SV661: $i,SV391: $i,SV59: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV59 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV391 @ SV661 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SV661 @ SV391 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1937,plain,
! [SV392: $i,SV60: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV60 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV392 @ SV392 @ SV60 )
= SV392 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1633]) ).
thf(1938,plain,
! [SV61: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV61 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV61 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= ( c_HOL_Ozero__class_Ozero @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1634]) ).
thf(1939,plain,
! [SV62: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV62 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= ( c_HOL_Ozero__class_Ozero @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1635]) ).
thf(1940,plain,
! [SV662: $i,SV393: $i,SV63: $i] :
( ( ! [SY1551: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV662 @ SV63 ) @ SY1551 @ SV63 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV393 @ SY1551 @ SV63 ) @ ( c_Power_Opower__class_Opower @ SV662 @ SY1551 @ SV63 ) @ SV63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1941,plain,
! [SV663: $i,SV394: $i,SV64: $i] :
( ( ! [SY1552: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV64 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV394 @ SV663 @ SV64 ) @ SY1552 @ SV64 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV394 @ SY1552 @ SV64 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SY1552 @ SV64 ) @ SV64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1942,plain,
! [SV664: $i,SV395: $i,SV65: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV65 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV65 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV395 @ SV664 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV395 @ SV65 ) @ SV664 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1943,plain,
! [SV665: $i,SV396: $i,SV66: $i] :
( ( ! [SY1553: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV396 @ SV665 @ SV66 ) @ SY1553 @ SV66 )
= ( c_HOL_Otimes__class_Otimes @ SV396 @ ( c_HOL_Otimes__class_Otimes @ SV665 @ SY1553 @ SV66 ) @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1944,plain,
! [SV666: $i,SV397: $i,SV67: $i] :
( ( ! [SY1554: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV666 @ SV67 ) @ SY1554 @ SV67 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SY1554 @ SV67 ) @ SV666 @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1945,plain,
! [SV667: $i,SV398: $i,SV68: $i] :
( ( ! [SY1555: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV398 @ SV667 @ SV68 ) @ SY1555 @ SV68 )
= ( c_HOL_Otimes__class_Otimes @ SV398 @ ( c_HOL_Otimes__class_Otimes @ SV667 @ SY1555 @ SV68 ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1946,plain,
! [SV668: $i,SV399: $i,SV69: $i] :
( ( ! [SY1556: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV69 )
| ( ( c_HOL_Otimes__class_Otimes @ SV399 @ ( c_HOL_Otimes__class_Otimes @ SV668 @ SY1556 @ SV69 ) @ SV69 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV399 @ SV668 @ SV69 ) @ SY1556 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(1947,plain,
! [SV669: $i,SV400: $i,SV70: $i] :
( ( ! [SY1557: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( c_HOL_Otimes__class_Otimes @ SV400 @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SY1557 @ SV70 ) @ SV70 )
= ( c_HOL_Otimes__class_Otimes @ SV669 @ ( c_HOL_Otimes__class_Otimes @ SV400 @ SY1557 @ SV70 ) @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1948,plain,
! [SV670: $i,SV401: $i,SV71: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV71 @ SV401 @ tc_nat ) @ SV670 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV71 @ ( c_HOL_Otimes__class_Otimes @ SV401 @ SV670 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1949,plain,
! [SV671: $i,SV402: $i,SV72: $i] :
( ( ! [SY1558: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Otimes__class_Otimes @ SV402 @ ( c_HOL_Otimes__class_Otimes @ SV671 @ SY1558 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV402 @ SV671 @ SV72 ) @ SY1558 @ SV72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1950,plain,
! [SV403: $i,SV73: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV73 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV403 @ SV73 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV73 ) @ SV403 @ SV73 ) )
| ( SV403
= ( c_HOL_Ozero__class_Ozero @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1951,plain,
! [SV404: $i,SV74: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV74 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV404 @ SV74 ) @ SV404 @ SV74 )
= ( c_HOL_Oone__class_Oone @ SV74 ) )
| ( SV404
= ( c_HOL_Ozero__class_Ozero @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1952,plain,
! [SV405: $i,SV75: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV75 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV405 @ SV75 ) @ SV405 @ SV75 )
= ( c_HOL_Oone__class_Oone @ SV75 ) )
| ( SV405
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1953,plain,
! [SV406: $i,SV76: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV76 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV406 @ ( c_HOL_Oinverse__class_Oinverse @ SV406 @ SV76 ) @ SV76 )
= ( c_HOL_Oone__class_Oone @ SV76 ) )
| ( SV406
= ( c_HOL_Ozero__class_Ozero @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1954,plain,
! [SV672: $i,SV407: $i,SV77: $i] :
( ( ! [SY1559: $i] :
( ~ ( class_Divides_Osemiring__div @ SV77 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV672 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SY1559 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SV672 @ SY1559 @ SV77 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1955,plain,
! [SV673: $i,SV408: $i,SV78: $i] :
( ( ! [SY1560: $i] :
( ~ ( class_Divides_Osemiring__div @ SV78 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV408 @ SV673 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SY1560 @ SV673 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SV408 @ SY1560 @ SV78 ) )
| ( SV673
= ( c_HOL_Ozero__class_Ozero @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1956,plain,
! [SV409: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV79 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ SV409 @ SV79 ) @ SV79 )
= ( c_HOL_Osgn__class_Osgn @ SV409 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1957,plain,
! [SV674: $i,SV410: $i,SV80: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ ( c_GCD_Ogcd__class_Ogcd @ SV410 @ SV674 @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ SV410 @ tc_nat ) @ ( c_GCD_Ogcd__class_Olcm @ SV80 @ SV674 @ tc_nat ) @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1958,plain,
! [SV675: $i,SV411: $i,SV81: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV81 @ ( c_GCD_Ogcd__class_Ogcd @ SV411 @ SV675 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV81 @ SV411 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV81 @ SV675 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1959,plain,
! [SV412: $i,SV82: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ SV412 @ SV82 )
= ( c_HOL_Otimes__class_Otimes @ SV412 @ ( c_HOL_Osgn__class_Osgn @ SV412 @ SV82 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1960,plain,
! [SV676: $i,SV413: $i,SV83: $i] :
( ( ! [SY1561: $i] :
( ~ ( class_Divides_Osemiring__div @ SV83 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SY1561 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SY1561 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1561 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1561 @ SV413 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1961,plain,
! [SV677: $i,SV414: $i,SV84: $i] :
( ( ! [SY1562: $i] :
( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SY1562 @ SV677 @ SV84 ) @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SY1562 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SY1562 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1962,plain,
! [SV415: $i,SV85: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV85 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV415 @ SV85 ) @ SV85 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV415 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1963,plain,
! [SV86: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV86 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV86 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1964,plain,
! [SV678: $i,SV416: $i,SV87: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ ( c_GCD_Ogcd__class_Olcm @ SV416 @ SV678 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV416 @ SV87 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ SV416 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1965,plain,
! [SV679: $i,SV417: $i,SV88: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ ( c_GCD_Ogcd__class_Olcm @ SV417 @ SV679 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV88 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ SV679 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1966,plain,
! [SV680: $i,SV418: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV89 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV89 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV680 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV418 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV680 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1967,plain,
! [SV681: $i,SV419: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV419 @ SV681 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV419 @ SV90 ) @ SV90 ) )
| ( SV681
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV419
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(1968,plain,
! [SV420: $i,SV91: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV91 ) )
= $true )
| ( ( ( SV420
= ( c_HOL_Ozero__class_Ozero @ SV91 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV420 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1969,plain,
! [SV421: $i,SV92: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV92 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV421 @ SV92 ) @ SV92 )
= SV421 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1970,plain,
! [SV93: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV93 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV93 )
= ( c_HOL_Ozero__class_Ozero @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1666]) ).
thf(1971,plain,
! [SV682: $i,SV422: $i,SV94: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1972,plain,
! [SV683: $i,SV423: $i,SV95: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV95 )
| ( SV423
= ( c_HOL_Ozero__class_Ozero @ SV95 ) )
| ( SV683
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV423 @ SV95 ) @ SV423 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1973,plain,
! [SV684: $i,SV424: $i,SV96: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV96 )
| ( SV424
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV424 @ SV96 ) @ SV424 @ SV96 )
= SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1974,plain,
! [SV685: $i,SV425: $i,SV97: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV97 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
| ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV685 @ SV97 ) @ SV685 @ SV97 ) )
| ( SV685
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(1975,plain,
! [SV686: $i,SV426: $i,SV98: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV98 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SV686 @ SV98 ) @ SV686 @ SV98 )
= SV426 )
| ( SV686
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1976,plain,
! [SV687: $i,SV427: $i,SV99: $i] :
( ( ! [SY1563: $i,SY1564: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SY1563 @ SY1564 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SY1563 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ SY1564 @ SV99 ) @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1977,plain,
! [SV688: $i,SV428: $i,SV100: $i] :
( ( ! [SY1565: $i,SY1566: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV428 @ SV688 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SY1565 @ SY1566 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SV428 @ ( c_HOL_Otimes__class_Otimes @ SV688 @ ( c_HOL_Otimes__class_Otimes @ SY1565 @ SY1566 @ SV100 ) @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(1978,plain,
! [SV689: $i,SV429: $i,SV101: $i] :
( ( ! [SY1567: $i,SY1568: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV689 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SY1567 @ SY1568 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SY1567 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SY1568 @ SV101 ) @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1979,plain,
! [SV690: $i,SV430: $i,SV102: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV102 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV690 @ SV102 ) @ SV690 @ SV102 )
= SV430 )
| ( SV690
= ( c_HOL_Ozero__class_Ozero @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(1980,plain,
! [SV691: $i,SV431: $i,SV103: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV103 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV691 @ SV103 ) @ SV431 @ SV103 )
= SV691 )
| ( SV431
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1981,plain,
! [SV432: $i,SV104: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV104 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= ( c_HOL_Ozero__class_Ozero @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1982,plain,
! [SV433: $i,SV105: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV105 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV433 @ SV105 )
= ( c_HOL_Ozero__class_Ozero @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1983,plain,
! [SV434: $i,SV106: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV106 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV106 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV106 ) @ SV434 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1984,plain,
! [SV435: $i,SV107: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV107 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV435 @ SV107 ) @ ( c_HOL_Oabs__class_Oabs @ SV435 @ SV107 ) @ SV107 )
= SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1985,plain,
! [SV436: $i,SV108: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV108 @ SV436 @ tc_nat )
= SV108 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV436 @ SV108 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1986,plain,
! [SV437: $i,SV109: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV109 @ SV437 @ tc_nat )
= SV109 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV437 @ SV109 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1987,plain,
! [SV438: $i,SV110: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV110 @ SV438 @ tc_nat )
= SV438 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV110 @ SV438 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1988,plain,
! [SV439: $i,SV111: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV111 @ SV439 @ tc_nat )
= SV111 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV439 @ SV111 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1989,plain,
! [SV440: $i,SV112: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV112 @ SV440 @ tc_nat )
= SV440 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV112 @ SV440 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1990,plain,
! [SV692: $i,SV441: $i,SV113: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV113 @ SV441 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV692 @ SV113 @ tc_nat ) @ SV441 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1991,plain,
! [SV693: $i,SV442: $i,SV114: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV114 @ SV442 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV114 @ SV693 @ tc_nat ) @ SV442 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1992,plain,
! [SV694: $i,SV443: $i,SV115: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ ( c_GCD_Ogcd__class_Olcm @ SV443 @ SV694 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ SV694 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1993,plain,
! [SV695: $i,SV444: $i,SV116: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ ( c_GCD_Ogcd__class_Olcm @ SV444 @ SV695 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ SV444 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1994,plain,
! [SV696: $i,SV445: $i,SV117: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV117 @ SV445 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV696 @ SV117 @ tc_nat ) @ SV445 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(1995,plain,
! [SV697: $i,SV446: $i,SV118: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV118 @ SV446 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV118 @ SV697 @ tc_nat ) @ SV446 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1996,plain,
! [SV698: $i,SV447: $i,SV119: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ ( c_GCD_Ogcd__class_Olcm @ SV447 @ SV698 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ SV447 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1997,plain,
! [SV699: $i,SV448: $i,SV120: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ ( c_GCD_Ogcd__class_Olcm @ SV448 @ SV699 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ SV699 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1998,plain,
! [SV449: $i,SV121: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV121 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV449 @ SV121 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV121 ) @ SV449 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1999,plain,
! [SV450: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV122 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV122 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV450 @ SV122 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV122 ) @ SV450 @ SV122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1695]) ).
thf(2000,plain,
! [SV700: $i,SV451: $i,SV123: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Otimes__class_Otimes @ SV700 @ SV451 @ SV123 ) @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2001,plain,
! [SV701: $i,SV452: $i,SV124: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV452 @ ( c_HOL_Otimes__class_Otimes @ SV452 @ SV701 @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2002,plain,
! [SV702: $i,SV453: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV125 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV453 @ ( c_HOL_Otimes__class_Otimes @ SV453 @ SV702 @ SV125 ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2003,plain,
! [SV703: $i,SV454: $i,SV126: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV126 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV126 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SV454 @ SV703 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SV454 @ SV126 ) @ SV703 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2004,plain,
! [SV455: $i,SV127: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV127 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV127 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV455 @ SV127 ) @ SV127 )
= SV455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(2005,plain,
! [SV704: $i,SV456: $i,SV128: $i] :
( ( ! [SY1569: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV456 @ SV704 @ SV128 ) @ SY1569 @ SV128 )
= ( c_Power_Opower__class_Opower @ SV456 @ ( c_HOL_Otimes__class_Otimes @ SV704 @ SY1569 @ tc_nat ) @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2006,plain,
! [SV705: $i,SV457: $i,SV129: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
| ( ( c_HOL_Otimes__class_Otimes @ SV457 @ SV705 @ SV129 )
= ( c_HOL_Otimes__class_Otimes @ SV705 @ SV457 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2007,plain,
! [SV706: $i,SV459: $i,SV131: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV131 )
| ( ( c_HOL_Otimes__class_Otimes @ SV459 @ SV706 @ SV131 )
= ( c_HOL_Otimes__class_Otimes @ SV706 @ SV459 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2008,plain,
! [SV132: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV132 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV132 ) @ SV132 )
= ( c_HOL_Ozero__class_Ozero @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(2009,plain,
! [SV460: $i,SV133: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV133 ) )
= $true )
| ( ( ( SV460
= ( c_HOL_Ozero__class_Ozero @ SV133 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV460 @ SV460 @ SV133 )
= ( c_HOL_Oone__class_Oone @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(2010,plain,
! [SV461: $i,SV134: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV134 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV461 @ SV461 @ SV134 )
= ( c_HOL_Oone__class_Oone @ SV134 ) )
| ( SV461
= ( c_HOL_Ozero__class_Ozero @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(2011,plain,
! [SV462: $i,SV135: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV135 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV135 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV462 @ SV462 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
| ( SV462
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(2012,plain,
! [SV707: $i,SV463: $i,SV136: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ SV463 @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ SV707 @ tc_nat ) @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV136 @ ( c_GCD_Ogcd__class_Olcm @ SV463 @ SV707 @ tc_nat ) @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2013,plain,
! [SV464: $i,SV138: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV138 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV138 ) @ SV464 @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(2014,plain,
! [SV465: $i,SV139: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV139 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV139 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV465 @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(2015,plain,
! [SV466: $i,SV140: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV140 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV140 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV466 @ ( c_HOL_Ozero__class_Ozero @ SV140 ) @ SV140 )
= ( c_HOL_Ozero__class_Ozero @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(2016,plain,
! [SV467: $i,SV141: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV141 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SV467 @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(2017,plain,
! [SV708: $i,SV468: $i,SV142: $i] :
( ( ! [SY1570: $i] :
( ~ ( class_Divides_Osemiring__div @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SV708 @ SV142 ) @ SY1570 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SY1570 @ SV142 ) @ SV708 @ SV142 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV468 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2018,plain,
! [SV709: $i,SV469: $i,SV143: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV143 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV469 @ SV143 ) @ SV709 @ SV143 )
= ( c_Power_Opower__class_Opower @ SV469 @ SV709 @ SV143 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV709 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2019,plain,
! [SV710: $i,SV470: $i,SV144: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV144 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV470 @ SV710 @ SV144 ) @ SV144 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV470 @ SV144 ) @ SV710 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2020,plain,
! [SV711: $i,SV471: $i,SV145: $i] :
( ( ! [SY1571: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SV711 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SY1571 @ SV711 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SY1571 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2021,plain,
! [SV472: $i,SV146: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV146 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV472 @ SV146 ) @ SV146 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV472 @ SV146 ) @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(2022,plain,
! [SV712: $i,SV473: $i,SV147: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV147 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV147 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV473 @ SV712 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV473 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SV712 @ SV147 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2023,plain,
! [SV713: $i,SV474: $i,SV148: $i] :
( ( ! [SY1572: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV148 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SY1572 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SY1572 @ SV148 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2024,plain,
! [SV714: $i,SV475: $i,SV149: $i] :
( ( ! [SY1573: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SY1573 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SY1573 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2025,plain,
! [SV715: $i,SV476: $i,SV150: $i] :
( ( ! [SY1574: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV150 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SV715 @ SV150 ) @ SY1574 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SY1574 @ SV150 ) @ SV715 @ SV150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2026,plain,
! [SV716: $i,SV477: $i,SV151: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV151 )
| ( ( c_HOL_Otimes__class_Otimes @ SV477 @ ( c_Divides_Odiv__class_Odiv @ SV716 @ SV477 @ SV151 ) @ SV151 )
= SV716 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV477 @ SV716 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2027,plain,
! [SV717: $i,SV478: $i,SV152: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV152 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV478 @ SV717 @ SV152 ) @ SV717 @ SV152 )
= SV478 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV478 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2028,plain,
! [SV718: $i,SV479: $i,SV153: $i] :
( ( ! [SY1575: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV153 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
| ( SY1575
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SY1575 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SY1575 @ SV153 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2029,plain,
! [SV719: $i,SV480: $i,SV154: $i] :
( ( ! [SY1576: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV154 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
| ( SY1576
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY1576 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SY1576 @ SV719 @ SV154 ) @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2030,plain,
! [SV720: $i,SV481: $i,SV155: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV155 @ SV481 @ tc_nat )
| ( SV720
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV155 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV481 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2031,plain,
! [SV721: $i,SV483: $i,SV157: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SV483 @ SV721 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV721 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV483 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2032,plain,
! [SV722: $i,SV484: $i,SV158: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SV484 @ SV722 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SV722 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV158 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2033,plain,
! [SV723: $i,SV485: $i,SV159: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SV485 @ SV723 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SV485 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV485 @ SV159 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2034,plain,
! [SV724: $i,SV486: $i,SV160: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SV486 @ SV724 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV724 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV486 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2035,plain,
! [SV725: $i,SV487: $i,SV161: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SV487 @ SV725 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV725 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV487 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2036,plain,
! [SV726: $i,SV494: $i,SV168: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SV494 @ SV726 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV726 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV494 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2037,plain,
! [SV727: $i,SV495: $i,SV169: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SV495 @ SV727 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV727 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV495 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2038,plain,
! [SV728: $i,SV496: $i,SV170: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SV496 @ SV728 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV728 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV496 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2039,plain,
! [SV729: $i,SV497: $i,SV171: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2040,plain,
! [SV730: $i,SV498: $i,SV172: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2041,plain,
! [SV499: $i,SV173: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV173 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV499 @ SV173 ) @ SV173 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV499 @ SV173 ) @ SV173 ) )
| ( SV499
= ( c_HOL_Ozero__class_Ozero @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(2042,plain,
! [SV731: $i,SV500: $i,SV174: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV174 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV500 @ SV731 @ SV174 ) @ SV174 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV500 @ SV174 ) @ ( c_HOL_Oabs__class_Oabs @ SV731 @ SV174 ) @ SV174 ) )
| ( SV731
= ( c_HOL_Ozero__class_Ozero @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2043,plain,
! [SV178: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV178 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV178 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV178 )
= ( c_HOL_Oone__class_Oone @ SV178 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(2044,plain,
! [SV502: $i,SV179: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV179 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV502 @ SV502 @ SV179 )
= ( c_HOL_Oone__class_Oone @ SV179 ) )
| ( SV502
= ( c_HOL_Ozero__class_Ozero @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1749]) ).
thf(2045,plain,
! [SV732: $i,SV503: $i,SV180: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV180 @ SV503 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV732 @ SV503 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2046,plain,
! [SV733: $i,SV504: $i,SV182: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV504 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV733 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV733 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2047,plain,
! [SV734: $i,SV505: $i,SV183: $i] :
( ( ! [SY1577: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV183 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV734 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SY1577 @ SV183 ) @ SV183 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV734 @ SY1577 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2048,plain,
! [SV735: $i,SV506: $i,SV184: $i] :
( ( ! [SY1578: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV184 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV735 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY1578 @ SV735 @ SV184 ) @ SV184 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SY1578 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2049,plain,
! [SV507: $i,SV185: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV185 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV507 @ SV185 ) @ SV185 )
= ( c_HOL_Oabs__class_Oabs @ SV507 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(2050,plain,
! [SV508: $i,SV186: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV186 @ SV508 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV508 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(2051,plain,
! [SV509: $i,SV187: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV187 @ SV509 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV187 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2052,plain,
! [SV736: $i,SV512: $i,SV191: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV512 @ SV736 @ SV191 ) @ SV512 @ SV191 )
= ( c_HOL_Otimes__class_Otimes @ SV512 @ ( c_Power_Opower__class_Opower @ SV512 @ SV736 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2053,plain,
! [SV513: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV192 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV192 )
| ( ( c_HOL_Ozero__class_Ozero @ SV192 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV513 @ SV192 ) @ SV513 @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2054,plain,
! [SV737: $i,SV514: $i,SV193: $i] :
( ( ! [SY1579: $i] :
( ~ ( class_Divides_Osemiring__div @ SV193 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SV737 @ SV193 ) @ SY1579 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SY1579 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV737 @ SY1579 @ SV193 ) @ SV193 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV737 @ SV514 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2055,plain,
! [SV738: $i,SV515: $i,SV194: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV194 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV515 @ SV738 @ tc_nat ) @ SV194 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV515 @ SV194 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV738 @ SV194 ) @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2056,plain,
! [SV516: $i,SV195: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV195 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV516 @ SV195 ) @ ( c_HOL_Oabs__class_Oabs @ SV516 @ SV195 ) @ SV195 )
= ( c_HOL_Otimes__class_Otimes @ SV516 @ SV516 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2057,plain,
! [SV739: $i,SV517: $i,SV196: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV196 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV517 @ SV739 @ SV196 ) @ SV196 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV517 @ SV196 ) @ SV739 @ SV196 ) )
| ( SV517
= ( c_HOL_Ozero__class_Ozero @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2058,plain,
! [SV740: $i,SV518: $i,SV197: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV197 @ ( c_GCD_Ogcd__class_Ogcd @ SV518 @ SV740 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV518 @ ( c_GCD_Ogcd__class_Ogcd @ SV197 @ SV740 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2059,plain,
! [SV741: $i,SV519: $i,SV198: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV198 @ SV519 @ tc_nat ) @ SV741 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV198 @ ( c_GCD_Ogcd__class_Ogcd @ SV519 @ SV741 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2060,plain,
! [SV742: $i,SV520: $i,SV199: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV199 @ SV520 @ tc_nat ) @ SV742 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV199 @ ( c_GCD_Ogcd__class_Ogcd @ SV520 @ SV742 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2061,plain,
! [SV521: $i,SV201: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV521 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(2062,plain,
! [SV743: $i,SV522: $i,SV202: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SV743 @ SV202 ) @ SV743 @ SV202 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2063,plain,
! [SV744: $i,SV523: $i,SV203: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SV744 @ SV203 ) @ SV744 @ SV203 )
= SV523 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2064,plain,
! [SV524: $i,SV204: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV204 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV524 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(2065,plain,
! [SV525: $i,SV205: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV205 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV525 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= ( c_HOL_Ozero__class_Ozero @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(2066,plain,
! [SV526: $i,SV206: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV206 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV526 @ SV206 )
= ( c_HOL_Ozero__class_Ozero @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(2067,plain,
! [SV527: $i,SV207: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV207 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SV527 @ SV207 )
= ( c_HOL_Ozero__class_Ozero @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(2068,plain,
! [SV528: $i,SV210: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV210 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV528 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 )
= ( c_HOL_Ozero__class_Ozero @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(2069,plain,
! [SV529: $i,SV211: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV211 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV529 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(2070,plain,
! [SV530: $i,SV212: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV212 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV530 @ SV212 )
= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(2071,plain,
! [SV531: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV213 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV531 @ SV213 )
= ( c_HOL_Ozero__class_Ozero @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(2072,plain,
! [SV532: $i,SV214: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV214 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV532 @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(2073,plain,
! [SV533: $i,SV215: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV215 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV533 @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(2074,plain,
! [SV534: $i,SV216: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV216 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1781]) ).
thf(2075,plain,
! [SV535: $i,SV217: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV217 ) )
= $true )
| ( ( ( SV535
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
| ~ ( c_Int_Oiszero @ SV535 @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(2076,plain,
! [SV745: $i,SV536: $i,SV218: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV218 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV536 @ SV745 @ SV218 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV536 @ SV218 ) @ SV745 @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2077,plain,
! [SV746: $i,SV537: $i,SV219: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV219 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV537 @ SV219 ) @ SV746 @ SV219 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV537 @ SV746 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2078,plain,
! [SV747: $i,SV538: $i,SV220: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV220 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ SV747 @ SV220 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ ( c_HOL_Oabs__class_Oabs @ SV747 @ SV220 ) @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2079,plain,
! [SV748: $i,SV539: $i,SV221: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ ( c_HOL_Oabs__class_Oabs @ SV748 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ SV748 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2080,plain,
! [SV223: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV223 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ SV223 )
= ( c_HOL_Ozero__class_Ozero @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2081,plain,
! [SV224: $i] :
( ( ( class_Ring__and__Field_Osgn__if @ SV224 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV224 )
= ( c_HOL_Ozero__class_Ozero @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2082,plain,
! [SV225: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV225 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ SV225 ) @ SV225 )
= ( c_HOL_Ozero__class_Ozero @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(2083,plain,
! [SV749: $i,SV541: $i,SV226: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ SV226 @ ( c_GCD_Ogcd__class_Olcm @ SV541 @ SV749 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV541 @ ( c_GCD_Ogcd__class_Olcm @ SV226 @ SV749 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2084,plain,
! [SV750: $i,SV542: $i,SV227: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ SV227 @ SV542 @ tc_nat ) @ SV750 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV227 @ ( c_GCD_Ogcd__class_Olcm @ SV542 @ SV750 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2085,plain,
! [SV751: $i,SV543: $i,SV228: $i] :
( ( ( c_GCD_Ogcd__class_Olcm @ ( c_GCD_Ogcd__class_Olcm @ SV228 @ SV543 @ tc_nat ) @ SV751 @ tc_nat )
= ( c_GCD_Ogcd__class_Olcm @ SV228 @ ( c_GCD_Ogcd__class_Olcm @ SV543 @ SV751 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2086,plain,
! [SV752: $i,SV544: $i,SV229: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV229 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV544 @ SV752 @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ SV544 @ ( c_HOL_Oinverse__class_Oinverse @ SV752 @ SV229 ) @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2087,plain,
! [SV753: $i,SV545: $i,SV230: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV230 )
| ~ ( class_Int_Onumber__ring @ SV230 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV545 @ SV753 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SV545 @ ( c_HOL_Oinverse__class_Oinverse @ SV753 @ SV230 ) @ SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2088,plain,
! [SV231: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV231 )
= $false )
| ( ( c_Int_Oiszero @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(2089,plain,
! [SV754: $i,SV546: $i,SV232: $i] :
( ( ! [SY1580: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV232 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV546 @ SV754 @ SV232 ) @ SY1580 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV546 @ SY1580 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV754 @ SY1580 @ SV232 ) @ SV232 ) )
| ( SV754
= ( c_HOL_Ozero__class_Ozero @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2090,plain,
! [SV755: $i,SV547: $i,SV233: $i] :
( ( ! [SY1581: $i,SY1582: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SY1581 @ SY1582 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SY1582 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SY1581 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2091,plain,
! [SV548: $i,SV234: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV234 @ SV548 @ tc_nat )
= SV548 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV548 @ SV234 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(2092,plain,
! [SV549: $i,SV235: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SV549 @ tc_nat )
= SV235 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV235 @ SV549 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(2093,plain,
! [SV550: $i,SV236: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV236 @ tc_nat )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV550 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV550 @ SV236 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(2094,plain,
! [SV553: $i,SV239: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV239 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV239 )
| ( ( c_HOL_Ozero__class_Ozero @ SV239 )
= ( c_HOL_Oinverse__class_Odivide @ SV553 @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1804]) ).
thf(2095,plain,
! [SV756: $i,SV555: $i,SV241: $i] :
( ( ! [SY1583: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV241 )
| ( ( c_Power_Opower__class_Opower @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SY1583 @ tc_nat ) @ SV241 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV555 @ SV756 @ SV241 ) @ SY1583 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2096,plain,
! [SV757: $i,SV556: $i,SV242: $i] :
( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV242 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV757 @ SV242 ) @ SV242 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV556 @ SV242 ) @ ( c_HOL_Osgn__class_Osgn @ SV757 @ SV242 ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2097,plain,
! [SV758: $i,SV557: $i,SV243: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV243 )
| ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV557 @ SV758 @ SV243 ) @ SV243 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV557 @ SV243 ) @ ( c_HOL_Osgn__class_Osgn @ SV758 @ SV243 ) @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2098,plain,
! [SV759: $i,SV558: $i,SV244: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV244 @ SV558 @ tc_nat ) @ SV759 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV759 @ SV244 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV244 @ SV759 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2099,plain,
! [SV760: $i,SV559: $i,SV245: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV245 @ SV559 @ tc_nat ) @ SV760 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV760 @ SV559 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV559 @ SV760 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2100,plain,
! [SV560: $i,SV246: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV246 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV246 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV560 @ SV246 ) @ SV560 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2101,plain,
! [SV761: $i,SV561: $i,SV247: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV561 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV761 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2102,plain,
! [SV762: $i,SV562: $i,SV248: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SV762 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV762 @ SV562 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV762 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2103,plain,
! [SV249: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV249 )
= $false )
| ( ( ~ ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ SV249 ) @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2104,plain,
! [SV250: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV250 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV250 ) @ SV250 )
= ( c_HOL_Oone__class_Oone @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(2105,plain,
! [SV251: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV251 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV251 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV251 ) @ SV251 )
= ( c_HOL_Oone__class_Oone @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(2106,plain,
! [SV563: $i,SV252: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV252 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV563 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV252 )
= SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2107,plain,
! [SV564: $i,SV253: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV564 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV253 )
= SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(2108,plain,
! [SV565: $i,SV256: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV256 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV565 @ SV256 )
= ( c_HOL_Oone__class_Oone @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2109,plain,
! [SV257: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV257 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV257 )
= ( c_HOL_Oone__class_Oone @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(2110,plain,
! [SV566: $i,SV258: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV258 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV566 @ ( c_HOL_Oone__class_Oone @ SV258 ) @ SV258 )
= SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2111,plain,
! [SV259: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV259 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ SV259 ) @ SV259 )
= ( c_HOL_Oone__class_Oone @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2112,plain,
! [SV263: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV263 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV263
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(2113,plain,
! [SV567: $i,SV264: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV264 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV264 ) @ SV567 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(2114,plain,
! [SV568: $i,SV267: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV267 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV568 @ ( c_HOL_Oone__class_Oone @ SV267 ) @ SV267 )
= SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(2115,plain,
! [SV569: $i,SV268: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV268 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV268 ) @ SV569 @ SV268 )
= SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2116,plain,
! [SV570: $i,SV269: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV269 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV269 ) @ SV570 @ SV269 )
= SV570 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2117,plain,
! [SV571: $i,SV270: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV270 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV270 ) @ SV571 @ SV270 )
= SV571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2118,plain,
! [SV572: $i,SV273: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV572 @ ( c_HOL_Oone__class_Oone @ SV273 ) @ SV273 )
= SV572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2119,plain,
! [SV573: $i,SV274: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV274 ) @ SV573 @ SV274 )
= SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2120,plain,
! [SV275: $i] :
( ( ( class_RealVector_Oreal__normed__algebra__1 @ SV275 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Oone__class_Oone @ SV275 ) @ SV275 )
= ( c_HOL_Oone__class_Oone @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(2121,plain,
! [SV574: $i,SV276: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV276 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV574 @ ( c_HOL_Oone__class_Oone @ SV276 ) @ SV276 )
= SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(2122,plain,
! [SV763: $i,SV575: $i,SV277: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
| ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SV763 @ SV277 )
!= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV763
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2123,plain,
! [SV576: $i,SV278: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV278 @ SV576 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV278
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2124,plain,
! [SV279: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV279 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV279 )
!= ( c_HOL_Oone__class_Oone @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(2125,plain,
! [SV577: $i,SV280: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV280 @ SV577 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV577
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2126,plain,
! [SV764: $i,SV578: $i,SV281: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ ( c_HOL_Otimes__class_Otimes @ SV578 @ SV764 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ SV578 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2127,plain,
! [SV765: $i,SV579: $i,SV282: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV282 @ SV579 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV282 @ SV765 @ tc_nat ) )
| ( SV282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV579 = SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2128,plain,
! [SV766: $i,SV580: $i,SV283: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV283 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
| ( SV580 = SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2129,plain,
! [SV581: $i,SV284: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV284 @ SV581 @ tc_nat )
!= SV581 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV284 @ SV581 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(2130,plain,
! [SV582: $i,SV285: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV285 @ SV582 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2131,plain,
! [SV583: $i,SV286: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV286 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV583 @ SV286 )
!= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ( SV583
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(2132,plain,
! [SV584: $i,SV287: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV287 @ SV584 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV584
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(2133,plain,
! [SV767: $i,SV585: $i,SV288: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV585 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV767 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV585 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2134,plain,
! [SV586: $i,SV290: $i] :
( ( ( SV290
!= ( c_HOL_Otimes__class_Otimes @ SV290 @ SV586 @ tc_nat ) )
= $true )
| ( ( ( SV290
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV586
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1846]) ).
thf(2135,plain,
! [SV587: $i,SV291: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV291 @ SV587 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV587
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2136,plain,
! [SV588: $i,SV292: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV292 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ SV588 @ tc_nat ) @ SV292 )
!= ( c_HOL_Ozero__class_Ozero @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2137,plain,
! [SV589: $i,SV293: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV293 @ SV589 @ tc_nat ) )
= $true )
| ( ( SV589
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2138,plain,
! [SV590: $i,SV294: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV294 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV590 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV590
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2139,plain,
! [SV295: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV295 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV295 )
!= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(2140,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2141,plain,
! [SV592: $i,SV297: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV297 @ SV592 @ tc_nat )
!= SV297 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV297 @ SV592 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2142,plain,
! [SV769: $i,SV593: $i,SV298: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ ( c_HOL_Otimes__class_Otimes @ SV593 @ SV769 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ SV769 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2143,plain,
! [SV594: $i,SV299: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV299 @ SV594 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV299
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2144,plain,
! [SV770: $i,SV595: $i,SV300: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV300 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
| ( SV595 = SV770 )
| ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2145,plain,
! [SV771: $i,SV596: $i,SV301: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV301 @ SV596 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV301 @ SV771 @ tc_nat ) )
| ( SV596 = SV771 )
| ( SV301
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2146,plain,
! [SV772: $i,SV597: $i,SV302: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV302 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SV772 @ SV302 )
!= ( c_HOL_Oone__class_Oone @ SV302 ) )
| ( SV772
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SV597 = SV772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2147,plain,
! [SV773: $i,SV598: $i,SV303: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV303 @ SV598 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV303 @ SV773 @ tc_nat ) @ SV598 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV773 @ SV598 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2148,plain,
! [SV599: $i,SV304: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__vector @ SV304 ) )
= $true )
| ( ( ( ( c_HOL_Osgn__class_Osgn @ SV599 @ SV304 )
!= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
| ( SV599
= ( c_HOL_Ozero__class_Ozero @ SV304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(2149,plain,
! [SV600: $i,SV305: $i] :
( ( ( ( c_Complex_Ocnj @ SV305 )
!= ( c_Complex_Ocnj @ SV600 ) )
= $true )
| ( ( SV305 = SV600 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2150,plain,
! [SV601: $i,SV306: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV306 @ SV601 @ tc_nat )
!= SV601 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV306 @ SV601 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2151,plain,
! [SV774: $i,SV602: $i,SV307: $i] :
( ( ! [SY1584: $i] :
( ( SV307
!= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( SV774
!= ( c_HOL_Otimes__class_Otimes @ SY1584 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SY1584 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2152,plain,
! [SV775: $i,SV603: $i,SV308: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV308 )
| ( ( c_HOL_Otimes__class_Otimes @ SV603 @ SV775 @ SV308 )
!= ( c_HOL_Oone__class_Oone @ SV308 ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV603 @ SV308 )
= SV775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2153,plain,
! [SV776: $i,SV604: $i,SV309: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SV604 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SV776 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SV776 @ SV604 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2154,plain,
! [SV605: $i,SV310: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV310 @ SV605 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV310
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(2155,plain,
! [SV777: $i,SV606: $i,SV311: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV311 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV606 @ SV311 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV777 @ SV311 ) )
| ( SV606 = SV777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2156,plain,
! [SV778: $i,SV607: $i,SV312: $i] :
( ( ! [SY1585: $i,SY1586: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV312 )
| ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SY1585 @ SY1586 @ SV312 ) )
| ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SY1586
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SY1586 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SY1585 @ SV778 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2157,plain,
! [SV608: $i,SV313: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV313 @ SV608 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV313 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(2158,plain,
! [SV779: $i,SV609: $i,SV314: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV314 )
| ( ( c_HOL_Oabs__class_Oabs @ SV609 @ SV314 )
!= ( c_HOL_Oabs__class_Oabs @ SV779 @ SV314 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV609 @ SV779 @ SV314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2159,plain,
! [SV780: $i,SV610: $i,SV315: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2160,plain,
! [SV611: $i,SV316: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV316 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2161,plain,
! [SV612: $i,SV318: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV318 @ SV612 @ tc_nat ) )
= $true )
| ( ( SV318
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2162,plain,
! [SV613: $i,SV319: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV319 @ SV613 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV613
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(2163,plain,
! [SV614: $i,SV320: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV320 @ SV614 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV320
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(2164,plain,
! [SV781: $i,SV615: $i,SV321: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
| ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SV781 @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2165,plain,
! [SV782: $i,SV616: $i,SV322: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2166,plain,
! [SV783: $i,SV617: $i,SV323: $i] :
( ( ! [SY1587: $i,SY1588: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SY1587 @ SY1588 @ SV323 ) )
| ( SY1588
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SY1588 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SY1587 @ SV783 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2167,plain,
! [SV618: $i,SV324: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV324 @ SV618 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV324
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1880]) ).
thf(2168,plain,
! [SV325: $i] :
( ( ( ( c_Complex_Ocnj @ SV325 )
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $false )
| ( ( SV325
= ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(2169,plain,
! [SV619: $i,SV326: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV326 @ SV619 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV326
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1882]) ).
thf(2170,plain,
! [SV620: $i,SV327: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV327 @ SV620 @ tc_nat )
!= SV327 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV620 @ SV327 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2171,plain,
! [SV784: $i,SV621: $i,SV328: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 )
| ( ( c_Power_Opower__class_Opower @ SV621 @ SV784 @ SV328 )
!= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
| ( SV621
= ( c_HOL_Ozero__class_Ozero @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2172,plain,
! [SV622: $i,SV329: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV329 @ SV622 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV622 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2173,plain,
! [SV785: $i,SV623: $i,SV330: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
| ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SV785 @ SV330 )
!= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV785
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2174,plain,
! [SV786: $i,SV624: $i,SV331: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV331 @ SV624 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV786 @ SV624 @ tc_nat ) )
| ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV331 = SV786 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2175,plain,
! [SV625: $i,SV332: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV332 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV332 )
| ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(2176,plain,
! [SV787: $i,SV626: $i,SV333: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2177,plain,
! [SV627: $i,SV334: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV334 @ SV627 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2178,plain,
! [SV788: $i,SV628: $i,SV335: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SV628 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SV788 @ SV628 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SV788 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2179,plain,
! [SV629: $i,SV336: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV336 ) )
= $true )
| ( ( ( ( c_HOL_Osgn__class_Osgn @ SV629 @ SV336 )
!= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
| ( SV629
= ( c_HOL_Ozero__class_Ozero @ SV336 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2180,plain,
! [SV630: $i,SV337: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV337 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
| ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2181,plain,
! [SV789: $i,SV631: $i,SV339: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV2 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SV631 @ SV2 ) @ SV789 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SV789 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SV631 @ SV789 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2182,plain,
! [SV340: $i,SV3: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV3 @ SV340 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV3 @ tc_nat )
| ( SV340 = SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2183,plain,
! [SV341: $i,SV4: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV4 @ SV341 @ tc_nat )
= $false )
| ( ( ( SV341 = SV4 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV341 @ SV4 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(2184,plain,
! [SV342: $i,SV5: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV5 @ SV342 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV342 @ SV5 @ tc_nat ) )
= $true )
| ( ( SV5 = SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2185,plain,
! [SV6: $i,SV343: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV343 @ SV6 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV6 @ SV343 @ tc_nat ) )
= $true )
| ( ( SV6 = SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2186,plain,
! [SV344: $i,SV7: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV7 @ SV344 @ tc_nat )
= $false )
| ( ( ( SV344 = SV7 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV344 @ SV7 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(2187,plain,
! [SV8: $i,SV345: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV345 @ SV8 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV8 @ SV345 @ tc_nat ) )
= $true )
| ( ( SV8 = SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2188,plain,
! [SV9: $i,SV346: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV346 @ SV9 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV9 @ SV346 @ tc_nat ) )
= $true )
| ( ( SV9 = SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2189,plain,
! [SV632: $i,SV348: $i,SV11: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ SV348 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ ( c_GCD_Ogcd__class_Ogcd @ SV632 @ SV348 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2190,plain,
! [SV633: $i,SV349: $i,SV12: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ SV349 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ ( c_GCD_Ogcd__class_Ogcd @ SV349 @ SV633 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2191,plain,
! [SV634: $i,SV350: $i,SV13: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ SV350 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ ( c_GCD_Ogcd__class_Ogcd @ SV350 @ SV634 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2192,plain,
! [SV635: $i,SV351: $i,SV14: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ SV351 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ ( c_GCD_Ogcd__class_Ogcd @ SV635 @ SV351 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1905]) ).
thf(2193,plain,
! [SV636: $i,SV352: $i,SV15: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV15 @ SV352 @ tc_nat ) @ SV636 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV15 @ SV636 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2194,plain,
! [SV637: $i,SV353: $i,SV16: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV16 @ SV353 @ tc_nat ) @ SV637 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV353 @ SV637 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2195,plain,
! [SV638: $i,SV354: $i,SV17: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ SV354 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ ( c_GCD_Ogcd__class_Ogcd @ SV354 @ SV638 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1908]) ).
thf(2196,plain,
! [SV639: $i,SV355: $i,SV18: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ SV355 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ ( c_GCD_Ogcd__class_Ogcd @ SV639 @ SV355 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2197,plain,
! [SV640: $i,SV356: $i,SV19: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV356 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV640 @ SV356 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV640 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2198,plain,
! [SV641: $i,SV357: $i,SV20: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2199,plain,
! [SV358: $i,SV22: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV22 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV358 @ SV358 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2200,plain,
! [SV790: $i,SV642: $i,SV359: $i,SV23: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2201,plain,
! [SV643: $i,SV361: $i,SV25: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV25 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV361 @ SV25 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV643 @ SV25 ) @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2202,plain,
! [SV644: $i,SV362: $i,SV26: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV26 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV362 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ ( c_HOL_Otimes__class_Otimes @ SV644 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2203,plain,
! [SV645: $i,SV363: $i,SV27: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV27 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV645 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV363 @ SV27 ) @ ( c_HOL_Oabs__class_Oabs @ SV645 @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2204,plain,
! [SV791: $i,SV646: $i,SV364: $i,SV28: $i] :
( ( ! [SY1589: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SV791 @ SY1589 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SV791 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SY1589 @ SV28 ) @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2205,plain,
! [SV647: $i,SV365: $i,SV29: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV365 @ ( c_HOL_Otimes__class_Otimes @ SV365 @ SV647 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV365 @ SV647 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2206,plain,
! [SV792: $i,SV648: $i,SV366: $i,SV30: $i] :
( ( ! [SY1590: $i] :
( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SY1590 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SY1590 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1590 @ SV792 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2207,plain,
! [SV367: $i,SV31: $i] :
( ( ( class_Power_Opower @ SV31 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV367 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV31 )
= ( c_HOL_Oone__class_Oone @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2208,plain,
! [SV368: $i,SV32: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV32 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV368 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 )
= ( c_HOL_Oone__class_Oone @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(2209,plain,
! [SV369: $i,SV33: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV33 )
| ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2210,plain,
! [SV370: $i,SV34: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV34 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV34 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV370 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
| ( SV370
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2211,plain,
! [SV649: $i,SV371: $i,SV35: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV35 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV371 @ SV35 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV649 @ SV35 ) @ SV35 )
= ( c_HOL_Ozero__class_Ozero @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2212,plain,
! [SV650: $i,SV372: $i,SV36: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SV372 @ tc_nat ) @ SV650 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV372 @ SV650 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SV650 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2213,plain,
! [SV651: $i,SV375: $i,SV39: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SV375 @ tc_nat ) @ SV651 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV375 @ SV651 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SV651 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2214,plain,
! [SV652: $i,SV378: $i,SV42: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SV378 @ tc_nat ) @ SV652 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV378 @ SV652 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SV652 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2215,plain,
! [SV653: $i,SV381: $i,SV45: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SV381 @ tc_nat ) @ SV653 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV381 @ SV653 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SV653 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2216,plain,
! [SV654: $i,SV382: $i,SV46: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SV382 @ tc_nat ) @ SV654 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV382 @ SV654 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SV654 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2217,plain,
! [SV655: $i,SV383: $i,SV47: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SV383 @ tc_nat ) @ SV655 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SV655 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV655 @ SV47 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2218,plain,
! [SV656: $i,SV384: $i,SV48: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SV384 @ tc_nat ) @ SV656 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV384 @ SV656 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV384 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2219,plain,
! [SV793: $i,SV657: $i,SV385: $i,SV49: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SV793 @ SV49 ) @ SV49 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SV793 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2220,plain,
! [SV794: $i,SV658: $i,SV386: $i,SV50: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV794 @ SV50 ) @ SV50 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SV658 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2221,plain,
! [SV795: $i,SV659: $i,SV387: $i,SV51: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SV659 @ SV51 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SV795 @ SV51 ) @ SV659 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2222,plain,
! [SV796: $i,SV660: $i,SV388: $i,SV52: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SV660 @ SV52 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV796 @ SV388 @ SV52 ) @ SV660 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2223,plain,
! [SV661: $i,SV391: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV59 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV391 @ SV661 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SV661 @ SV391 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2224,plain,
! [SV392: $i,SV60: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV60 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV392 @ SV392 @ SV60 )
= SV392 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2225,plain,
! [SV61: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV61 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= ( c_HOL_Ozero__class_Ozero @ SV61 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1938]) ).
thf(2226,plain,
! [SV797: $i,SV662: $i,SV393: $i,SV63: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV662 @ SV63 ) @ SV797 @ SV63 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV393 @ SV797 @ SV63 ) @ ( c_Power_Opower__class_Opower @ SV662 @ SV797 @ SV63 ) @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2227,plain,
! [SV798: $i,SV663: $i,SV394: $i,SV64: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV64 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV394 @ SV663 @ SV64 ) @ SV798 @ SV64 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV394 @ SV798 @ SV64 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV798 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2228,plain,
! [SV664: $i,SV395: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV65 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV65 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV395 @ SV664 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV395 @ SV65 ) @ SV664 @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1942]) ).
thf(2229,plain,
! [SV799: $i,SV665: $i,SV396: $i,SV66: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV66 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV396 @ SV665 @ SV66 ) @ SV799 @ SV66 )
= ( c_HOL_Otimes__class_Otimes @ SV396 @ ( c_HOL_Otimes__class_Otimes @ SV665 @ SV799 @ SV66 ) @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2230,plain,
! [SV800: $i,SV666: $i,SV397: $i,SV67: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV666 @ SV67 ) @ SV800 @ SV67 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV800 @ SV67 ) @ SV666 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2231,plain,
! [SV801: $i,SV667: $i,SV398: $i,SV68: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV398 @ SV667 @ SV68 ) @ SV801 @ SV68 )
= ( c_HOL_Otimes__class_Otimes @ SV398 @ ( c_HOL_Otimes__class_Otimes @ SV667 @ SV801 @ SV68 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2232,plain,
! [SV802: $i,SV668: $i,SV399: $i,SV69: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV69 )
| ( ( c_HOL_Otimes__class_Otimes @ SV399 @ ( c_HOL_Otimes__class_Otimes @ SV668 @ SV802 @ SV69 ) @ SV69 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV399 @ SV668 @ SV69 ) @ SV802 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2233,plain,
! [SV803: $i,SV669: $i,SV400: $i,SV70: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
| ( ( c_HOL_Otimes__class_Otimes @ SV400 @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV803 @ SV70 ) @ SV70 )
= ( c_HOL_Otimes__class_Otimes @ SV669 @ ( c_HOL_Otimes__class_Otimes @ SV400 @ SV803 @ SV70 ) @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2234,plain,
! [SV804: $i,SV671: $i,SV402: $i,SV72: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_HOL_Otimes__class_Otimes @ SV402 @ ( c_HOL_Otimes__class_Otimes @ SV671 @ SV804 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV402 @ SV671 @ SV72 ) @ SV804 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2235,plain,
! [SV403: $i,SV73: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV73 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV403 @ SV73 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV73 ) @ SV403 @ SV73 ) )
| ( SV403
= ( c_HOL_Ozero__class_Ozero @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1950]) ).
thf(2236,plain,
! [SV404: $i,SV74: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV74 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV404 @ SV74 ) @ SV404 @ SV74 )
= ( c_HOL_Oone__class_Oone @ SV74 ) )
| ( SV404
= ( c_HOL_Ozero__class_Ozero @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2237,plain,
! [SV405: $i,SV75: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV75 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV405 @ SV75 ) @ SV405 @ SV75 )
= ( c_HOL_Oone__class_Oone @ SV75 ) )
| ( SV405
= ( c_HOL_Ozero__class_Ozero @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2238,plain,
! [SV406: $i,SV76: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV76 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV406 @ ( c_HOL_Oinverse__class_Oinverse @ SV406 @ SV76 ) @ SV76 )
= ( c_HOL_Oone__class_Oone @ SV76 ) )
| ( SV406
= ( c_HOL_Ozero__class_Ozero @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2239,plain,
! [SV805: $i,SV672: $i,SV407: $i,SV77: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV77 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV672 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV805 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SV672 @ SV805 @ SV77 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2240,plain,
! [SV806: $i,SV673: $i,SV408: $i,SV78: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV78 )
| ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV408 @ SV673 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV673 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SV408 @ SV806 @ SV78 ) )
| ( SV673
= ( c_HOL_Ozero__class_Ozero @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2241,plain,
! [SV409: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV79 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ SV409 @ SV79 ) @ SV79 )
= ( c_HOL_Osgn__class_Osgn @ SV409 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2242,plain,
! [SV412: $i,SV82: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV82 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ SV412 @ SV82 )
= ( c_HOL_Otimes__class_Otimes @ SV412 @ ( c_HOL_Osgn__class_Osgn @ SV412 @ SV82 ) @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2243,plain,
! [SV807: $i,SV676: $i,SV413: $i,SV83: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV83 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2244,plain,
! [SV808: $i,SV677: $i,SV414: $i,SV84: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2245,plain,
! [SV415: $i,SV85: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV85 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV415 @ SV85 ) @ SV85 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV415 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2246,plain,
! [SV86: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV86 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1963]) ).
thf(2247,plain,
! [SV678: $i,SV416: $i,SV87: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ ( c_GCD_Ogcd__class_Olcm @ SV416 @ SV678 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV416 @ SV87 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ SV416 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1964]) ).
thf(2248,plain,
! [SV679: $i,SV417: $i,SV88: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ ( c_GCD_Ogcd__class_Olcm @ SV417 @ SV679 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV88 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ SV679 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2249,plain,
! [SV680: $i,SV418: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV89 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV89 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV680 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV418 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV680 @ SV89 ) @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2250,plain,
! [SV681: $i,SV419: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV90 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV419 @ SV681 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV419 @ SV90 ) @ SV90 ) )
| ( SV681
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV419
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1967]) ).
thf(2251,plain,
! [SV420: $i,SV91: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV91 )
= $false )
| ( ( ( SV420
= ( c_HOL_Ozero__class_Ozero @ SV91 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV420 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2252,plain,
! [SV421: $i,SV92: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV92 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV421 @ SV92 ) @ SV92 )
= SV421 )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2253,plain,
! [SV682: $i,SV422: $i,SV94: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2254,plain,
! [SV683: $i,SV423: $i,SV95: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV95 ) )
= $true )
| ( ( ( SV423
= ( c_HOL_Ozero__class_Ozero @ SV95 ) )
| ( SV683
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV423 @ SV95 ) @ SV423 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2255,plain,
! [SV684: $i,SV424: $i,SV96: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV96 ) )
= $true )
| ( ( ( SV424
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV424 @ SV96 ) @ SV424 @ SV96 )
= SV684 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2256,plain,
! [SV685: $i,SV425: $i,SV97: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV97 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
| ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV685 @ SV97 ) @ SV685 @ SV97 ) )
| ( SV685
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(2257,plain,
! [SV686: $i,SV426: $i,SV98: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV98 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SV686 @ SV98 ) @ SV686 @ SV98 )
= SV426 )
| ( SV686
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2258,plain,
! [SV809: $i,SV687: $i,SV427: $i,SV99: $i] :
( ( ! [SY1591: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SV809 @ SY1591 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SV809 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ SY1591 @ SV99 ) @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2259,plain,
! [SV810: $i,SV688: $i,SV428: $i,SV100: $i] :
( ( ! [SY1592: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV428 @ SV688 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SY1592 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SV428 @ ( c_HOL_Otimes__class_Otimes @ SV688 @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SY1592 @ SV100 ) @ SV100 ) @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2260,plain,
! [SV811: $i,SV689: $i,SV429: $i,SV101: $i] :
( ( ! [SY1593: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV689 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SY1593 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV811 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SY1593 @ SV101 ) @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2261,plain,
! [SV690: $i,SV430: $i,SV102: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV102 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV690 @ SV102 ) @ SV690 @ SV102 )
= SV430 )
| ( SV690
= ( c_HOL_Ozero__class_Ozero @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2262,plain,
! [SV691: $i,SV431: $i,SV103: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV103 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV691 @ SV103 ) @ SV431 @ SV103 )
= SV691 )
| ( SV431
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2263,plain,
! [SV432: $i,SV104: $i] :
( ( ( class_Divides_Osemiring__div @ SV104 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV432 @ ( c_HOL_Ozero__class_Ozero @ SV104 ) @ SV104 )
= ( c_HOL_Ozero__class_Ozero @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2264,plain,
! [SV433: $i,SV105: $i] :
( ( ( class_Divides_Osemiring__div @ SV105 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV433 @ SV105 )
= ( c_HOL_Ozero__class_Ozero @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2265,plain,
! [SV434: $i,SV106: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV106 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV106 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV106 ) @ SV434 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2266,plain,
! [SV435: $i,SV107: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV107 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV435 @ SV107 ) @ ( c_HOL_Oabs__class_Oabs @ SV435 @ SV107 ) @ SV107 )
= SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2267,plain,
! [SV108: $i,SV436: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV436 @ SV108 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Olcm @ SV108 @ SV436 @ tc_nat )
= SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2268,plain,
! [SV109: $i,SV437: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV437 @ SV109 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Olcm @ SV109 @ SV437 @ tc_nat )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2269,plain,
! [SV438: $i,SV110: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV110 @ SV438 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Olcm @ SV110 @ SV438 @ tc_nat )
= SV438 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2270,plain,
! [SV111: $i,SV439: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV439 @ SV111 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Olcm @ SV111 @ SV439 @ tc_nat )
= SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2271,plain,
! [SV440: $i,SV112: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV112 @ SV440 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Olcm @ SV112 @ SV440 @ tc_nat )
= SV440 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2272,plain,
! [SV692: $i,SV441: $i,SV113: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV113 @ SV441 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV692 @ SV113 @ tc_nat ) @ SV441 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2273,plain,
! [SV693: $i,SV442: $i,SV114: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV114 @ SV442 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV114 @ SV693 @ tc_nat ) @ SV442 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2274,plain,
! [SV694: $i,SV443: $i,SV115: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ ( c_GCD_Ogcd__class_Olcm @ SV443 @ SV694 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ SV694 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2275,plain,
! [SV695: $i,SV444: $i,SV116: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ ( c_GCD_Ogcd__class_Olcm @ SV444 @ SV695 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ SV444 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2276,plain,
! [SV696: $i,SV445: $i,SV117: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV117 @ SV445 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV696 @ SV117 @ tc_nat ) @ SV445 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2277,plain,
! [SV697: $i,SV446: $i,SV118: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV118 @ SV446 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV118 @ SV697 @ tc_nat ) @ SV446 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2278,plain,
! [SV698: $i,SV447: $i,SV119: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ ( c_GCD_Ogcd__class_Olcm @ SV447 @ SV698 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ SV447 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2279,plain,
! [SV699: $i,SV448: $i,SV120: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ ( c_GCD_Ogcd__class_Olcm @ SV448 @ SV699 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ SV699 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2280,plain,
! [SV449: $i,SV121: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV121 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV449 @ SV121 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV121 ) @ SV449 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2281,plain,
! [SV450: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV122 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV122 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV450 @ SV122 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV122 ) @ SV450 @ SV122 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2282,plain,
! [SV700: $i,SV451: $i,SV123: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Otimes__class_Otimes @ SV700 @ SV451 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2000]) ).
thf(2283,plain,
! [SV701: $i,SV452: $i,SV124: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV452 @ ( c_HOL_Otimes__class_Otimes @ SV452 @ SV701 @ SV124 ) @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2284,plain,
! [SV702: $i,SV453: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV125 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV453 @ ( c_HOL_Otimes__class_Otimes @ SV453 @ SV702 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2285,plain,
! [SV703: $i,SV454: $i,SV126: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV126 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV126 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SV454 @ SV703 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SV454 @ SV126 ) @ SV703 @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2286,plain,
! [SV455: $i,SV127: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV127 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV127 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV455 @ SV127 ) @ SV127 )
= SV455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2287,plain,
! [SV812: $i,SV704: $i,SV456: $i,SV128: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
| ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV456 @ SV704 @ SV128 ) @ SV812 @ SV128 )
= ( c_Power_Opower__class_Opower @ SV456 @ ( c_HOL_Otimes__class_Otimes @ SV704 @ SV812 @ tc_nat ) @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2288,plain,
! [SV705: $i,SV457: $i,SV129: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV457 @ SV705 @ SV129 )
= ( c_HOL_Otimes__class_Otimes @ SV705 @ SV457 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2289,plain,
! [SV706: $i,SV459: $i,SV131: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV131 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV459 @ SV706 @ SV131 )
= ( c_HOL_Otimes__class_Otimes @ SV706 @ SV459 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2290,plain,
! [SV460: $i,SV133: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV133 )
= $false )
| ( ( ( SV460
= ( c_HOL_Ozero__class_Ozero @ SV133 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV460 @ SV460 @ SV133 )
= ( c_HOL_Oone__class_Oone @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2291,plain,
! [SV461: $i,SV134: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV134 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV461 @ SV461 @ SV134 )
= ( c_HOL_Oone__class_Oone @ SV134 ) )
| ( SV461
= ( c_HOL_Ozero__class_Ozero @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2292,plain,
! [SV462: $i,SV135: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV135 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV135 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV462 @ SV462 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
| ( SV462
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2293,plain,
! [SV464: $i,SV138: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV138 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV138 ) @ SV464 @ SV138 )
= ( c_HOL_Ozero__class_Ozero @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2294,plain,
! [SV465: $i,SV139: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV139 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV139 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV465 @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2295,plain,
! [SV466: $i,SV140: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV140 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV140 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV466 @ ( c_HOL_Ozero__class_Ozero @ SV140 ) @ SV140 )
= ( c_HOL_Ozero__class_Ozero @ SV140 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2296,plain,
! [SV467: $i,SV141: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV141 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SV467 @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2297,plain,
! [SV813: $i,SV708: $i,SV468: $i,SV142: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV142 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SV708 @ SV142 ) @ SV813 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV813 @ SV142 ) @ SV708 @ SV142 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV468 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2298,plain,
! [SV709: $i,SV469: $i,SV143: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV143 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV469 @ SV143 ) @ SV709 @ SV143 )
= ( c_Power_Opower__class_Opower @ SV469 @ SV709 @ SV143 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV709 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2299,plain,
! [SV710: $i,SV470: $i,SV144: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV144 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV470 @ SV710 @ SV144 ) @ SV144 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV470 @ SV144 ) @ SV710 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2300,plain,
! [SV814: $i,SV711: $i,SV471: $i,SV145: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SV711 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SV814 @ SV711 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SV814 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2301,plain,
! [SV472: $i,SV146: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV146 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV146 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV472 @ SV146 ) @ SV146 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV472 @ SV146 ) @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2302,plain,
! [SV712: $i,SV473: $i,SV147: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV147 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV147 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV473 @ SV712 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV473 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SV712 @ SV147 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2303,plain,
! [SV815: $i,SV713: $i,SV474: $i,SV148: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV148 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SV815 @ SV148 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2304,plain,
! [SV816: $i,SV714: $i,SV475: $i,SV149: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV149 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV816 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SV816 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2305,plain,
! [SV817: $i,SV715: $i,SV476: $i,SV150: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV150 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SV715 @ SV150 ) @ SV817 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV817 @ SV150 ) @ SV715 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2306,plain,
! [SV716: $i,SV477: $i,SV151: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV151 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV477 @ ( c_Divides_Odiv__class_Odiv @ SV716 @ SV477 @ SV151 ) @ SV151 )
= SV716 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV477 @ SV716 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2307,plain,
! [SV717: $i,SV478: $i,SV152: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV152 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV478 @ SV717 @ SV152 ) @ SV717 @ SV152 )
= SV478 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV478 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2308,plain,
! [SV818: $i,SV718: $i,SV479: $i,SV153: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV153 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
| ( SV818
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV818 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SV818 @ SV153 ) @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2309,plain,
! [SV819: $i,SV719: $i,SV480: $i,SV154: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV154 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
| ( SV819
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV719 @ SV154 ) @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2310,plain,
! [SV720: $i,SV481: $i,SV155: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV155 @ SV481 @ tc_nat )
= $true )
| ( ( ( SV720
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV155 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV481 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2311,plain,
! [SV721: $i,SV483: $i,SV157: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SV483 @ SV721 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV721 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV483 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2312,plain,
! [SV722: $i,SV484: $i,SV158: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SV484 @ SV722 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SV722 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV158 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2032]) ).
thf(2313,plain,
! [SV723: $i,SV485: $i,SV159: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SV485 @ SV723 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SV485 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV485 @ SV159 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2314,plain,
! [SV724: $i,SV486: $i,SV160: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SV486 @ SV724 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV724 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV486 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2315,plain,
! [SV725: $i,SV487: $i,SV161: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SV487 @ SV725 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV725 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV487 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2035]) ).
thf(2316,plain,
! [SV726: $i,SV494: $i,SV168: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SV494 @ SV726 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV726 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV494 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2317,plain,
! [SV727: $i,SV495: $i,SV169: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SV495 @ SV727 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV727 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV495 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2037]) ).
thf(2318,plain,
! [SV728: $i,SV496: $i,SV170: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SV496 @ SV728 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV728 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV496 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2319,plain,
! [SV729: $i,SV497: $i,SV171: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2320,plain,
! [SV730: $i,SV498: $i,SV172: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2321,plain,
! [SV499: $i,SV173: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV173 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV499 @ SV173 ) @ SV173 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV499 @ SV173 ) @ SV173 ) )
| ( SV499
= ( c_HOL_Ozero__class_Ozero @ SV173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2322,plain,
! [SV731: $i,SV500: $i,SV174: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV174 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV500 @ SV731 @ SV174 ) @ SV174 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV500 @ SV174 ) @ ( c_HOL_Oabs__class_Oabs @ SV731 @ SV174 ) @ SV174 ) )
| ( SV731
= ( c_HOL_Ozero__class_Ozero @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2323,plain,
! [SV178: $i] :
( ( ( ~ ( class_Power_Opower @ SV178 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV178 )
= ( c_HOL_Oone__class_Oone @ SV178 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2324,plain,
! [SV502: $i,SV179: $i] :
( ( ( class_Divides_Osemiring__div @ SV179 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ SV502 @ SV502 @ SV179 )
= ( c_HOL_Oone__class_Oone @ SV179 ) )
| ( SV502
= ( c_HOL_Ozero__class_Ozero @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2325,plain,
! [SV733: $i,SV504: $i,SV182: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV504 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV733 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV733 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2326,plain,
! [SV820: $i,SV734: $i,SV505: $i,SV183: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV183 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV734 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV820 @ SV183 ) @ SV183 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV734 @ SV820 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2327,plain,
! [SV821: $i,SV735: $i,SV506: $i,SV184: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV184 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV735 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV821 @ SV735 @ SV184 ) @ SV184 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SV821 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2328,plain,
! [SV507: $i,SV185: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV185 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV507 @ SV185 ) @ SV185 )
= ( c_HOL_Oabs__class_Oabs @ SV507 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2329,plain,
! [SV186: $i,SV508: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV508 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV186 @ SV508 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2330,plain,
! [SV509: $i,SV187: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV187 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV187 @ SV509 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2331,plain,
! [SV736: $i,SV512: $i,SV191: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV191 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV512 @ SV736 @ SV191 ) @ SV512 @ SV191 )
= ( c_HOL_Otimes__class_Otimes @ SV512 @ ( c_Power_Opower__class_Opower @ SV512 @ SV736 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2332,plain,
! [SV513: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV192 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV192 )
| ( ( c_HOL_Ozero__class_Ozero @ SV192 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV513 @ SV192 ) @ SV513 @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2333,plain,
! [SV822: $i,SV737: $i,SV514: $i,SV193: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV193 )
| ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SV737 @ SV193 ) @ SV822 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SV822 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV737 @ SV822 @ SV193 ) @ SV193 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV737 @ SV514 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2334,plain,
! [SV738: $i,SV515: $i,SV194: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV194 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV515 @ SV738 @ tc_nat ) @ SV194 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV515 @ SV194 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV738 @ SV194 ) @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2335,plain,
! [SV516: $i,SV195: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV195 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV516 @ SV195 ) @ ( c_HOL_Oabs__class_Oabs @ SV516 @ SV195 ) @ SV195 )
= ( c_HOL_Otimes__class_Otimes @ SV516 @ SV516 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2336,plain,
! [SV739: $i,SV517: $i,SV196: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV196 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV517 @ SV739 @ SV196 ) @ SV196 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV517 @ SV196 ) @ SV739 @ SV196 ) )
| ( SV517
= ( c_HOL_Ozero__class_Ozero @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2337,plain,
! [SV521: $i,SV201: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV521 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2338,plain,
! [SV743: $i,SV522: $i,SV202: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV202 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SV743 @ SV202 ) @ SV743 @ SV202 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2339,plain,
! [SV744: $i,SV523: $i,SV203: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV203 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SV744 @ SV203 ) @ SV744 @ SV203 )
= SV523 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2340,plain,
! [SV524: $i,SV204: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV204 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV524 @ SV204 )
= ( c_HOL_Ozero__class_Ozero @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2341,plain,
! [SV525: $i,SV205: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV205 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV525 @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV205 )
= ( c_HOL_Ozero__class_Ozero @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2065]) ).
thf(2342,plain,
! [SV526: $i,SV206: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV206 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV206 ) @ SV526 @ SV206 )
= ( c_HOL_Ozero__class_Ozero @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2343,plain,
! [SV527: $i,SV207: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV207 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV207 ) @ SV527 @ SV207 )
= ( c_HOL_Ozero__class_Ozero @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2344,plain,
! [SV528: $i,SV210: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV210 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV528 @ ( c_HOL_Ozero__class_Ozero @ SV210 ) @ SV210 )
= ( c_HOL_Ozero__class_Ozero @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2345,plain,
! [SV529: $i,SV211: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV211 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV529 @ ( c_HOL_Ozero__class_Ozero @ SV211 ) @ SV211 )
= ( c_HOL_Ozero__class_Ozero @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2346,plain,
! [SV530: $i,SV212: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV212 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV212 ) @ SV530 @ SV212 )
= ( c_HOL_Ozero__class_Ozero @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2347,plain,
! [SV531: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV213 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV531 @ SV213 )
= ( c_HOL_Ozero__class_Ozero @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2348,plain,
! [SV532: $i,SV214: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV214 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV532 @ ( c_HOL_Ozero__class_Ozero @ SV214 ) @ SV214 )
= ( c_HOL_Ozero__class_Ozero @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2349,plain,
! [SV533: $i,SV215: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV215 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV215 ) @ SV533 @ SV215 )
= ( c_HOL_Ozero__class_Ozero @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2073]) ).
thf(2350,plain,
! [SV534: $i,SV216: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV216 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV216 ) @ SV216 )
= ( c_HOL_Ozero__class_Ozero @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2351,plain,
! [SV535: $i,SV217: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV217 )
= $false )
| ( ( ( SV535
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
| ~ ( c_Int_Oiszero @ SV535 @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2352,plain,
! [SV745: $i,SV536: $i,SV218: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV218 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV536 @ SV745 @ SV218 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV536 @ SV218 ) @ SV745 @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2353,plain,
! [SV746: $i,SV537: $i,SV219: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV219 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV537 @ SV219 ) @ SV746 @ SV219 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV537 @ SV746 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2354,plain,
! [SV747: $i,SV538: $i,SV220: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV220 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ SV747 @ SV220 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ ( c_HOL_Oabs__class_Oabs @ SV747 @ SV220 ) @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2355,plain,
! [SV748: $i,SV539: $i,SV221: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV221 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ ( c_HOL_Oabs__class_Oabs @ SV748 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ SV748 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2079]) ).
thf(2356,plain,
! [SV752: $i,SV544: $i,SV229: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV229 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV544 @ SV752 @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ SV544 @ ( c_HOL_Oinverse__class_Oinverse @ SV752 @ SV229 ) @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2357,plain,
! [SV753: $i,SV545: $i,SV230: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV230 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV230 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV545 @ SV753 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SV545 @ ( c_HOL_Oinverse__class_Oinverse @ SV753 @ SV230 ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2358,plain,
! [SV823: $i,SV754: $i,SV546: $i,SV232: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV232 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV546 @ SV754 @ SV232 ) @ SV823 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV546 @ SV823 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV754 @ SV823 @ SV232 ) @ SV232 ) )
| ( SV754
= ( c_HOL_Ozero__class_Ozero @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2359,plain,
! [SV824: $i,SV755: $i,SV547: $i,SV233: $i] :
( ( ! [SY1594: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SY1594 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SY1594 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2360,plain,
! [SV234: $i,SV548: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV548 @ SV234 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV234 @ SV548 @ tc_nat )
= SV548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2361,plain,
! [SV549: $i,SV235: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV235 @ SV549 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SV549 @ tc_nat )
= SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2362,plain,
! [SV236: $i,SV550: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV550 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV550 @ SV236 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV236 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2363,plain,
! [SV553: $i,SV239: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV239 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV239 )
| ( ( c_HOL_Ozero__class_Ozero @ SV239 )
= ( c_HOL_Oinverse__class_Odivide @ SV553 @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2364,plain,
! [SV825: $i,SV756: $i,SV555: $i,SV241: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV241 )
| ( ( c_Power_Opower__class_Opower @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV825 @ tc_nat ) @ SV241 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV555 @ SV756 @ SV241 ) @ SV825 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2365,plain,
! [SV757: $i,SV556: $i,SV242: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__div__algebra @ SV242 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV757 @ SV242 ) @ SV242 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV556 @ SV242 ) @ ( c_HOL_Osgn__class_Osgn @ SV757 @ SV242 ) @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2366,plain,
! [SV758: $i,SV557: $i,SV243: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV243 ) )
= $true )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV557 @ SV758 @ SV243 ) @ SV243 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV557 @ SV243 ) @ ( c_HOL_Osgn__class_Osgn @ SV758 @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2097]) ).
thf(2367,plain,
! [SV759: $i,SV558: $i,SV244: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV244 @ SV558 @ tc_nat ) @ SV759 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV759 @ SV244 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV244 @ SV759 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2098]) ).
thf(2368,plain,
! [SV760: $i,SV559: $i,SV245: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV245 @ SV559 @ tc_nat ) @ SV760 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV760 @ SV559 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV559 @ SV760 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2369,plain,
! [SV560: $i,SV246: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV246 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV246 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV560 @ SV246 ) @ SV560 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2370,plain,
! [SV761: $i,SV561: $i,SV247: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV561 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV761 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2371,plain,
! [SV762: $i,SV562: $i,SV248: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SV762 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV762 @ SV562 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV762 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2372,plain,
! [SV249: $i] :
( ( ( c_Int_Oiszero @ ( c_HOL_Oone__class_Oone @ SV249 ) @ SV249 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2373,plain,
! [SV251: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV251 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV251 ) @ SV251 )
= ( c_HOL_Oone__class_Oone @ SV251 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2374,plain,
! [SV563: $i,SV252: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV252 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV563 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV252 )
= SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2375,plain,
! [SV564: $i,SV253: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV253 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV564 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV253 )
= SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2376,plain,
! [SV565: $i,SV256: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV256 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV256 ) @ SV565 @ SV256 )
= ( c_HOL_Oone__class_Oone @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2377,plain,
! [SV566: $i,SV258: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV258 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV566 @ ( c_HOL_Oone__class_Oone @ SV258 ) @ SV258 )
= SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2378,plain,
! [SV567: $i,SV264: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV264 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV264 ) @ SV567 @ SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2379,plain,
! [SV568: $i,SV267: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV267 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV568 @ ( c_HOL_Oone__class_Oone @ SV267 ) @ SV267 )
= SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2380,plain,
! [SV569: $i,SV268: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV268 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV268 ) @ SV569 @ SV268 )
= SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2381,plain,
! [SV570: $i,SV269: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV269 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV269 ) @ SV570 @ SV269 )
= SV570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2382,plain,
! [SV571: $i,SV270: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV270 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV270 ) @ SV571 @ SV270 )
= SV571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2383,plain,
! [SV572: $i,SV273: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV572 @ ( c_HOL_Oone__class_Oone @ SV273 ) @ SV273 )
= SV572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2384,plain,
! [SV573: $i,SV274: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ SV274 ) @ SV573 @ SV274 )
= SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2385,plain,
! [SV574: $i,SV276: $i] :
( ( ( class_Divides_Osemiring__div @ SV276 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ SV574 @ ( c_HOL_Oone__class_Oone @ SV276 ) @ SV276 )
= SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2386,plain,
! [SV763: $i,SV575: $i,SV277: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SV763 @ SV277 )
!= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV763
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2387,plain,
! [SV576: $i,SV278: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV278 @ SV576 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV278
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2388,plain,
! [SV279: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV279 )
= ( c_HOL_Oone__class_Oone @ SV279 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2389,plain,
! [SV577: $i,SV280: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV280 @ SV577 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( SV577
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2390,plain,
! [SV764: $i,SV578: $i,SV281: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ ( c_HOL_Otimes__class_Otimes @ SV578 @ SV764 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ SV578 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2391,plain,
! [SV765: $i,SV579: $i,SV282: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV282 @ SV579 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV282 @ SV765 @ tc_nat ) )
= $true )
| ( ( ( SV282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV579 = SV765 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2392,plain,
! [SV766: $i,SV580: $i,SV283: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV283 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
| ( SV580 = SV766 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2393,plain,
! [SV581: $i,SV284: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV284 @ SV581 @ tc_nat )
= SV581 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV284 @ SV581 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2394,plain,
! [SV582: $i,SV285: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV285 @ SV582 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2395,plain,
! [SV583: $i,SV286: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV286 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV583 @ SV286 )
!= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
| ( SV583
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2396,plain,
! [SV584: $i,SV287: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV287 @ SV584 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV584
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2132]) ).
thf(2397,plain,
! [SV767: $i,SV585: $i,SV288: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV585 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV767 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV585 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2398,plain,
! [SV586: $i,SV290: $i] :
( ( ( SV290
= ( c_HOL_Otimes__class_Otimes @ SV290 @ SV586 @ tc_nat ) )
= $false )
| ( ( ( SV290
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV586
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2399,plain,
! [SV587: $i,SV291: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV291 @ SV587 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( SV587
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2400,plain,
! [SV588: $i,SV292: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV292 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ SV588 @ tc_nat ) @ SV292 )
!= ( c_HOL_Ozero__class_Ozero @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2401,plain,
! [SV589: $i,SV293: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV293 @ SV589 @ tc_nat ) )
= $false )
| ( ( SV589
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2402,plain,
! [SV590: $i,SV294: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV294 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV590 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
| ( SV590
= ( c_HOL_Ozero__class_Ozero @ SV294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2403,plain,
! [SV295: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV295 )
= ( c_HOL_Ozero__class_Ozero @ SV295 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2404,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV296 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2405,plain,
! [SV592: $i,SV297: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV297 @ SV592 @ tc_nat )
= SV297 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV297 @ SV592 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2406,plain,
! [SV769: $i,SV593: $i,SV298: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ ( c_HOL_Otimes__class_Otimes @ SV593 @ SV769 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ SV769 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2142]) ).
thf(2407,plain,
! [SV594: $i,SV299: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV299 @ SV594 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( SV299
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2408,plain,
! [SV770: $i,SV595: $i,SV300: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV300 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
| ( SV595 = SV770 )
| ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2409,plain,
! [SV771: $i,SV596: $i,SV301: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV301 @ SV596 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV301 @ SV771 @ tc_nat ) )
= $true )
| ( ( ( SV596 = SV771 )
| ( SV301
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2410,plain,
! [SV772: $i,SV597: $i,SV302: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV302 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SV772 @ SV302 )
!= ( c_HOL_Oone__class_Oone @ SV302 ) )
| ( SV772
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SV597 = SV772 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2411,plain,
! [SV773: $i,SV598: $i,SV303: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV303 @ SV598 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV303 @ SV773 @ tc_nat ) @ SV598 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV773 @ SV598 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2412,plain,
! [SV599: $i,SV304: $i] :
( ( ( class_RealVector_Oreal__normed__vector @ SV304 )
= $false )
| ( ( ( ( c_HOL_Osgn__class_Osgn @ SV599 @ SV304 )
!= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
| ( SV599
= ( c_HOL_Ozero__class_Ozero @ SV304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2413,plain,
! [SV600: $i,SV305: $i] :
( ( ( ( c_Complex_Ocnj @ SV305 )
= ( c_Complex_Ocnj @ SV600 ) )
= $false )
| ( ( SV305 = SV600 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2149]) ).
thf(2414,plain,
! [SV601: $i,SV306: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV306 @ SV601 @ tc_nat )
= SV601 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV306 @ SV601 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2415,plain,
! [SV826: $i,SV774: $i,SV602: $i,SV307: $i] :
( ( ( SV307
!= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( SV774
!= ( c_HOL_Otimes__class_Otimes @ SV826 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV826 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2416,plain,
! [SV775: $i,SV603: $i,SV308: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV308 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV603 @ SV775 @ SV308 )
!= ( c_HOL_Oone__class_Oone @ SV308 ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV603 @ SV308 )
= SV775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2417,plain,
! [SV776: $i,SV604: $i,SV309: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SV604 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SV776 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SV776 @ SV604 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2418,plain,
! [SV605: $i,SV310: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV310 @ SV605 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV310
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2419,plain,
! [SV777: $i,SV606: $i,SV311: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV311 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV606 @ SV311 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV777 @ SV311 ) )
| ( SV606 = SV777 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2420,plain,
! [SV827: $i,SV778: $i,SV607: $i,SV312: $i] :
( ( ! [SY1595: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV312 )
| ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SV827 @ SY1595 @ SV312 ) )
| ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SY1595
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SY1595 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2421,plain,
! [SV608: $i,SV313: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV313 @ SV608 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV313 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2422,plain,
! [SV779: $i,SV609: $i,SV314: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV314 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV609 @ SV314 )
!= ( c_HOL_Oabs__class_Oabs @ SV779 @ SV314 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV609 @ SV779 @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2423,plain,
! [SV780: $i,SV610: $i,SV315: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2424,plain,
! [SV611: $i,SV316: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV316 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2425,plain,
! [SV612: $i,SV318: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV318 @ SV612 @ tc_nat ) )
= $false )
| ( ( SV318
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2426,plain,
! [SV613: $i,SV319: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV319 @ SV613 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( SV613
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2427,plain,
! [SV614: $i,SV320: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV320 @ SV614 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( SV320
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2428,plain,
! [SV781: $i,SV615: $i,SV321: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV321 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SV781 @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2429,plain,
! [SV782: $i,SV616: $i,SV322: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2430,plain,
! [SV828: $i,SV783: $i,SV617: $i,SV323: $i] :
( ( ! [SY1596: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SY1596 @ SV323 ) )
| ( SY1596
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SY1596 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2431,plain,
! [SV618: $i,SV324: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV324 @ SV618 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV324
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2432,plain,
! [SV619: $i,SV326: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV326 @ SV619 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( SV326
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2433,plain,
! [SV620: $i,SV327: $i] :
( ( ( ( c_GCD_Ogcd__class_Olcm @ SV327 @ SV620 @ tc_nat )
= SV327 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV620 @ SV327 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2434,plain,
! [SV784: $i,SV621: $i,SV328: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV621 @ SV784 @ SV328 )
!= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
| ( SV621
= ( c_HOL_Ozero__class_Ozero @ SV328 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2171]) ).
thf(2435,plain,
! [SV622: $i,SV329: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV329 @ SV622 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV622 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2436,plain,
! [SV785: $i,SV623: $i,SV330: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV330 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SV785 @ SV330 )
!= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV785
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2437,plain,
! [SV786: $i,SV624: $i,SV331: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV331 @ SV624 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV786 @ SV624 @ tc_nat ) )
= $true )
| ( ( ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV331 = SV786 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2438,plain,
! [SV625: $i,SV332: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV332 )
| ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2439,plain,
! [SV787: $i,SV626: $i,SV333: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2440,plain,
! [SV627: $i,SV334: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV334 @ SV627 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2441,plain,
! [SV788: $i,SV628: $i,SV335: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SV628 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SV788 @ SV628 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SV788 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2442,plain,
! [SV629: $i,SV336: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV336 )
= $false )
| ( ( ( ( c_HOL_Osgn__class_Osgn @ SV629 @ SV336 )
!= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
| ( SV629
= ( c_HOL_Ozero__class_Ozero @ SV336 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2443,plain,
! [SV630: $i,SV337: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV337 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
| ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2444,plain,
! [SV789: $i,SV631: $i,SV339: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV2 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SV631 @ SV2 ) @ SV789 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SV789 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SV631 @ SV789 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2445,plain,
! [SV3: $i,SV340: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV3 @ tc_nat ) )
= $true )
| ( ( SV340 = SV3 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV3 @ SV340 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2446,plain,
! [SV4: $i,SV341: $i] :
( ( ( SV341 = SV4 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV341 @ SV4 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV4 @ SV341 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2447,plain,
! [SV342: $i,SV5: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV5 @ SV342 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV342 @ SV5 @ tc_nat ) )
= $true )
| ( ( SV5 = SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2448,plain,
! [SV6: $i,SV343: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV343 @ SV6 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV6 @ SV343 @ tc_nat ) )
= $true )
| ( ( SV6 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2449,plain,
! [SV7: $i,SV344: $i] :
( ( ( SV344 = SV7 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV344 @ SV7 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV7 @ SV344 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2450,plain,
! [SV8: $i,SV345: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV345 @ SV8 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV8 @ SV345 @ tc_nat ) )
= $true )
| ( ( SV8 = SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2451,plain,
! [SV9: $i,SV346: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV346 @ SV9 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV9 @ SV346 @ tc_nat ) )
= $true )
| ( ( SV9 = SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2452,plain,
! [SV348: $i,SV632: $i,SV11: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ ( c_GCD_Ogcd__class_Ogcd @ SV632 @ SV348 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV11 @ SV348 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2453,plain,
! [SV633: $i,SV349: $i,SV12: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ ( c_GCD_Ogcd__class_Ogcd @ SV349 @ SV633 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV12 @ SV349 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2454,plain,
! [SV634: $i,SV350: $i,SV13: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ ( c_GCD_Ogcd__class_Ogcd @ SV350 @ SV634 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV13 @ SV350 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2455,plain,
! [SV351: $i,SV635: $i,SV14: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ ( c_GCD_Ogcd__class_Ogcd @ SV635 @ SV351 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV14 @ SV351 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2456,plain,
! [SV352: $i,SV636: $i,SV15: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV15 @ SV636 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV15 @ SV352 @ tc_nat ) @ SV636 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2457,plain,
! [SV16: $i,SV637: $i,SV353: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV353 @ SV637 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV16 @ SV353 @ tc_nat ) @ SV637 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2458,plain,
! [SV638: $i,SV354: $i,SV17: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ ( c_GCD_Ogcd__class_Ogcd @ SV354 @ SV638 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV17 @ SV354 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2459,plain,
! [SV355: $i,SV639: $i,SV18: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ ( c_GCD_Ogcd__class_Ogcd @ SV639 @ SV355 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV18 @ SV355 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2460,plain,
! [SV19: $i,SV356: $i,SV640: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV640 @ SV356 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV640 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV356 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2197]) ).
thf(2461,plain,
! [SV20: $i,SV641: $i,SV357: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2462,plain,
! [SV790: $i,SV642: $i,SV359: $i,SV23: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2463,plain,
! [SV643: $i,SV361: $i,SV25: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV25 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV361 @ SV25 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV643 @ SV25 ) @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2464,plain,
! [SV644: $i,SV362: $i,SV26: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV26 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV362 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ ( c_HOL_Otimes__class_Otimes @ SV644 @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2465,plain,
! [SV645: $i,SV363: $i,SV27: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV27 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV645 @ SV27 ) @ SV27 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV363 @ SV27 ) @ ( c_HOL_Oabs__class_Oabs @ SV645 @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2466,plain,
! [SV829: $i,SV791: $i,SV646: $i,SV364: $i,SV28: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SV791 @ SV829 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SV791 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SV829 @ SV28 ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2467,plain,
! [SV647: $i,SV365: $i,SV29: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV29 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV365 @ ( c_HOL_Otimes__class_Otimes @ SV365 @ SV647 @ SV29 ) @ SV29 )
= ( c_HOL_Otimes__class_Otimes @ SV365 @ SV647 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2468,plain,
! [SV830: $i,SV792: $i,SV648: $i,SV366: $i,SV30: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV30 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2469,plain,
! [SV369: $i,SV33: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV33 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV33 )
| ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2470,plain,
! [SV370: $i,SV34: $i] :
( ( ( ~ ( class_Power_Opower @ SV34 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV370 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
| ( SV370
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2471,plain,
! [SV649: $i,SV371: $i,SV35: $i] :
( ( ( class_Divides_Osemiring__div @ SV35 )
= $false )
| ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV371 @ SV35 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV649 @ SV35 ) @ SV35 )
= ( c_HOL_Ozero__class_Ozero @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2472,plain,
! [SV36: $i,SV650: $i,SV372: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV372 @ SV650 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SV650 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SV372 @ tc_nat ) @ SV650 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2473,plain,
! [SV39: $i,SV651: $i,SV375: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV375 @ SV651 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SV651 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SV375 @ tc_nat ) @ SV651 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2474,plain,
! [SV42: $i,SV652: $i,SV378: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV378 @ SV652 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SV652 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SV378 @ tc_nat ) @ SV652 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2475,plain,
! [SV45: $i,SV653: $i,SV381: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV381 @ SV653 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SV653 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SV381 @ tc_nat ) @ SV653 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2476,plain,
! [SV46: $i,SV654: $i,SV382: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV382 @ SV654 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SV654 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SV382 @ tc_nat ) @ SV654 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2477,plain,
! [SV655: $i,SV383: $i,SV47: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SV383 @ tc_nat ) @ SV655 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SV655 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV655 @ SV47 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2478,plain,
! [SV656: $i,SV384: $i,SV48: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SV384 @ tc_nat ) @ SV656 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV384 @ SV656 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV384 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2479,plain,
! [SV793: $i,SV657: $i,SV385: $i,SV49: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SV793 @ SV49 ) @ SV49 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SV793 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2480,plain,
! [SV794: $i,SV658: $i,SV386: $i,SV50: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV794 @ SV50 ) @ SV50 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SV658 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2481,plain,
! [SV795: $i,SV659: $i,SV387: $i,SV51: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SV659 @ SV51 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SV795 @ SV51 ) @ SV659 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2482,plain,
! [SV796: $i,SV660: $i,SV388: $i,SV52: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SV660 @ SV52 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV796 @ SV388 @ SV52 ) @ SV660 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2483,plain,
! [SV661: $i,SV391: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV59 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV391 @ SV661 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SV661 @ SV391 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2484,plain,
! [SV61: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV61 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= ( c_HOL_Ozero__class_Ozero @ SV61 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2485,plain,
! [SV797: $i,SV662: $i,SV393: $i,SV63: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV662 @ SV63 ) @ SV797 @ SV63 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV393 @ SV797 @ SV63 ) @ ( c_Power_Opower__class_Opower @ SV662 @ SV797 @ SV63 ) @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2486,plain,
! [SV798: $i,SV663: $i,SV394: $i,SV64: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ SV64 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV394 @ SV663 @ SV64 ) @ SV798 @ SV64 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV394 @ SV798 @ SV64 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV798 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2227]) ).
thf(2487,plain,
! [SV664: $i,SV395: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV65 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV65 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV395 @ SV664 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV395 @ SV65 ) @ SV664 @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2488,plain,
! [SV799: $i,SV665: $i,SV396: $i,SV66: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV66 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV396 @ SV665 @ SV66 ) @ SV799 @ SV66 )
= ( c_HOL_Otimes__class_Otimes @ SV396 @ ( c_HOL_Otimes__class_Otimes @ SV665 @ SV799 @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2229]) ).
thf(2489,plain,
! [SV800: $i,SV666: $i,SV397: $i,SV67: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV666 @ SV67 ) @ SV800 @ SV67 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV800 @ SV67 ) @ SV666 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2490,plain,
! [SV801: $i,SV667: $i,SV398: $i,SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV398 @ SV667 @ SV68 ) @ SV801 @ SV68 )
= ( c_HOL_Otimes__class_Otimes @ SV398 @ ( c_HOL_Otimes__class_Otimes @ SV667 @ SV801 @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2491,plain,
! [SV802: $i,SV668: $i,SV399: $i,SV69: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV69 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV399 @ ( c_HOL_Otimes__class_Otimes @ SV668 @ SV802 @ SV69 ) @ SV69 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV399 @ SV668 @ SV69 ) @ SV802 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2492,plain,
! [SV803: $i,SV669: $i,SV400: $i,SV70: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV400 @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV803 @ SV70 ) @ SV70 )
= ( c_HOL_Otimes__class_Otimes @ SV669 @ ( c_HOL_Otimes__class_Otimes @ SV400 @ SV803 @ SV70 ) @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2493,plain,
! [SV804: $i,SV671: $i,SV402: $i,SV72: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV402 @ ( c_HOL_Otimes__class_Otimes @ SV671 @ SV804 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV402 @ SV671 @ SV72 ) @ SV804 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2494,plain,
! [SV73: $i,SV403: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV403 @ SV73 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV73 ) @ SV403 @ SV73 ) )
= $true )
| ( ( SV403
= ( c_HOL_Ozero__class_Ozero @ SV73 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2495,plain,
! [SV74: $i,SV404: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV404 @ SV74 ) @ SV404 @ SV74 )
= ( c_HOL_Oone__class_Oone @ SV74 ) )
= $true )
| ( ( SV404
= ( c_HOL_Ozero__class_Ozero @ SV74 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2496,plain,
! [SV75: $i,SV405: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV405 @ SV75 ) @ SV405 @ SV75 )
= ( c_HOL_Oone__class_Oone @ SV75 ) )
= $true )
| ( ( SV405
= ( c_HOL_Ozero__class_Ozero @ SV75 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2497,plain,
! [SV76: $i,SV406: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV406 @ ( c_HOL_Oinverse__class_Oinverse @ SV406 @ SV76 ) @ SV76 )
= ( c_HOL_Oone__class_Oone @ SV76 ) )
= $true )
| ( ( SV406
= ( c_HOL_Ozero__class_Ozero @ SV76 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2498,plain,
! [SV805: $i,SV672: $i,SV407: $i,SV77: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV77 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV672 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV805 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SV672 @ SV805 @ SV77 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2499,plain,
! [SV806: $i,SV673: $i,SV408: $i,SV78: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV78 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV408 @ SV673 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV673 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SV408 @ SV806 @ SV78 ) )
| ( SV673
= ( c_HOL_Ozero__class_Ozero @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2500,plain,
! [SV807: $i,SV676: $i,SV413: $i,SV83: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV83 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2501,plain,
! [SV808: $i,SV677: $i,SV414: $i,SV84: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV84 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2502,plain,
! [SV86: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV86 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ ( c_HOL_Ozero__class_Ozero @ SV86 ) @ SV86 )
= ( c_HOL_Ozero__class_Ozero @ SV86 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2503,plain,
! [SV678: $i,SV87: $i,SV416: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV416 @ SV87 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ SV416 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ ( c_GCD_Ogcd__class_Olcm @ SV416 @ SV678 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2504,plain,
! [SV417: $i,SV88: $i,SV679: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV88 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ SV679 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ ( c_GCD_Ogcd__class_Olcm @ SV417 @ SV679 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2505,plain,
! [SV680: $i,SV418: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV89 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV89 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV680 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV418 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV680 @ SV89 ) @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2506,plain,
! [SV681: $i,SV419: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV90 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV419 @ SV681 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV419 @ SV90 ) @ SV90 ) )
| ( SV681
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV419
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2507,plain,
! [SV91: $i,SV420: $i] :
( ( ( SV420
= ( c_HOL_Ozero__class_Ozero @ SV91 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV420 @ SV91 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2251]) ).
thf(2508,plain,
! [SV92: $i,SV421: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV421 @ SV92 ) @ SV92 )
= SV421 )
= $true )
| ( ( SV421
= ( c_HOL_Ozero__class_Ozero @ SV92 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2509,plain,
! [SV682: $i,SV422: $i,SV94: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2510,plain,
! [SV683: $i,SV423: $i,SV95: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV95 )
= $false )
| ( ( ( SV423
= ( c_HOL_Ozero__class_Ozero @ SV95 ) )
| ( SV683
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV423 @ SV95 ) @ SV423 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2511,plain,
! [SV684: $i,SV424: $i,SV96: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV96 )
= $false )
| ( ( ( SV424
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV424 @ SV96 ) @ SV424 @ SV96 )
= SV684 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2512,plain,
! [SV685: $i,SV425: $i,SV97: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV97 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
| ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV685 @ SV97 ) @ SV685 @ SV97 ) )
| ( SV685
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2513,plain,
! [SV686: $i,SV426: $i,SV98: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV98 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SV686 @ SV98 ) @ SV686 @ SV98 )
= SV426 )
| ( SV686
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2514,plain,
! [SV831: $i,SV809: $i,SV687: $i,SV427: $i,SV99: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SV809 @ SV831 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SV809 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ SV831 @ SV99 ) @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2515,plain,
! [SV832: $i,SV810: $i,SV688: $i,SV428: $i,SV100: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV428 @ SV688 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV832 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SV428 @ ( c_HOL_Otimes__class_Otimes @ SV688 @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV832 @ SV100 ) @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2516,plain,
! [SV833: $i,SV811: $i,SV689: $i,SV429: $i,SV101: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV689 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SV833 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV811 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SV833 @ SV101 ) @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2517,plain,
! [SV690: $i,SV430: $i,SV102: $i] :
( ( ( class_Divides_Osemiring__div @ SV102 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV690 @ SV102 ) @ SV690 @ SV102 )
= SV430 )
| ( SV690
= ( c_HOL_Ozero__class_Ozero @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2518,plain,
! [SV691: $i,SV431: $i,SV103: $i] :
( ( ( class_Divides_Osemiring__div @ SV103 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV691 @ SV103 ) @ SV431 @ SV103 )
= SV691 )
| ( SV431
= ( c_HOL_Ozero__class_Ozero @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2519,plain,
! [SV441: $i,SV113: $i,SV692: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV692 @ SV113 @ tc_nat ) @ SV441 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV113 @ SV441 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2520,plain,
! [SV442: $i,SV693: $i,SV114: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV114 @ SV693 @ tc_nat ) @ SV442 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV114 @ SV442 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2521,plain,
! [SV443: $i,SV694: $i,SV115: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ SV694 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV115 @ ( c_GCD_Ogcd__class_Olcm @ SV443 @ SV694 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2522,plain,
! [SV695: $i,SV444: $i,SV116: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ SV444 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV116 @ ( c_GCD_Ogcd__class_Olcm @ SV444 @ SV695 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2523,plain,
! [SV445: $i,SV117: $i,SV696: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV696 @ SV117 @ tc_nat ) @ SV445 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV117 @ SV445 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2524,plain,
! [SV446: $i,SV697: $i,SV118: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV118 @ SV697 @ tc_nat ) @ SV446 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV118 @ SV446 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2525,plain,
! [SV698: $i,SV447: $i,SV119: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ SV447 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV119 @ ( c_GCD_Ogcd__class_Olcm @ SV447 @ SV698 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2526,plain,
! [SV448: $i,SV699: $i,SV120: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ SV699 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV120 @ ( c_GCD_Ogcd__class_Olcm @ SV448 @ SV699 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2527,plain,
! [SV450: $i,SV122: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV122 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV450 @ SV122 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV122 ) @ SV450 @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2281]) ).
thf(2528,plain,
! [SV700: $i,SV451: $i,SV123: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV123 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV451 @ ( c_HOL_Otimes__class_Otimes @ SV700 @ SV451 @ SV123 ) @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2282]) ).
thf(2529,plain,
! [SV701: $i,SV452: $i,SV124: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV124 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV452 @ ( c_HOL_Otimes__class_Otimes @ SV452 @ SV701 @ SV124 ) @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2530,plain,
! [SV702: $i,SV453: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV125 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV453 @ ( c_HOL_Otimes__class_Otimes @ SV453 @ SV702 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2531,plain,
! [SV703: $i,SV454: $i,SV126: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV126 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV126 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SV454 @ SV703 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SV454 @ SV126 ) @ SV703 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2532,plain,
! [SV455: $i,SV127: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV127 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV455 @ SV127 ) @ SV127 )
= SV455 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2533,plain,
! [SV812: $i,SV704: $i,SV456: $i,SV128: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV456 @ SV704 @ SV128 ) @ SV812 @ SV128 )
= ( c_Power_Opower__class_Opower @ SV456 @ ( c_HOL_Otimes__class_Otimes @ SV704 @ SV812 @ tc_nat ) @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2534,plain,
! [SV705: $i,SV457: $i,SV129: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV129 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV457 @ SV705 @ SV129 )
= ( c_HOL_Otimes__class_Otimes @ SV705 @ SV457 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2535,plain,
! [SV706: $i,SV459: $i,SV131: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV131 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV459 @ SV706 @ SV131 )
= ( c_HOL_Otimes__class_Otimes @ SV706 @ SV459 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2536,plain,
! [SV133: $i,SV460: $i] :
( ( ( SV460
= ( c_HOL_Ozero__class_Ozero @ SV133 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV460 @ SV460 @ SV133 )
= ( c_HOL_Oone__class_Oone @ SV133 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2537,plain,
! [SV134: $i,SV461: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV461 @ SV461 @ SV134 )
= ( c_HOL_Oone__class_Oone @ SV134 ) )
= $true )
| ( ( SV461
= ( c_HOL_Ozero__class_Ozero @ SV134 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2538,plain,
! [SV462: $i,SV135: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV135 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV462 @ SV462 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
| ( SV462
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2539,plain,
! [SV465: $i,SV139: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV139 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV465 @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2540,plain,
! [SV466: $i,SV140: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV140 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV466 @ ( c_HOL_Ozero__class_Ozero @ SV140 ) @ SV140 )
= ( c_HOL_Ozero__class_Ozero @ SV140 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2541,plain,
! [SV813: $i,SV708: $i,SV468: $i,SV142: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV142 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SV708 @ SV142 ) @ SV813 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV813 @ SV142 ) @ SV708 @ SV142 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV468 @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2542,plain,
! [SV709: $i,SV469: $i,SV143: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV143 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV469 @ SV143 ) @ SV709 @ SV143 )
= ( c_Power_Opower__class_Opower @ SV469 @ SV709 @ SV143 ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV709 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2543,plain,
! [SV710: $i,SV470: $i,SV144: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV144 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ SV470 @ SV710 @ SV144 ) @ SV144 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV470 @ SV144 ) @ SV710 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2544,plain,
! [SV814: $i,SV711: $i,SV471: $i,SV145: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SV711 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SV814 @ SV711 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SV814 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2545,plain,
! [SV472: $i,SV146: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV146 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV472 @ SV146 ) @ SV146 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV472 @ SV146 ) @ SV146 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2546,plain,
! [SV712: $i,SV473: $i,SV147: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV147 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV147 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV473 @ SV712 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV473 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SV712 @ SV147 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2547,plain,
! [SV815: $i,SV713: $i,SV474: $i,SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV148 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SV815 @ SV148 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2548,plain,
! [SV816: $i,SV714: $i,SV475: $i,SV149: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV149 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV816 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SV816 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2304]) ).
thf(2549,plain,
! [SV817: $i,SV715: $i,SV476: $i,SV150: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV150 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SV715 @ SV150 ) @ SV817 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV817 @ SV150 ) @ SV715 @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2550,plain,
! [SV716: $i,SV477: $i,SV151: $i] :
( ( ( class_Divides_Osemiring__div @ SV151 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV477 @ ( c_Divides_Odiv__class_Odiv @ SV716 @ SV477 @ SV151 ) @ SV151 )
= SV716 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV477 @ SV716 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2551,plain,
! [SV717: $i,SV478: $i,SV152: $i] :
( ( ( class_Divides_Osemiring__div @ SV152 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV478 @ SV717 @ SV152 ) @ SV717 @ SV152 )
= SV478 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV478 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2552,plain,
! [SV818: $i,SV718: $i,SV479: $i,SV153: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV153 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
| ( SV818
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV818 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SV818 @ SV153 ) @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2553,plain,
! [SV819: $i,SV719: $i,SV480: $i,SV154: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV154 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
| ( SV819
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV719 @ SV154 ) @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2554,plain,
! [SV481: $i,SV155: $i,SV720: $i] :
( ( ( SV720
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV155 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV481 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV155 @ SV481 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2555,plain,
! [SV483: $i,SV721: $i,SV157: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV721 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV483 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SV483 @ SV721 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2556,plain,
! [SV722: $i,SV484: $i,SV158: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SV484 @ SV722 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SV722 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV158 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2557,plain,
! [SV723: $i,SV485: $i,SV159: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SV485 @ SV723 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SV485 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV485 @ SV159 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2558,plain,
! [SV486: $i,SV724: $i,SV160: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV724 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV486 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SV486 @ SV724 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2559,plain,
! [SV487: $i,SV725: $i,SV161: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV725 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV487 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SV487 @ SV725 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2560,plain,
! [SV494: $i,SV726: $i,SV168: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV726 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV494 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SV494 @ SV726 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2561,plain,
! [SV495: $i,SV727: $i,SV169: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV727 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV495 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SV495 @ SV727 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2562,plain,
! [SV496: $i,SV728: $i,SV170: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV728 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV496 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SV496 @ SV728 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2563,plain,
! [SV729: $i,SV497: $i,SV171: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2564,plain,
! [SV730: $i,SV498: $i,SV172: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2565,plain,
! [SV173: $i,SV499: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV499 @ SV173 ) @ SV173 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV499 @ SV173 ) @ SV173 ) )
= $true )
| ( ( SV499
= ( c_HOL_Ozero__class_Ozero @ SV173 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2321]) ).
thf(2566,plain,
! [SV731: $i,SV500: $i,SV174: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV174 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV500 @ SV731 @ SV174 ) @ SV174 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV500 @ SV174 ) @ ( c_HOL_Oabs__class_Oabs @ SV731 @ SV174 ) @ SV174 ) )
| ( SV731
= ( c_HOL_Ozero__class_Ozero @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2567,plain,
! [SV178: $i] :
( ( ( class_Power_Opower @ SV178 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV178 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV178 )
= ( c_HOL_Oone__class_Oone @ SV178 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2568,plain,
! [SV179: $i,SV502: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ SV502 @ SV502 @ SV179 )
= ( c_HOL_Oone__class_Oone @ SV179 ) )
= $true )
| ( ( SV502
= ( c_HOL_Ozero__class_Ozero @ SV179 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2569,plain,
! [SV182: $i,SV733: $i,SV504: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV733 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV504 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV182 @ SV733 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2570,plain,
! [SV820: $i,SV734: $i,SV505: $i,SV183: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV183 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV734 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV820 @ SV183 ) @ SV183 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV734 @ SV820 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2571,plain,
! [SV821: $i,SV735: $i,SV506: $i,SV184: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV184 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV735 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV821 @ SV735 @ SV184 ) @ SV184 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SV821 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2572,plain,
! [SV736: $i,SV512: $i,SV191: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV191 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV512 @ SV736 @ SV191 ) @ SV512 @ SV191 )
= ( c_HOL_Otimes__class_Otimes @ SV512 @ ( c_Power_Opower__class_Opower @ SV512 @ SV736 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2573,plain,
! [SV513: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV192 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV192 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV513 @ SV192 ) @ SV513 @ SV192 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2574,plain,
! [SV822: $i,SV737: $i,SV514: $i,SV193: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV193 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SV737 @ SV193 ) @ SV822 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SV822 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV737 @ SV822 @ SV193 ) @ SV193 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV737 @ SV514 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2575,plain,
! [SV738: $i,SV515: $i,SV194: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV194 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV515 @ SV738 @ tc_nat ) @ SV194 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV515 @ SV194 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV738 @ SV194 ) @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2334]) ).
thf(2576,plain,
! [SV739: $i,SV517: $i,SV196: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV196 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV517 @ SV739 @ SV196 ) @ SV196 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV517 @ SV196 ) @ SV739 @ SV196 ) )
| ( SV517
= ( c_HOL_Ozero__class_Ozero @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2577,plain,
! [SV743: $i,SV522: $i,SV202: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV202 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SV743 @ SV202 ) @ SV743 @ SV202 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2578,plain,
! [SV744: $i,SV523: $i,SV203: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV203 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SV744 @ SV203 ) @ SV744 @ SV203 )
= SV523 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2579,plain,
! [SV217: $i,SV535: $i] :
( ( ( SV535
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
= $true )
| ( ( ~ ( c_Int_Oiszero @ SV535 @ SV217 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2580,plain,
! [SV745: $i,SV536: $i,SV218: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV218 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV536 @ SV745 @ SV218 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV536 @ SV218 ) @ SV745 @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2581,plain,
! [SV746: $i,SV537: $i,SV219: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV219 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV537 @ SV219 ) @ SV746 @ SV219 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV537 @ SV746 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2582,plain,
! [SV747: $i,SV538: $i,SV220: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV220 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ SV747 @ SV220 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ ( c_HOL_Oabs__class_Oabs @ SV747 @ SV220 ) @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2583,plain,
! [SV748: $i,SV539: $i,SV221: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV221 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ ( c_HOL_Oabs__class_Oabs @ SV748 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ SV748 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2584,plain,
! [SV752: $i,SV544: $i,SV229: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV229 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV544 @ SV752 @ SV229 )
= ( c_HOL_Otimes__class_Otimes @ SV544 @ ( c_HOL_Oinverse__class_Oinverse @ SV752 @ SV229 ) @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2356]) ).
thf(2585,plain,
! [SV753: $i,SV545: $i,SV230: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV230 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV230 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV545 @ SV753 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SV545 @ ( c_HOL_Oinverse__class_Oinverse @ SV753 @ SV230 ) @ SV230 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2357]) ).
thf(2586,plain,
! [SV823: $i,SV754: $i,SV546: $i,SV232: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV232 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV546 @ SV754 @ SV232 ) @ SV823 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV546 @ SV823 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV754 @ SV823 @ SV232 ) @ SV232 ) )
| ( SV754
= ( c_HOL_Ozero__class_Ozero @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2587,plain,
! [SV834: $i,SV824: $i,SV755: $i,SV547: $i,SV233: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2588,plain,
! [SV236: $i,SV550: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV550 @ SV236 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV550 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV236 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2362]) ).
thf(2589,plain,
! [SV553: $i,SV239: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV239 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV239 )
= ( c_HOL_Oinverse__class_Odivide @ SV553 @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2590,plain,
! [SV825: $i,SV756: $i,SV555: $i,SV241: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV241 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV825 @ tc_nat ) @ SV241 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV555 @ SV756 @ SV241 ) @ SV825 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2591,plain,
! [SV757: $i,SV556: $i,SV242: $i] :
( ( ( class_RealVector_Oreal__normed__div__algebra @ SV242 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV556 @ SV757 @ SV242 ) @ SV242 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV556 @ SV242 ) @ ( c_HOL_Osgn__class_Osgn @ SV757 @ SV242 ) @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2365]) ).
thf(2592,plain,
! [SV758: $i,SV557: $i,SV243: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV243 )
= $false )
| ( ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ SV557 @ SV758 @ SV243 ) @ SV243 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ SV557 @ SV243 ) @ ( c_HOL_Osgn__class_Osgn @ SV758 @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2593,plain,
! [SV558: $i,SV244: $i,SV759: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV759 @ SV244 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV244 @ SV759 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV244 @ SV558 @ tc_nat ) @ SV759 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2594,plain,
! [SV245: $i,SV559: $i,SV760: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV760 @ SV559 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV559 @ SV760 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV245 @ SV559 @ tc_nat ) @ SV760 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2595,plain,
! [SV560: $i,SV246: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV246 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV560 @ SV246 ) @ SV560 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2596,plain,
! [SV247: $i,SV561: $i,SV761: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV561 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV761 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2597,plain,
! [SV248: $i,SV762: $i,SV562: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SV762 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV762 @ SV562 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV762 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2598,plain,
! [SV251: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV251 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV251 ) @ SV251 )
= ( c_HOL_Oone__class_Oone @ SV251 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2599,plain,
! [SV763: $i,SV575: $i,SV277: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SV763 @ SV277 )
!= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV763
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2600,plain,
! [SV764: $i,SV578: $i,SV281: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ ( c_HOL_Otimes__class_Otimes @ SV578 @ SV764 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ SV578 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2601,plain,
! [SV765: $i,SV579: $i,SV282: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV282 @ SV579 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV282 @ SV765 @ tc_nat ) )
= $false )
| ( ( ( SV282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV579 = SV765 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2602,plain,
! [SV766: $i,SV580: $i,SV283: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV283 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
| ( SV580 = SV766 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2603,plain,
! [SV285: $i,SV582: $i] :
( ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV285
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Olcm @ SV285 @ SV582 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2604,plain,
! [SV286: $i,SV583: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV583 @ SV286 )
!= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( SV583
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2605,plain,
! [SV767: $i,SV585: $i,SV288: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV585 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV767 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV585 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2606,plain,
! [SV586: $i,SV290: $i] :
( ( ( SV290
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV586
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV290
= ( c_HOL_Otimes__class_Otimes @ SV290 @ SV586 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2607,plain,
! [SV292: $i,SV588: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Fact_Ofact__class_Ofact @ SV588 @ tc_nat ) @ SV292 )
= ( c_HOL_Ozero__class_Ozero @ SV292 ) )
= $false )
| ( ( class_Nat_Osemiring__char__0 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2608,plain,
! [SV294: $i,SV590: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV590 @ SV294 )
!= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $true )
| ( ( SV590
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2609,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2404]) ).
thf(2610,plain,
! [SV769: $i,SV593: $i,SV298: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ ( c_HOL_Otimes__class_Otimes @ SV593 @ SV769 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV298 @ SV769 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2611,plain,
! [SV770: $i,SV595: $i,SV300: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV300 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
| ( SV595 = SV770 )
| ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2612,plain,
! [SV771: $i,SV596: $i,SV301: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV301 @ SV596 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV301 @ SV771 @ tc_nat ) )
= $false )
| ( ( ( SV596 = SV771 )
| ( SV301
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2613,plain,
! [SV772: $i,SV597: $i,SV302: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV302 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SV772 @ SV302 )
!= ( c_HOL_Oone__class_Oone @ SV302 ) )
| ( SV772
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SV597 = SV772 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2614,plain,
! [SV773: $i,SV598: $i,SV303: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV303 @ SV598 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Otimes__class_Otimes @ SV303 @ SV773 @ tc_nat ) @ SV598 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV773 @ SV598 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2615,plain,
! [SV304: $i,SV599: $i] :
( ( ( ( c_HOL_Osgn__class_Osgn @ SV599 @ SV304 )
!= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
= $true )
| ( ( SV599
= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2616,plain,
! [SV826: $i,SV774: $i,SV602: $i,SV307: $i] :
( ( ( SV307
!= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( SV774
!= ( c_HOL_Otimes__class_Otimes @ SV826 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV826 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2617,plain,
! [SV775: $i,SV603: $i,SV308: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV308 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV603 @ SV775 @ SV308 )
!= ( c_HOL_Oone__class_Oone @ SV308 ) )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV603 @ SV308 )
= SV775 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2618,plain,
! [SV776: $i,SV604: $i,SV309: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SV604 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SV776 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SV776 @ SV604 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2619,plain,
! [SV777: $i,SV606: $i,SV311: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV311 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV606 @ SV311 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV777 @ SV311 ) )
| ( SV606 = SV777 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2620,plain,
! [SV835: $i,SV827: $i,SV778: $i,SV607: $i,SV312: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV312 )
| ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
| ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(2621,plain,
! [SV779: $i,SV609: $i,SV314: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV314 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV609 @ SV314 )
!= ( c_HOL_Oabs__class_Oabs @ SV779 @ SV314 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV609 @ SV779 @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2622,plain,
! [SV780: $i,SV610: $i,SV315: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2623,plain,
! [SV611: $i,SV316: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV316 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2624,plain,
! [SV781: $i,SV615: $i,SV321: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SV781 @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2625,plain,
! [SV782: $i,SV616: $i,SV322: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2626,plain,
! [SV836: $i,SV828: $i,SV783: $i,SV617: $i,SV323: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
| ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2627,plain,
! [SV324: $i,SV618: $i] :
( ( ( SV618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV324
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV324 @ SV618 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2431]) ).
thf(2628,plain,
! [SV784: $i,SV621: $i,SV328: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV621 @ SV784 @ SV328 )
!= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
| ( SV621
= ( c_HOL_Ozero__class_Ozero @ SV328 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2629,plain,
! [SV785: $i,SV623: $i,SV330: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SV785 @ SV330 )
!= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV785
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2630,plain,
! [SV786: $i,SV624: $i,SV331: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV331 @ SV624 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV786 @ SV624 @ tc_nat ) )
= $false )
| ( ( ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV331 = SV786 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2631,plain,
! [SV625: $i,SV332: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV332 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV332 )
| ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2632,plain,
! [SV787: $i,SV626: $i,SV333: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2633,plain,
! [SV788: $i,SV628: $i,SV335: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SV628 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SV788 @ SV628 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SV788 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2634,plain,
! [SV336: $i,SV629: $i] :
( ( ( ( c_HOL_Osgn__class_Osgn @ SV629 @ SV336 )
!= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
= $true )
| ( ( SV629
= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2635,plain,
! [SV630: $i,SV337: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV337 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
| ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2636,plain,
! [SV789: $i,SV631: $i,SV339: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV2 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SV631 @ SV2 ) @ SV789 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SV789 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SV631 @ SV789 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2637,plain,
! [SV3: $i,SV340: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV3 @ tc_nat )
= $false )
| ( ( SV340 = SV3 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV3 @ SV340 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2638,plain,
! [SV4: $i,SV341: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV341 @ SV4 @ tc_nat )
= $false )
| ( ( SV341 = SV4 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV4 @ SV341 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2639,plain,
! [SV5: $i,SV342: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV342 @ SV5 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV5 @ SV342 @ tc_nat )
= $false )
| ( ( SV5 = SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2640,plain,
! [SV343: $i,SV6: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV6 @ SV343 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV343 @ SV6 @ tc_nat )
= $false )
| ( ( SV6 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2641,plain,
! [SV7: $i,SV344: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV344 @ SV7 @ tc_nat )
= $false )
| ( ( SV344 = SV7 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV7 @ SV344 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2642,plain,
! [SV345: $i,SV8: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV8 @ SV345 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV345 @ SV8 @ tc_nat )
= $false )
| ( ( SV8 = SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2643,plain,
! [SV346: $i,SV9: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV9 @ SV346 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV346 @ SV9 @ tc_nat )
= $false )
| ( ( SV9 = SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2644,plain,
! [SV19: $i,SV356: $i,SV640: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV640 @ SV356 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV640 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV356 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2645,plain,
! [SV20: $i,SV357: $i,SV641: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2646,plain,
! [SV790: $i,SV642: $i,SV359: $i,SV23: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2462]) ).
thf(2647,plain,
! [SV829: $i,SV791: $i,SV646: $i,SV364: $i,SV28: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV28 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SV791 @ SV829 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SV791 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SV829 @ SV28 ) @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2466]) ).
thf(2648,plain,
! [SV830: $i,SV792: $i,SV648: $i,SV366: $i,SV30: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV30 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2649,plain,
! [SV369: $i,SV33: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV33 )
| ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2650,plain,
! [SV370: $i,SV34: $i] :
( ( ( class_Power_Opower @ SV34 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV370 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
| ( SV370
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2470]) ).
thf(2651,plain,
! [SV36: $i,SV650: $i,SV372: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV372 @ SV650 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SV650 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SV372 @ tc_nat ) @ SV650 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2652,plain,
! [SV39: $i,SV651: $i,SV375: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV375 @ SV651 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SV651 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SV375 @ tc_nat ) @ SV651 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2653,plain,
! [SV42: $i,SV652: $i,SV378: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV378 @ SV652 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SV652 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SV378 @ tc_nat ) @ SV652 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2654,plain,
! [SV45: $i,SV653: $i,SV381: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV381 @ SV653 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SV653 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SV381 @ tc_nat ) @ SV653 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2655,plain,
! [SV46: $i,SV654: $i,SV382: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV382 @ SV654 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SV654 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SV382 @ tc_nat ) @ SV654 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2656,plain,
! [SV383: $i,SV655: $i,SV47: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SV655 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV655 @ SV47 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SV383 @ tc_nat ) @ SV655 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2657,plain,
! [SV48: $i,SV656: $i,SV384: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV384 @ SV656 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV384 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SV384 @ tc_nat ) @ SV656 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2658,plain,
! [SV793: $i,SV657: $i,SV385: $i,SV49: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SV793 @ SV49 ) @ SV49 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SV793 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2479]) ).
thf(2659,plain,
! [SV794: $i,SV658: $i,SV386: $i,SV50: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV794 @ SV50 ) @ SV50 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SV658 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2660,plain,
! [SV795: $i,SV659: $i,SV387: $i,SV51: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SV659 @ SV51 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SV795 @ SV51 ) @ SV659 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2661,plain,
! [SV796: $i,SV660: $i,SV388: $i,SV52: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SV660 @ SV52 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV796 @ SV388 @ SV52 ) @ SV660 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2662,plain,
! [SV661: $i,SV391: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV59 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV391 @ SV661 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SV661 @ SV391 @ SV59 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2663,plain,
! [SV797: $i,SV662: $i,SV393: $i,SV63: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV63 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV662 @ SV63 ) @ SV797 @ SV63 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV393 @ SV797 @ SV63 ) @ ( c_Power_Opower__class_Opower @ SV662 @ SV797 @ SV63 ) @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2664,plain,
! [SV798: $i,SV663: $i,SV394: $i,SV64: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__mult @ SV64 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ SV394 @ SV663 @ SV64 ) @ SV798 @ SV64 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ SV394 @ SV798 @ SV64 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV798 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2665,plain,
! [SV664: $i,SV395: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV65 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV395 @ SV664 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV395 @ SV65 ) @ SV664 @ SV65 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2666,plain,
! [SV799: $i,SV665: $i,SV396: $i,SV66: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV66 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV396 @ SV665 @ SV66 ) @ SV799 @ SV66 )
= ( c_HOL_Otimes__class_Otimes @ SV396 @ ( c_HOL_Otimes__class_Otimes @ SV665 @ SV799 @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2667,plain,
! [SV800: $i,SV666: $i,SV397: $i,SV67: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV67 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV666 @ SV67 ) @ SV800 @ SV67 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV800 @ SV67 ) @ SV666 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2668,plain,
! [SV801: $i,SV667: $i,SV398: $i,SV68: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV68 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV398 @ SV667 @ SV68 ) @ SV801 @ SV68 )
= ( c_HOL_Otimes__class_Otimes @ SV398 @ ( c_HOL_Otimes__class_Otimes @ SV667 @ SV801 @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2669,plain,
! [SV802: $i,SV668: $i,SV399: $i,SV69: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV69 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV399 @ ( c_HOL_Otimes__class_Otimes @ SV668 @ SV802 @ SV69 ) @ SV69 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV399 @ SV668 @ SV69 ) @ SV802 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2670,plain,
! [SV803: $i,SV669: $i,SV400: $i,SV70: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV70 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV400 @ ( c_HOL_Otimes__class_Otimes @ SV669 @ SV803 @ SV70 ) @ SV70 )
= ( c_HOL_Otimes__class_Otimes @ SV669 @ ( c_HOL_Otimes__class_Otimes @ SV400 @ SV803 @ SV70 ) @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2671,plain,
! [SV804: $i,SV671: $i,SV402: $i,SV72: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV402 @ ( c_HOL_Otimes__class_Otimes @ SV671 @ SV804 @ SV72 ) @ SV72 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV402 @ SV671 @ SV72 ) @ SV804 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2672,plain,
! [SV805: $i,SV672: $i,SV407: $i,SV77: $i] :
( ( ( class_Divides_Osemiring__div @ SV77 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV672 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV805 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SV672 @ SV805 @ SV77 ) )
| ( SV407
= ( c_HOL_Ozero__class_Ozero @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2673,plain,
! [SV806: $i,SV673: $i,SV408: $i,SV78: $i] :
( ( ( class_Divides_Osemiring__div @ SV78 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV408 @ SV673 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV673 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SV408 @ SV806 @ SV78 ) )
| ( SV673
= ( c_HOL_Ozero__class_Ozero @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2674,plain,
! [SV807: $i,SV676: $i,SV413: $i,SV83: $i] :
( ( ( class_Divides_Osemiring__div @ SV83 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2675,plain,
! [SV808: $i,SV677: $i,SV414: $i,SV84: $i] :
( ( ( class_Divides_Osemiring__div @ SV84 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2676,plain,
! [SV678: $i,SV416: $i,SV87: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ SV416 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV416 @ SV87 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV87 @ ( c_GCD_Ogcd__class_Olcm @ SV416 @ SV678 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2677,plain,
! [SV417: $i,SV679: $i,SV88: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ SV679 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV679 @ SV88 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV88 @ ( c_GCD_Ogcd__class_Olcm @ SV417 @ SV679 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2678,plain,
! [SV680: $i,SV418: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV680 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV418 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV680 @ SV89 ) @ SV89 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2679,plain,
! [SV90: $i,SV681: $i,SV419: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV419 @ SV681 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV419 @ SV90 ) @ SV90 ) )
= $true )
| ( ( ( SV681
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
| ( SV419
= ( c_HOL_Ozero__class_Ozero @ SV90 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2506]) ).
thf(2680,plain,
! [SV420: $i,SV91: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV91 ) @ SV420 @ SV91 )
= $false )
| ( ( SV420
= ( c_HOL_Ozero__class_Ozero @ SV91 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2681,plain,
! [SV422: $i,SV682: $i,SV94: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2682,plain,
! [SV683: $i,SV95: $i,SV423: $i] :
( ( ( SV423
= ( c_HOL_Ozero__class_Ozero @ SV95 ) )
= $true )
| ( ( SV683
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV683 @ SV423 @ SV95 ) @ SV423 @ SV95 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2683,plain,
! [SV684: $i,SV96: $i,SV424: $i] :
( ( ( SV424
= ( c_HOL_Ozero__class_Ozero @ SV96 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV684 @ SV424 @ SV96 ) @ SV424 @ SV96 )
= SV684 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2684,plain,
! [SV685: $i,SV425: $i,SV97: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV97 ) )
= $true )
| ( ( ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV685 @ SV97 ) @ SV685 @ SV97 ) )
| ( SV685
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2685,plain,
! [SV686: $i,SV426: $i,SV98: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV98 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SV686 @ SV98 ) @ SV686 @ SV98 )
= SV426 )
| ( SV686
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2686,plain,
! [SV831: $i,SV809: $i,SV687: $i,SV427: $i,SV99: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SV809 @ SV831 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SV809 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ SV831 @ SV99 ) @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2687,plain,
! [SV832: $i,SV810: $i,SV688: $i,SV428: $i,SV100: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV428 @ SV688 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV832 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SV428 @ ( c_HOL_Otimes__class_Otimes @ SV688 @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV832 @ SV100 ) @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2688,plain,
! [SV833: $i,SV811: $i,SV689: $i,SV429: $i,SV101: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV689 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SV833 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV811 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SV833 @ SV101 ) @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2689,plain,
! [SV102: $i,SV690: $i,SV430: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV430 @ SV690 @ SV102 ) @ SV690 @ SV102 )
= SV430 )
= $true )
| ( ( SV690
= ( c_HOL_Ozero__class_Ozero @ SV102 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2690,plain,
! [SV103: $i,SV691: $i,SV431: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV431 @ SV691 @ SV103 ) @ SV431 @ SV103 )
= SV691 )
= $true )
| ( ( SV431
= ( c_HOL_Ozero__class_Ozero @ SV103 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2691,plain,
! [SV450: $i,SV122: $i] :
( ( ( class_Int_Onumber__ring @ SV122 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV450 @ SV122 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV122 ) @ SV450 @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2692,plain,
! [SV703: $i,SV454: $i,SV126: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV126 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SV454 @ SV703 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SV454 @ SV126 ) @ SV703 @ SV126 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2693,plain,
! [SV455: $i,SV127: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV127 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV455 @ SV127 ) @ SV127 )
= SV455 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2694,plain,
! [SV812: $i,SV704: $i,SV456: $i,SV128: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV128 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV456 @ SV704 @ SV128 ) @ SV812 @ SV128 )
= ( c_Power_Opower__class_Opower @ SV456 @ ( c_HOL_Otimes__class_Otimes @ SV704 @ SV812 @ tc_nat ) @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2533]) ).
thf(2695,plain,
! [SV462: $i,SV135: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV135 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV462 @ SV462 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
| ( SV462
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2696,plain,
! [SV465: $i,SV139: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV139 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV465 @ ( c_HOL_Ozero__class_Ozero @ SV139 ) @ SV139 )
= ( c_HOL_Ozero__class_Ozero @ SV139 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2697,plain,
! [SV466: $i,SV140: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV140 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV466 @ ( c_HOL_Ozero__class_Ozero @ SV140 ) @ SV140 )
= ( c_HOL_Ozero__class_Ozero @ SV140 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2698,plain,
! [SV813: $i,SV708: $i,SV468: $i,SV142: $i] :
( ( ( class_Divides_Osemiring__div @ SV142 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SV708 @ SV142 ) @ SV813 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV813 @ SV142 ) @ SV708 @ SV142 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV468 @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2699,plain,
! [SV709: $i,SV143: $i,SV469: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV469 @ SV143 ) @ SV709 @ SV143 )
= ( c_Power_Opower__class_Opower @ SV469 @ SV709 @ SV143 ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV709 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2542]) ).
thf(2700,plain,
! [SV814: $i,SV711: $i,SV471: $i,SV145: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SV711 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SV814 @ SV711 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SV814 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2701,plain,
! [SV472: $i,SV146: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV146 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ SV472 @ SV146 ) @ SV146 )
= ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ SV472 @ SV146 ) @ SV146 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2702,plain,
! [SV712: $i,SV473: $i,SV147: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV147 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV473 @ SV712 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV473 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SV712 @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2703,plain,
! [SV815: $i,SV713: $i,SV474: $i,SV148: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV148 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SV815 @ SV148 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2704,plain,
! [SV816: $i,SV714: $i,SV475: $i,SV149: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV816 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SV816 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2705,plain,
! [SV817: $i,SV715: $i,SV476: $i,SV150: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV150 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SV715 @ SV150 ) @ SV817 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV817 @ SV150 ) @ SV715 @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2706,plain,
! [SV151: $i,SV716: $i,SV477: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV477 @ ( c_Divides_Odiv__class_Odiv @ SV716 @ SV477 @ SV151 ) @ SV151 )
= SV716 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV477 @ SV716 @ SV151 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2707,plain,
! [SV152: $i,SV717: $i,SV478: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV478 @ SV717 @ SV152 ) @ SV717 @ SV152 )
= SV478 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV478 @ SV152 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2708,plain,
! [SV818: $i,SV718: $i,SV479: $i,SV153: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV153 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
| ( SV818
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV818 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SV818 @ SV153 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2709,plain,
! [SV819: $i,SV719: $i,SV480: $i,SV154: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV154 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
| ( SV819
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV719 @ SV154 ) @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2710,plain,
! [SV481: $i,SV155: $i,SV720: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV155 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV720 @ SV481 @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV720
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV155 @ SV481 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2711,plain,
! [SV483: $i,SV721: $i,SV157: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV721 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV483 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SV483 @ SV721 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2712,plain,
! [SV484: $i,SV722: $i,SV158: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SV722 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV158 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SV484 @ SV722 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2713,plain,
! [SV723: $i,SV485: $i,SV159: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SV485 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV485 @ SV159 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SV485 @ SV723 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2714,plain,
! [SV486: $i,SV724: $i,SV160: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV724 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV486 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SV486 @ SV724 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2715,plain,
! [SV487: $i,SV725: $i,SV161: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV725 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV487 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SV487 @ SV725 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2716,plain,
! [SV494: $i,SV726: $i,SV168: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV726 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV494 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SV494 @ SV726 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2717,plain,
! [SV495: $i,SV727: $i,SV169: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV727 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV495 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SV495 @ SV727 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2718,plain,
! [SV496: $i,SV728: $i,SV170: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV728 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV496 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SV496 @ SV728 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2719,plain,
! [SV497: $i,SV729: $i,SV171: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2720,plain,
! [SV498: $i,SV172: $i,SV730: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2721,plain,
! [SV174: $i,SV731: $i,SV500: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV500 @ SV731 @ SV174 ) @ SV174 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV500 @ SV174 ) @ ( c_HOL_Oabs__class_Oabs @ SV731 @ SV174 ) @ SV174 ) )
= $true )
| ( ( SV731
= ( c_HOL_Ozero__class_Ozero @ SV174 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2722,plain,
! [SV820: $i,SV734: $i,SV505: $i,SV183: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV183 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV734 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV820 @ SV183 ) @ SV183 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV734 @ SV820 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2723,plain,
! [SV821: $i,SV735: $i,SV506: $i,SV184: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV184 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV735 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV821 @ SV735 @ SV184 ) @ SV184 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SV821 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2724,plain,
! [SV513: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV192 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV192 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV513 @ SV192 ) @ SV513 @ SV192 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2725,plain,
! [SV822: $i,SV737: $i,SV514: $i,SV193: $i] :
( ( ( class_Divides_Osemiring__div @ SV193 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SV737 @ SV193 ) @ SV822 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SV822 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV737 @ SV822 @ SV193 ) @ SV193 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV737 @ SV514 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2574]) ).
thf(2726,plain,
! [SV196: $i,SV739: $i,SV517: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV517 @ SV739 @ SV196 ) @ SV196 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV517 @ SV196 ) @ SV739 @ SV196 ) )
= $true )
| ( ( SV517
= ( c_HOL_Ozero__class_Ozero @ SV196 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2727,plain,
! [SV743: $i,SV522: $i,SV202: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 ) )
= $true )
| ( ( ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SV743 @ SV202 ) @ SV743 @ SV202 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2728,plain,
! [SV744: $i,SV523: $i,SV203: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SV744 @ SV203 ) @ SV744 @ SV203 )
= SV523 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2578]) ).
thf(2729,plain,
! [SV217: $i,SV535: $i] :
( ( ( c_Int_Oiszero @ SV535 @ SV217 )
= $false )
| ( ( SV535
= ( c_HOL_Ozero__class_Ozero @ SV217 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2730,plain,
! [SV218: $i,SV745: $i,SV536: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV536 @ SV745 @ SV218 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV536 @ SV218 ) @ SV745 @ SV218 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2731,plain,
! [SV746: $i,SV219: $i,SV537: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV537 @ SV219 ) @ SV746 @ SV219 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV537 @ SV746 @ SV219 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2732,plain,
! [SV220: $i,SV747: $i,SV538: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ SV747 @ SV220 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ ( c_HOL_Oabs__class_Oabs @ SV747 @ SV220 ) @ SV220 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2733,plain,
! [SV221: $i,SV748: $i,SV539: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ ( c_HOL_Oabs__class_Oabs @ SV748 @ SV221 ) @ SV221 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ SV748 @ SV221 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2734,plain,
! [SV753: $i,SV545: $i,SV230: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV230 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV545 @ SV753 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SV545 @ ( c_HOL_Oinverse__class_Oinverse @ SV753 @ SV230 ) @ SV230 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2735,plain,
! [SV823: $i,SV754: $i,SV546: $i,SV232: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV232 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV546 @ SV754 @ SV232 ) @ SV823 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV546 @ SV823 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV754 @ SV823 @ SV232 ) @ SV232 ) )
| ( SV754
= ( c_HOL_Ozero__class_Ozero @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2586]) ).
thf(2736,plain,
! [SV834: $i,SV824: $i,SV755: $i,SV547: $i,SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2737,plain,
! [SV553: $i,SV239: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV239 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV239 )
= ( c_HOL_Oinverse__class_Odivide @ SV553 @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2589]) ).
thf(2738,plain,
! [SV825: $i,SV756: $i,SV555: $i,SV241: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV241 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV555 @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV825 @ tc_nat ) @ SV241 )
= ( c_Power_Opower__class_Opower @ ( c_Power_Opower__class_Opower @ SV555 @ SV756 @ SV241 ) @ SV825 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2739,plain,
! [SV558: $i,SV759: $i,SV244: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV244 @ SV759 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV759 @ SV244 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV244 @ SV558 @ tc_nat ) @ SV759 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2740,plain,
! [SV245: $i,SV760: $i,SV559: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV559 @ SV760 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV760 @ SV559 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV245 @ SV559 @ tc_nat ) @ SV760 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2741,plain,
! [SV560: $i,SV246: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV246 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV246 ) @ SV560 @ SV246 ) @ SV560 @ SV246 )
= ( c_HOL_Ozero__class_Ozero @ SV246 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2742,plain,
! [SV247: $i,SV561: $i,SV761: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV561 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV761 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2743,plain,
! [SV248: $i,SV562: $i,SV762: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV762 @ SV562 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV762 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SV762 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2744,plain,
! [SV277: $i,SV763: $i,SV575: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SV763 @ SV277 )
!= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
= $true )
| ( ( ( SV763
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2745,plain,
! [SV765: $i,SV579: $i,SV282: $i] :
( ( ( SV282
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV579 = SV765 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV282 @ SV579 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV282 @ SV765 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2746,plain,
! [SV766: $i,SV580: $i,SV283: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV283 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
| ( SV580 = SV766 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2602]) ).
thf(2747,plain,
! [SV286: $i,SV583: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV583 @ SV286 )
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $false )
| ( ( SV583
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2748,plain,
! [SV585: $i,SV767: $i,SV288: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV767 @ tc_nat )
!= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV585 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV585 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2749,plain,
! [SV294: $i,SV590: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV590 @ SV294 )
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $false )
| ( ( SV590
= ( c_HOL_Ozero__class_Ozero @ SV294 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2750,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV296 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2751,plain,
! [SV770: $i,SV300: $i,SV595: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
= $true )
| ( ( ( SV595 = SV770 )
| ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2752,plain,
! [SV301: $i,SV771: $i,SV596: $i] :
( ( ( SV596 = SV771 )
= $true )
| ( ( SV301
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV301 @ SV596 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV301 @ SV771 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2753,plain,
! [SV302: $i,SV772: $i,SV597: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SV772 @ SV302 )
!= ( c_HOL_Oone__class_Oone @ SV302 ) )
= $true )
| ( ( ( SV772
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SV597 = SV772 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2754,plain,
! [SV304: $i,SV599: $i] :
( ( ( ( c_HOL_Osgn__class_Osgn @ SV599 @ SV304 )
= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
= $false )
| ( ( SV599
= ( c_HOL_Ozero__class_Ozero @ SV304 ) )
= $true )
| ( ( class_RealVector_Oreal__normed__vector @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2755,plain,
! [SV826: $i,SV774: $i,SV602: $i,SV307: $i] :
( ( ( SV307
= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( ( SV774
!= ( c_HOL_Otimes__class_Otimes @ SV826 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV826 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2756,plain,
! [SV308: $i,SV775: $i,SV603: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV603 @ SV775 @ SV308 )
!= ( c_HOL_Oone__class_Oone @ SV308 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV603 @ SV308 )
= SV775 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(2757,plain,
! [SV604: $i,SV776: $i,SV309: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SV776 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SV776 @ SV604 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SV604 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2758,plain,
! [SV777: $i,SV311: $i,SV606: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV606 @ SV311 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV777 @ SV311 ) )
= $true )
| ( ( SV606 = SV777 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2619]) ).
thf(2759,plain,
! [SV835: $i,SV827: $i,SV778: $i,SV607: $i,SV312: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV312 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
| ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2760,plain,
! [SV779: $i,SV314: $i,SV609: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV609 @ SV314 )
!= ( c_HOL_Oabs__class_Oabs @ SV779 @ SV314 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV609 @ SV779 @ SV314 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(2761,plain,
! [SV315: $i,SV610: $i,SV780: $i] :
( ( ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2762,plain,
! [SV611: $i,SV316: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
| ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2763,plain,
! [SV321: $i,SV781: $i,SV615: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SV781 @ SV321 )
!= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2764,plain,
! [SV322: $i,SV616: $i,SV782: $i] :
( ( ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2625]) ).
thf(2765,plain,
! [SV836: $i,SV828: $i,SV783: $i,SV617: $i,SV323: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV323 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
| ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2766,plain,
! [SV328: $i,SV784: $i,SV621: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV621 @ SV784 @ SV328 )
!= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
= $true )
| ( ( SV621
= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2767,plain,
! [SV330: $i,SV785: $i,SV623: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SV785 @ SV330 )
!= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $true )
| ( ( ( SV785
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2768,plain,
! [SV786: $i,SV331: $i,SV624: $i] :
( ( ( SV624
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV331 = SV786 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV331 @ SV624 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV786 @ SV624 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2769,plain,
! [SV625: $i,SV332: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV332 )
| ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2770,plain,
! [SV333: $i,SV787: $i,SV626: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2771,plain,
! [SV628: $i,SV788: $i,SV335: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SV788 @ SV628 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SV788 @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SV628 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(2772,plain,
! [SV336: $i,SV629: $i] :
( ( ( ( c_HOL_Osgn__class_Osgn @ SV629 @ SV336 )
= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
= $false )
| ( ( SV629
= ( c_HOL_Ozero__class_Ozero @ SV336 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2773,plain,
! [SV630: $i,SV337: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
| ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2774,plain,
! [SV789: $i,SV631: $i,SV339: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV2 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SV631 @ SV2 ) @ SV789 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SV789 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SV631 @ SV789 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2775,plain,
! [SV356: $i,SV640: $i,SV19: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV640 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV640 @ SV356 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV19 @ SV356 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2776,plain,
! [SV20: $i,SV357: $i,SV641: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2777,plain,
! [SV790: $i,SV23: $i,SV642: $i,SV359: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2778,plain,
! [SV829: $i,SV791: $i,SV646: $i,SV364: $i,SV28: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV28 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SV791 @ SV829 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SV791 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SV829 @ SV28 ) @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2779,plain,
! [SV830: $i,SV792: $i,SV648: $i,SV366: $i,SV30: $i] :
( ( ( class_Divides_Osemiring__div @ SV30 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2780,plain,
! [SV369: $i,SV33: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV33 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(2781,plain,
! [SV370: $i,SV34: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV370 @ SV34 )
= ( c_HOL_Ozero__class_Ozero @ SV34 ) )
= $true )
| ( ( SV370
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV34 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2782,plain,
! [SV372: $i,SV650: $i,SV36: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV36 @ SV650 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV372 @ SV650 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV36 @ SV372 @ tc_nat ) @ SV650 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2783,plain,
! [SV375: $i,SV651: $i,SV39: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV39 @ SV651 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV375 @ SV651 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV39 @ SV375 @ tc_nat ) @ SV651 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2784,plain,
! [SV378: $i,SV652: $i,SV42: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV42 @ SV652 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV378 @ SV652 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV42 @ SV378 @ tc_nat ) @ SV652 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2653]) ).
thf(2785,plain,
! [SV381: $i,SV653: $i,SV45: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV45 @ SV653 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV381 @ SV653 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV45 @ SV381 @ tc_nat ) @ SV653 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2786,plain,
! [SV382: $i,SV654: $i,SV46: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV46 @ SV654 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV382 @ SV654 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV46 @ SV382 @ tc_nat ) @ SV654 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2787,plain,
! [SV383: $i,SV47: $i,SV655: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV655 @ SV47 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV47 @ SV655 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV47 @ SV383 @ tc_nat ) @ SV655 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2788,plain,
! [SV48: $i,SV384: $i,SV656: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV656 @ SV384 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV384 @ SV656 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Olcm @ SV48 @ SV384 @ tc_nat ) @ SV656 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2789,plain,
! [SV49: $i,SV793: $i,SV657: $i,SV385: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SV793 @ SV49 ) @ SV49 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SV793 @ SV49 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2790,plain,
! [SV50: $i,SV794: $i,SV658: $i,SV386: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV794 @ SV50 ) @ SV50 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SV658 @ SV50 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2791,plain,
! [SV795: $i,SV51: $i,SV659: $i,SV387: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SV659 @ SV51 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SV795 @ SV51 ) @ SV659 @ SV51 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2792,plain,
! [SV796: $i,SV52: $i,SV660: $i,SV388: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SV660 @ SV52 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV796 @ SV388 @ SV52 ) @ SV660 @ SV52 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2661]) ).
thf(2793,plain,
! [SV661: $i,SV391: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV59 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV391 @ SV661 @ SV59 ) @ SV59 )
= ( c_HOL_Oinverse__class_Odivide @ SV661 @ SV391 @ SV59 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2794,plain,
! [SV664: $i,SV395: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV65 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV395 @ SV664 @ SV65 ) @ SV65 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV395 @ SV65 ) @ SV664 @ SV65 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2795,plain,
! [SV805: $i,SV77: $i,SV672: $i,SV407: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV672 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV407 @ SV805 @ SV77 ) @ SV77 )
= ( c_Divides_Odiv__class_Odiv @ SV672 @ SV805 @ SV77 ) )
= $true )
| ( ( SV407
= ( c_HOL_Ozero__class_Ozero @ SV77 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(2796,plain,
! [SV806: $i,SV78: $i,SV673: $i,SV408: $i] :
( ( ( ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV408 @ SV673 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV806 @ SV673 @ SV78 ) @ SV78 )
= ( c_Divides_Odiv__class_Odiv @ SV408 @ SV806 @ SV78 ) )
= $true )
| ( ( SV673
= ( c_HOL_Ozero__class_Ozero @ SV78 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2673]) ).
thf(2797,plain,
! [SV807: $i,SV83: $i,SV676: $i,SV413: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2798,plain,
! [SV808: $i,SV84: $i,SV677: $i,SV414: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(2799,plain,
! [SV680: $i,SV418: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV89 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV418 @ SV680 @ SV89 ) @ SV89 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV418 @ SV89 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV680 @ SV89 ) @ SV89 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2800,plain,
! [SV419: $i,SV90: $i,SV681: $i] :
( ( ( SV681
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
= $true )
| ( ( SV419
= ( c_HOL_Ozero__class_Ozero @ SV90 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ SV419 @ SV681 @ SV90 ) @ SV90 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV90 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV419 @ SV90 ) @ SV90 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2801,plain,
! [SV422: $i,SV94: $i,SV682: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(2802,plain,
! [SV685: $i,SV425: $i,SV97: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
= $false )
| ( ( ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV685 @ SV97 ) @ SV685 @ SV97 ) )
| ( SV685
= ( c_HOL_Ozero__class_Ozero @ SV97 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2803,plain,
! [SV686: $i,SV426: $i,SV98: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SV686 @ SV98 ) @ SV686 @ SV98 )
= SV426 )
| ( SV686
= ( c_HOL_Ozero__class_Ozero @ SV98 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2804,plain,
! [SV831: $i,SV809: $i,SV687: $i,SV427: $i,SV99: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV99 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ ( c_HOL_Otimes__class_Otimes @ SV809 @ SV831 @ SV99 ) @ SV99 )
= ( c_HOL_Otimes__class_Otimes @ SV809 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV427 @ SV687 @ SV99 ) @ SV831 @ SV99 ) @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2805,plain,
! [SV832: $i,SV810: $i,SV688: $i,SV428: $i,SV100: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV100 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV428 @ SV688 @ SV100 ) @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV832 @ SV100 ) @ SV100 )
= ( c_HOL_Otimes__class_Otimes @ SV428 @ ( c_HOL_Otimes__class_Otimes @ SV688 @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV832 @ SV100 ) @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2806,plain,
! [SV833: $i,SV811: $i,SV689: $i,SV429: $i,SV101: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV101 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV689 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV811 @ SV833 @ SV101 ) @ SV101 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV429 @ SV811 @ SV101 ) @ ( c_HOL_Otimes__class_Otimes @ SV689 @ SV833 @ SV101 ) @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2807,plain,
! [SV703: $i,SV454: $i,SV126: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV126 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ ( c_Power_Opower__class_Opower @ SV454 @ SV703 @ SV126 ) @ SV126 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV126 ) @ SV454 @ SV126 ) @ SV703 @ SV126 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2808,plain,
! [SV135: $i,SV462: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV462 @ SV462 @ SV135 )
= ( c_HOL_Oone__class_Oone @ SV135 ) )
= $true )
| ( ( SV462
= ( c_HOL_Ozero__class_Ozero @ SV135 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV135 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2695]) ).
thf(2809,plain,
! [SV813: $i,SV142: $i,SV708: $i,SV468: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SV708 @ SV142 ) @ SV813 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV813 @ SV142 ) @ SV708 @ SV142 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV468 @ SV142 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2698]) ).
thf(2810,plain,
! [SV143: $i,SV469: $i,SV709: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV709 @ tc_nat )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ SV469 @ SV143 ) @ SV709 @ SV143 )
= ( c_Power_Opower__class_Opower @ SV469 @ SV709 @ SV143 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2811,plain,
! [SV814: $i,SV145: $i,SV711: $i,SV471: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SV711 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SV814 @ SV711 @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SV814 @ SV145 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(2812,plain,
! [SV712: $i,SV473: $i,SV147: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV147 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ SV473 @ SV712 @ SV147 ) @ SV147 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ SV473 @ SV147 ) @ ( c_HOL_Oabs__class_Oabs @ SV712 @ SV147 ) @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2813,plain,
! [SV815: $i,SV713: $i,SV474: $i,SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV148 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SV815 @ SV148 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2814,plain,
! [SV816: $i,SV714: $i,SV475: $i,SV149: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV149 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV816 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SV816 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2704]) ).
thf(2815,plain,
! [SV817: $i,SV715: $i,SV476: $i,SV150: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV150 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SV715 @ SV150 ) @ SV817 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV817 @ SV150 ) @ SV715 @ SV150 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2816,plain,
! [SV151: $i,SV716: $i,SV477: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV477 @ SV716 @ SV151 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV477 @ ( c_Divides_Odiv__class_Odiv @ SV716 @ SV477 @ SV151 ) @ SV151 )
= SV716 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2817,plain,
! [SV152: $i,SV478: $i,SV717: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV478 @ SV152 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV478 @ SV717 @ SV152 ) @ SV717 @ SV152 )
= SV478 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2818,plain,
! [SV818: $i,SV153: $i,SV718: $i,SV479: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
= $true )
| ( ( ( SV818
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV818 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SV818 @ SV153 ) @ SV153 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2819,plain,
! [SV819: $i,SV154: $i,SV719: $i,SV480: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
= $true )
| ( ( ( SV819
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV719 @ SV154 ) @ SV154 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2820,plain,
! [SV721: $i,SV483: $i,SV157: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV483 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV721 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ ( c_GCD_Ogcd__class_Ogcd @ SV483 @ SV721 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2821,plain,
! [SV484: $i,SV158: $i,SV722: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV158 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ SV722 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV158 @ ( c_GCD_Ogcd__class_Ogcd @ SV484 @ SV722 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2822,plain,
! [SV723: $i,SV159: $i,SV485: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV485 @ SV159 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ SV485 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV159 @ ( c_GCD_Ogcd__class_Ogcd @ SV485 @ SV723 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2823,plain,
! [SV724: $i,SV486: $i,SV160: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV486 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ SV724 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV160 @ ( c_GCD_Ogcd__class_Ogcd @ SV486 @ SV724 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2824,plain,
! [SV725: $i,SV487: $i,SV161: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV487 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ SV725 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV161 @ ( c_GCD_Ogcd__class_Ogcd @ SV487 @ SV725 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2825,plain,
! [SV726: $i,SV494: $i,SV168: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV494 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ SV726 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV168 @ ( c_GCD_Ogcd__class_Ogcd @ SV494 @ SV726 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2826,plain,
! [SV727: $i,SV495: $i,SV169: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV495 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ SV727 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV169 @ ( c_GCD_Ogcd__class_Ogcd @ SV495 @ SV727 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2827,plain,
! [SV728: $i,SV496: $i,SV170: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV496 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ SV728 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV170 @ ( c_GCD_Ogcd__class_Ogcd @ SV496 @ SV728 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2828,plain,
! [SV497: $i,SV171: $i,SV729: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2829,plain,
! [SV498: $i,SV172: $i,SV730: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2830,plain,
! [SV820: $i,SV183: $i,SV734: $i,SV505: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV734 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV820 @ SV183 ) @ SV183 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV734 @ SV820 @ SV183 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2722]) ).
thf(2831,plain,
! [SV821: $i,SV184: $i,SV735: $i,SV506: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV735 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV821 @ SV735 @ SV184 ) @ SV184 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SV821 @ SV184 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(2832,plain,
! [SV822: $i,SV193: $i,SV737: $i,SV514: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SV737 @ SV193 ) @ SV822 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SV822 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV737 @ SV822 @ SV193 ) @ SV193 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV737 @ SV514 @ SV193 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2833,plain,
! [SV743: $i,SV522: $i,SV202: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SV743 @ SV202 ) @ SV743 @ SV202 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ SV202 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2834,plain,
! [SV744: $i,SV523: $i,SV203: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SV744 @ SV203 ) @ SV744 @ SV203 )
= SV523 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ SV203 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2835,plain,
! [SV745: $i,SV218: $i,SV536: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV536 @ SV218 ) @ SV745 @ SV218 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV536 @ SV745 @ SV218 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2836,plain,
! [SV219: $i,SV746: $i,SV537: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV537 @ SV746 @ SV219 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV537 @ SV219 ) @ SV746 @ SV219 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2837,plain,
! [SV220: $i,SV747: $i,SV538: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ ( c_HOL_Oabs__class_Oabs @ SV747 @ SV220 ) @ SV220 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV538 @ SV747 @ SV220 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2838,plain,
! [SV221: $i,SV748: $i,SV539: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ SV748 @ SV221 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV539 @ ( c_HOL_Oabs__class_Oabs @ SV748 @ SV221 ) @ SV221 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2839,plain,
! [SV753: $i,SV545: $i,SV230: $i] :
( ( ( class_Int_Onumber__ring @ SV230 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV545 @ SV753 @ SV230 )
= ( c_HOL_Otimes__class_Otimes @ SV545 @ ( c_HOL_Oinverse__class_Oinverse @ SV753 @ SV230 ) @ SV230 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(2840,plain,
! [SV823: $i,SV232: $i,SV754: $i,SV546: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV546 @ SV754 @ SV232 ) @ SV823 @ SV232 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV546 @ SV823 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV754 @ SV823 @ SV232 ) @ SV232 ) )
= $true )
| ( ( SV754
= ( c_HOL_Ozero__class_Ozero @ SV232 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2841,plain,
! [SV834: $i,SV824: $i,SV755: $i,SV547: $i,SV233: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2842,plain,
! [SV561: $i,SV247: $i,SV761: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV247 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV761 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV561 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(2843,plain,
! [SV248: $i,SV562: $i,SV762: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV762 @ SV562 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV762 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SV762 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2844,plain,
! [SV277: $i,SV763: $i,SV575: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SV763 @ SV277 )
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
= $false )
| ( ( ( SV763
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
| ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(2845,plain,
! [SV766: $i,SV580: $i,SV283: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
| ( SV580 = SV766 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2846,plain,
! [SV585: $i,SV767: $i,SV288: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV767 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ ( c_HOL_Otimes__class_Otimes @ SV767 @ SV585 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV288 @ SV585 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(2847,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV296 )
| ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2848,plain,
! [SV770: $i,SV300: $i,SV595: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
= $false )
| ( ( ( SV595 = SV770 )
| ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2849,plain,
! [SV302: $i,SV772: $i,SV597: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SV772 @ SV302 )
= ( c_HOL_Oone__class_Oone @ SV302 ) )
= $false )
| ( ( ( SV772
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
| ( SV597 = SV772 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2850,plain,
! [SV602: $i,SV307: $i,SV826: $i,SV774: $i] :
( ( ( SV774
!= ( c_HOL_Otimes__class_Otimes @ SV826 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV826 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true )
| ( ( SV307
= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(2851,plain,
! [SV308: $i,SV775: $i,SV603: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV603 @ SV775 @ SV308 )
= ( c_HOL_Oone__class_Oone @ SV308 ) )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV603 @ SV308 )
= SV775 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2852,plain,
! [SV604: $i,SV776: $i,SV309: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ ( c_HOL_Otimes__class_Otimes @ SV776 @ SV604 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV309 @ SV776 @ tc_nat )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV309 @ SV604 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2853,plain,
! [SV777: $i,SV311: $i,SV606: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV606 @ SV311 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV777 @ SV311 ) )
= $false )
| ( ( SV606 = SV777 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2854,plain,
! [SV835: $i,SV827: $i,SV778: $i,SV607: $i,SV312: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV312 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
| ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(2855,plain,
! [SV779: $i,SV314: $i,SV609: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV609 @ SV314 )
= ( c_HOL_Oabs__class_Oabs @ SV779 @ SV314 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV609 @ SV779 @ SV314 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2856,plain,
! [SV315: $i,SV610: $i,SV780: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat ) )
= $true )
| ( ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(2857,plain,
! [SV316: $i,SV611: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
!= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $true )
| ( ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(2858,plain,
! [SV321: $i,SV781: $i,SV615: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SV781 @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $false )
| ( ( ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ( SV781
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2859,plain,
! [SV322: $i,SV616: $i,SV782: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat ) )
= $true )
| ( ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(2860,plain,
! [SV836: $i,SV828: $i,SV783: $i,SV617: $i,SV323: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV323 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
| ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2861,plain,
! [SV328: $i,SV784: $i,SV621: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV621 @ SV784 @ SV328 )
= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
= $false )
| ( ( SV621
= ( c_HOL_Ozero__class_Ozero @ SV328 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2862,plain,
! [SV330: $i,SV785: $i,SV623: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SV785 @ SV330 )
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $false )
| ( ( ( SV785
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
| ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2863,plain,
! [SV625: $i,SV332: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV332 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2864,plain,
! [SV333: $i,SV787: $i,SV626: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2865,plain,
! [SV628: $i,SV788: $i,SV335: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ SV788 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV335 @ ( c_HOL_Otimes__class_Otimes @ SV788 @ SV628 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV335 @ SV628 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2866,plain,
! [SV337: $i,SV630: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
!= ( c_HOL_Oone__class_Oone @ SV337 ) )
= $true )
| ( ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(2867,plain,
! [SV789: $i,SV631: $i,SV339: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV2 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV339 @ SV631 @ SV2 ) @ SV789 @ SV2 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV339 @ SV789 @ SV2 ) @ ( c_Power_Opower__class_Opower @ SV631 @ SV789 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2868,plain,
! [SV357: $i,SV20: $i,SV641: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2869,plain,
! [SV359: $i,SV23: $i,SV642: $i,SV790: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2870,plain,
! [SV829: $i,SV791: $i,SV646: $i,SV364: $i,SV28: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SV791 @ SV829 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SV791 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SV829 @ SV28 ) @ SV28 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(2871,plain,
! [SV830: $i,SV792: $i,SV30: $i,SV648: $i,SV366: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2872,plain,
! [SV369: $i,SV33: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV33 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV33 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(2873,plain,
! [SV657: $i,SV49: $i,SV793: $i,SV385: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ SV793 @ SV49 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV385 @ ( c_HOL_Otimes__class_Otimes @ SV657 @ SV793 @ SV49 ) @ SV49 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2874,plain,
! [SV794: $i,SV50: $i,SV658: $i,SV386: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ SV658 @ SV50 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV386 @ ( c_HOL_Otimes__class_Otimes @ SV658 @ SV794 @ SV50 ) @ SV50 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2875,plain,
! [SV659: $i,SV51: $i,SV795: $i,SV387: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV387 @ SV795 @ SV51 ) @ SV659 @ SV51 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV387 @ SV659 @ SV51 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2876,plain,
! [SV660: $i,SV52: $i,SV388: $i,SV796: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV796 @ SV388 @ SV52 ) @ SV660 @ SV52 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV388 @ SV660 @ SV52 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2877,plain,
! [SV676: $i,SV83: $i,SV807: $i,SV413: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2878,plain,
! [SV677: $i,SV84: $i,SV808: $i,SV414: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2798]) ).
thf(2879,plain,
! [SV422: $i,SV94: $i,SV682: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2880,plain,
! [SV97: $i,SV685: $i,SV425: $i] :
( ( ( SV425
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV425 @ SV685 @ SV97 ) @ SV685 @ SV97 ) )
= $true )
| ( ( SV685
= ( c_HOL_Ozero__class_Ozero @ SV97 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV97 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(2881,plain,
! [SV98: $i,SV686: $i,SV426: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV426 @ SV686 @ SV98 ) @ SV686 @ SV98 )
= SV426 )
= $true )
| ( ( SV686
= ( c_HOL_Ozero__class_Ozero @ SV98 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV98 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(2882,plain,
! [SV813: $i,SV142: $i,SV468: $i,SV708: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV708 @ SV468 @ SV142 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV468 @ SV708 @ SV142 ) @ SV813 @ SV142 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV468 @ SV813 @ SV142 ) @ SV708 @ SV142 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(2883,plain,
! [SV711: $i,SV145: $i,SV814: $i,SV471: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV471 @ SV814 @ SV145 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV471 @ SV711 @ SV145 ) @ ( c_Power_Opower__class_Opower @ SV814 @ SV711 @ SV145 ) @ SV145 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(2884,plain,
! [SV815: $i,SV713: $i,SV474: $i,SV148: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SV815 @ SV148 ) )
| ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2885,plain,
! [SV816: $i,SV714: $i,SV475: $i,SV149: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV816 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SV816 @ SV149 ) )
| ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2886,plain,
! [SV817: $i,SV715: $i,SV476: $i,SV150: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV150 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV476 @ SV715 @ SV150 ) @ SV817 @ SV150 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV476 @ SV817 @ SV150 ) @ SV715 @ SV150 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2887,plain,
! [SV718: $i,SV479: $i,SV153: $i,SV818: $i] :
( ( ( SV818
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV818 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SV818 @ SV153 ) @ SV153 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(2888,plain,
! [SV719: $i,SV480: $i,SV154: $i,SV819: $i] :
( ( ( SV819
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV719 @ SV154 ) @ SV154 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(2889,plain,
! [SV497: $i,SV171: $i,SV729: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2890,plain,
! [SV172: $i,SV498: $i,SV730: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(2891,plain,
! [SV505: $i,SV183: $i,SV820: $i,SV734: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV734 @ SV820 @ SV183 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV734 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV505 @ SV820 @ SV183 ) @ SV183 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2892,plain,
! [SV735: $i,SV184: $i,SV821: $i,SV506: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV506 @ SV821 @ SV184 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV506 @ SV735 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV821 @ SV735 @ SV184 ) @ SV184 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(2893,plain,
! [SV822: $i,SV193: $i,SV514: $i,SV737: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV737 @ SV514 @ SV193 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_Divides_Odiv__class_Odiv @ SV514 @ SV737 @ SV193 ) @ SV822 @ SV193 )
= ( c_Divides_Odiv__class_Odiv @ ( c_Power_Opower__class_Opower @ SV514 @ SV822 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV737 @ SV822 @ SV193 ) @ SV193 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(2894,plain,
! [SV202: $i,SV743: $i,SV522: $i] :
( ( ( SV522
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV522 @ SV743 @ SV202 ) @ SV743 @ SV202 ) )
= $true )
| ( ( SV743
= ( c_HOL_Ozero__class_Ozero @ SV202 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(2895,plain,
! [SV203: $i,SV744: $i,SV523: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV523 @ SV744 @ SV203 ) @ SV744 @ SV203 )
= SV523 )
= $true )
| ( ( SV744
= ( c_HOL_Ozero__class_Ozero @ SV203 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(2896,plain,
! [SV834: $i,SV824: $i,SV233: $i,SV755: $i,SV547: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(2897,plain,
! [SV561: $i,SV761: $i,SV247: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV761 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV247 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV761 @ SV561 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV247 @ SV561 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(2898,plain,
! [SV562: $i,SV762: $i,SV248: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV762 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV762 @ SV562 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV562 @ SV762 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV248 @ SV562 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(2899,plain,
! [SV575: $i,SV277: $i,SV763: $i] :
( ( ( SV763
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
= $true )
| ( ( SV575
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV575 @ SV763 @ SV277 )
= ( c_HOL_Ozero__class_Ozero @ SV277 ) )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2900,plain,
! [SV766: $i,SV283: $i,SV580: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
= $true )
| ( ( SV580 = SV766 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(2901,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV296 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(2902,plain,
! [SV300: $i,SV770: $i,SV595: $i] :
( ( ( SV595 = SV770 )
= $true )
| ( ( ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
| ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(2903,plain,
! [SV597: $i,SV302: $i,SV772: $i] :
( ( ( SV772
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
= $true )
| ( ( SV597 = SV772 )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV597 @ SV772 @ SV302 )
= ( c_HOL_Oone__class_Oone @ SV302 ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2849]) ).
thf(2904,plain,
! [SV602: $i,SV307: $i,SV826: $i,SV774: $i] :
( ( ( SV774
= ( c_HOL_Otimes__class_Otimes @ SV826 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_GCD_Ogcd__class_Ogcd @ SV826 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) ) )
= $true )
| ( ( SV307
= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2905,plain,
! [SV835: $i,SV827: $i,SV312: $i,SV778: $i,SV607: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
!= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
= $true )
| ( ( ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(2906,plain,
! [SV315: $i,SV610: $i,SV780: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat ) )
= $true )
| ( ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(2907,plain,
! [SV316: $i,SV611: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV611 @ SV316 )
= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $false )
| ( ( SV611
= ( c_HOL_Ozero__class_Ozero @ SV316 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV316 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(2908,plain,
! [SV781: $i,SV321: $i,SV615: $i] :
( ( ( SV615
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( SV781
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV615 @ SV781 @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(2909,plain,
! [SV322: $i,SV616: $i,SV782: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat ) )
= $true )
| ( ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(2910,plain,
! [SV836: $i,SV828: $i,SV323: $i,SV783: $i,SV617: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
!= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
= $true )
| ( ( ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(2911,plain,
! [SV623: $i,SV330: $i,SV785: $i] :
( ( ( SV785
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $true )
| ( ( SV623
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV623 @ SV785 @ SV330 )
= ( c_HOL_Ozero__class_Ozero @ SV330 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV330 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(2912,plain,
! [SV625: $i,SV332: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV332 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV332 )
| ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(2913,plain,
! [SV626: $i,SV787: $i,SV333: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(2914,plain,
! [SV337: $i,SV630: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV630 @ SV337 )
= ( c_HOL_Oone__class_Oone @ SV337 ) )
= $false )
| ( ( SV630
= ( c_HOL_Oone__class_Oone @ SV337 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV337 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(2915,plain,
! [SV357: $i,SV641: $i,SV20: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV641 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV20 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV641 @ SV357 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV357 @ SV641 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV357 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(2916,plain,
! [SV359: $i,SV23: $i,SV642: $i,SV790: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(2917,plain,
! [SV829: $i,SV791: $i,SV646: $i,SV364: $i,SV28: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ SV364 @ SV646 @ SV28 ) @ ( c_HOL_Oinverse__class_Odivide @ SV791 @ SV829 @ SV28 ) @ SV28 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV364 @ SV791 @ SV28 ) @ ( c_HOL_Otimes__class_Otimes @ SV646 @ SV829 @ SV28 ) @ SV28 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(2918,plain,
! [SV366: $i,SV648: $i,SV30: $i,SV792: $i,SV830: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(2919,plain,
! [SV369: $i,SV33: $i] :
( ( ( ~ ( class_Power_Opower @ SV33 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(2920,plain,
! [SV676: $i,SV83: $i,SV807: $i,SV413: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(2921,plain,
! [SV677: $i,SV84: $i,SV808: $i,SV414: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2878]) ).
thf(2922,plain,
! [SV94: $i,SV422: $i,SV682: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2879]) ).
thf(2923,plain,
! [SV815: $i,SV148: $i,SV713: $i,SV474: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV474 @ SV713 @ SV148 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV713 @ SV148 ) @ SV148 )
= ( c_HOL_Oinverse__class_Odivide @ SV474 @ SV815 @ SV148 ) )
= $true )
| ( ( SV713
= ( c_HOL_Ozero__class_Ozero @ SV148 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV148 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2884]) ).
thf(2924,plain,
! [SV816: $i,SV149: $i,SV714: $i,SV475: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV714 @ SV149 ) @ ( c_HOL_Otimes__class_Otimes @ SV475 @ SV816 @ SV149 ) @ SV149 )
= ( c_HOL_Oinverse__class_Odivide @ SV714 @ SV816 @ SV149 ) )
= $true )
| ( ( SV475
= ( c_HOL_Ozero__class_Ozero @ SV149 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV149 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2885]) ).
thf(2925,plain,
! [SV718: $i,SV153: $i,SV818: $i,SV479: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV479 @ SV818 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV718 @ SV818 @ SV153 ) @ SV153 )
= $false )
| ( ( SV818
= ( c_HOL_Ozero__class_Ozero @ SV153 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV479 @ SV718 @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(2926,plain,
! [SV719: $i,SV154: $i,SV480: $i,SV819: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV480 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV819 @ SV719 @ SV154 ) @ SV154 )
= $false )
| ( ( SV819
= ( c_HOL_Ozero__class_Ozero @ SV154 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV480 @ SV719 @ SV154 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(2927,plain,
! [SV171: $i,SV729: $i,SV497: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV497 @ SV729 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV729 @ SV171 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV729 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV171 @ SV497 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(2928,plain,
! [SV172: $i,SV730: $i,SV498: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV498 @ SV730 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV498 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV730 @ SV172 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV172 @ SV498 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2890]) ).
thf(2929,plain,
! [SV824: $i,SV547: $i,SV233: $i,SV834: $i,SV755: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(2930,plain,
! [SV766: $i,SV283: $i,SV580: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV580 @ SV283 )
= ( c_HOL_Oinverse__class_Oinverse @ SV766 @ SV283 ) )
= $false )
| ( ( SV580 = SV766 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV283 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(2931,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV296 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV296 )
| ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(2932,plain,
! [SV595: $i,SV300: $i,SV770: $i] :
( ( ( SV770
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
= $true )
| ( ( SV595
= ( c_HOL_Ozero__class_Ozero @ SV300 ) )
= $true )
| ( ( SV595 = SV770 )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV595 @ SV300 )
= ( c_HOL_Oinverse__class_Oinverse @ SV770 @ SV300 ) )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(2933,plain,
! [SV602: $i,SV826: $i,SV307: $i,SV774: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV826 @ SV602 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( SV774
= ( c_HOL_Otimes__class_Otimes @ SV826 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( SV307
= ( c_HOL_Otimes__class_Otimes @ SV602 @ ( c_GCD_Ogcd__class_Ogcd @ SV774 @ SV307 @ tc_nat ) @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(2934,plain,
! [SV835: $i,SV827: $i,SV312: $i,SV778: $i,SV607: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
= $false )
| ( ( ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2935,plain,
! [SV610: $i,SV315: $i,SV780: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV315 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV780 @ SV610 @ tc_nat )
= $false )
| ( ( SV780
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV315 @ SV610 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(2936,plain,
! [SV616: $i,SV322: $i,SV782: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV322 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV782 @ SV616 @ tc_nat )
= $false )
| ( ( SV782
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $true )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV322 @ SV616 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(2937,plain,
! [SV836: $i,SV828: $i,SV323: $i,SV783: $i,SV617: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
= $false )
| ( ( ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(2938,plain,
! [SV625: $i,SV332: $i] :
( ( ( ~ ( class_Power_Opower @ SV332 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(2939,plain,
! [SV626: $i,SV787: $i,SV333: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV333 @ SV787 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV333 @ SV626 @ tc_nat ) @ SV787 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV626 @ SV787 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV333 @ SV626 @ tc_nat )
= ( c_HOL_Oone__class_Oone @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2940,plain,
! [SV642: $i,SV23: $i,SV790: $i,SV359: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV790 @ SV23 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV790 @ SV642 @ SV23 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV359 @ SV642 @ SV23 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(2941,plain,
! [SV366: $i,SV648: $i,SV30: $i,SV792: $i,SV830: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(2942,plain,
! [SV369: $i,SV33: $i] :
( ( ( class_Power_Opower @ SV33 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
| ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(2943,plain,
! [SV413: $i,SV83: $i,SV676: $i,SV807: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(2944,plain,
! [SV414: $i,SV84: $i,SV808: $i,SV677: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(2945,plain,
! [SV94: $i,SV682: $i,SV422: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV422 @ SV682 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV422 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV682 @ SV94 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV682 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV422 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(2946,plain,
! [SV824: $i,SV547: $i,SV233: $i,SV834: $i,SV755: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(2947,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( ~ ( class_Power_Opower @ SV296 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(2948,plain,
! [SV827: $i,SV607: $i,SV835: $i,SV312: $i,SV778: $i] :
( ( ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
= $true )
| ( ( ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(2949,plain,
! [SV828: $i,SV617: $i,SV783: $i,SV323: $i,SV836: $i] :
( ( ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= $true )
| ( ( ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
| ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(2950,plain,
! [SV625: $i,SV332: $i] :
( ( ( class_Power_Opower @ SV332 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
!= ( c_HOL_Ozero__class_Ozero @ SV332 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(2951,plain,
! [SV792: $i,SV830: $i,SV30: $i,SV366: $i,SV648: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV648 @ SV366 @ SV30 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV830 @ SV792 @ SV30 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Odiv @ SV366 @ SV648 @ SV30 ) @ ( c_Divides_Odiv__class_Odiv @ SV792 @ SV830 @ SV30 ) @ SV30 )
= ( c_Divides_Odiv__class_Odiv @ ( c_HOL_Otimes__class_Otimes @ SV366 @ SV792 @ SV30 ) @ ( c_HOL_Otimes__class_Otimes @ SV648 @ SV830 @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(2952,plain,
! [SV369: $i,SV33: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV369 @ SV33 )
= ( c_HOL_Ozero__class_Ozero @ SV33 ) )
= $true )
| ( ( SV369
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(2953,plain,
! [SV413: $i,SV83: $i,SV676: $i,SV807: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(2954,plain,
! [SV414: $i,SV84: $i,SV808: $i,SV677: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2944]) ).
thf(2955,plain,
! [SV834: $i,SV755: $i,SV233: $i,SV824: $i,SV547: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV547 @ SV824 @ SV233 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV755 @ SV834 @ SV233 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV547 @ SV755 @ SV233 ) @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV834 @ SV233 ) @ SV233 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(2956,plain,
! [SV768: $i,SV591: $i,SV296: $i] :
( ( ( class_Power_Opower @ SV296 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2947]) ).
thf(2957,plain,
! [SV778: $i,SV827: $i,SV607: $i,SV312: $i,SV835: $i] :
( ( ( SV835
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV607 @ SV835 @ SV312 )
= ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV778 @ SV312 ) )
= $true )
| ( ( SV778
= ( c_HOL_Ozero__class_Ozero @ SV312 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV607 @ SV778 @ SV312 )
= ( c_HOL_Otimes__class_Otimes @ SV827 @ SV835 @ SV312 ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(2958,plain,
! [SV828: $i,SV836: $i,SV617: $i,SV323: $i,SV783: $i] :
( ( ( SV783
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV617 @ SV836 @ SV323 )
= ( c_HOL_Otimes__class_Otimes @ SV828 @ SV783 @ SV323 ) )
= $true )
| ( ( SV836
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV617 @ SV783 @ SV323 )
= ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV836 @ SV323 ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(2959,plain,
! [SV332: $i,SV625: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV625 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 )
= ( c_HOL_Ozero__class_Ozero @ SV332 ) )
= $false )
| ( ( class_Power_Opower @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV332 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2950]) ).
thf(2960,plain,
! [SV676: $i,SV83: $i,SV413: $i,SV807: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV413 @ SV83 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV807 @ SV676 @ SV83 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV413 @ SV807 @ SV83 ) @ ( c_Divides_Odiv__class_Odiv @ SV676 @ SV807 @ SV83 ) @ SV83 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV413 @ SV676 @ SV83 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(2961,plain,
! [SV808: $i,SV84: $i,SV414: $i,SV677: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV414 @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV677 @ SV808 @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV808 @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Divides_Odiv__class_Odiv @ SV414 @ SV677 @ SV84 ) @ ( c_Divides_Odiv__class_Odiv @ SV808 @ SV677 @ SV84 ) @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(2962,plain,
! [SV296: $i,SV768: $i,SV591: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
!= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
= $true )
| ( ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
= $true )
| ( ( class_Power_Opower @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(2963,plain,
! [SV296: $i,SV768: $i,SV591: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV591 @ SV768 @ SV296 )
= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
= $false )
| ( ( SV591
= ( c_HOL_Ozero__class_Ozero @ SV296 ) )
= $true )
| ( ( class_Power_Opower @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(2964,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[935,2963,2961,2960,2959,2958,2957,2955,2952,2951,2945,2940,2939,2936,2935,2933,2932,2930,2928,2927,2926,2925,2924,2923,2917,2915,2914,2911,2908,2907,2903,2899,2898,2897,2895,2894,2893,2892,2891,2886,2883,2882,2881,2880,2876,2875,2874,2873,2867,2865,2861,2855,2853,2852,2851,2846,2840,2839,2838,2837,2836,2835,2827,2826,2825,2824,2823,2822,2821,2820,2817,2816,2812,2810,2808,2807,2806,2805,2804,2800,2799,2796,2795,2794,2793,2788,2787,2786,2785,2784,2783,2782,2781,2775,2772,2768,2754,2752,2749,2747,2745,2741,2740,2739,2738,2737,2729,2726,2724,2721,2710,2701,2697,2696,2694,2693,2691,2690,2689,2683,2682,2680,2677,2676,2671,2670,2669,2668,2667,2666,2664,2663,2643,2642,2641,2640,2639,2638,2637,2627,2614,2610,2607,2606,2603,2600,2598,2592,2591,2588,2584,2575,2572,2569,2568,2567,2565,2543,2537,2536,2535,2534,2530,2529,2528,2526,2525,2524,2523,2522,2521,2520,2519,2508,2502,2497,2496,2495,2494,2484,2471,2467,2465,2464,2463,2459,2458,2457,2456,2455,2454,2453,2452,2440,2435,2433,2432,2427,2426,2425,2421,2418,2414,2413,2407,2405,2403,2401,2399,2396,2393,2389,2388,2387,2385,2384,2383,2382,2381,2380,2379,2378,2377,2376,2375,2374,2372,2361,2360,2350,2349,2348,2347,2346,2345,2344,2343,2342,2341,2340,2337,2335,2330,2329,2328,2296,2293,2280,2271,2270,2269,2268,2267,2266,2265,2264,2263,2245,2242,2241,2224,2208,2207,2199,2168,2120,2112,2111,2109,2104,2088,2085,2084,2083,2082,2081,2080,2060,2059,2058,2045,2012,2008,1970,1958,1957,1948,1939,1873,1845,1805,1803,1802,1787,1758,1757,1747,1739,1738,1737,1736,1735,1734,1728,1703,1631,1630,1621,1620,1618,1617,1615,1614,1601,1588,1579,1565,1534,1524,1514,1509,1508,1503,1502,1499,1498,1497,1496,1491,1490,1445,1444,1436,1424,1417,1413,1412,1373,1292,1291,1290,1289,1257,1171,1170,1169,1168,1167,1166,1165,1164,1163,1162,1161,1160,1159,1158,1157,1156,1155,1154,1153,1152,1151,1150,1149,1148,1147,1146,1145,1144,1143,1142,1141,1140,1139,1138,1137,1136,1135,1133,1131,1119,1116,1106,1093,1092,1064,1011,952]) ).
thf(2965,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV629-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 16:45:29 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.31/6.55 ..
% 37.31/6.55
% 37.31/6.55 No.of.Axioms: 389
% 37.31/6.55
% 37.31/6.55 Length.of.Defs: 0
% 37.31/6.55
% 37.31/6.55 Contains.Choice.Funs: false
% 37.31/6.55 ....................................................................................
% 37.31/6.55
% 37.31/6.55 ********************************
% 37.31/6.55 * All subproblems solved! *
% 37.31/6.55 ********************************
% 37.31/6.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:389,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2964,loop_count:0,foatp_calls:1,translation:fof_full)
% 37.31/6.55
% 37.31/6.55 %**** Beginning of derivation protocol ****
% 37.31/6.55 % SZS output start CNFRefutation
% See solution above
% 37.31/6.57
% 37.31/6.57 %**** End of derivation protocol ****
% 37.31/6.57 %**** no. of clauses in derivation: 2965 ****
% 37.31/6.57 %**** clause counter: 2964 ****
% 37.31/6.57
% 37.31/6.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:389,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2964,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------