%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV689-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 10:58:31 AM UTC 2026
% Result : Unsatisfiable 237.51s 39.90s
% Output : CNFRefutation 39.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 799
% Syntax : Number of formulae : 7149 (4055 unt; 0 typ; 0 def)
% Number of atoms : 41787 (14401 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 113227 (10369 ~;13620 |; 0 &;89238 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 69 usr; 6 con; 0-3 aty)
% Number of variables : 22455 ( 0 ^;22455 !; 0 ?;22455 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_HOL_Oabs__class_Oabs,type,
c_HOL_Oabs__class_Oabs: $i > $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $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_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(tp_c_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: $i > $i > $i > $i ).
thf(tp_c_Parity_Oeven__odd__class_Oeven,type,
c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).
thf(tp_c_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_Divides_Oring__div,type,
class_Divides_Oring__div: $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__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $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_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add__abs,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add__abs,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__algebra,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(tp_class_Ring__and__Field_Oabs__if,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $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_Odvd,type,
class_Ring__and__Field_Odvd: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $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__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $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_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__ring__abs,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
thf(tp_class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $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,type,
class_Ring__and__Field_Osemiring: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_i,type,
v_i: $i ).
thf(tp_v_k,type,
v_k: $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(1,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(2,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(3,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(4,axiom,
class_Ring__and__Field_Odvd @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
thf(5,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(6,axiom,
class_Divides_Osemiring__div @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
thf(7,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(8,axiom,
class_Ring__and__Field_Osemiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
thf(9,axiom,
class_Ring__and__Field_Omult__mono @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
thf(10,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(11,axiom,
class_Ring__and__Field_Omult__mono1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
thf(12,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(13,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(14,axiom,
class_Ring__and__Field_Ocomm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
thf(15,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(16,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
thf(17,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(18,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(19,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(20,axiom,
class_Ring__and__Field_Oordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
thf(21,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
thf(22,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(23,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(24,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(25,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(26,axiom,
class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
thf(27,axiom,
class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
thf(28,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
thf(29,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(30,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(31,axiom,
c_HOL_Oord__class_Oless @ v_i @ v_n @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(32,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(33,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(34,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(35,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(36,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(37,axiom,
c_HOL_Oord__class_Oless @ v_i @ v_n @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_0) ).
thf(38,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(39,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(40,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(41,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(42,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(43,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(44,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(45,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(46,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(47,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(48,axiom,
! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(49,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(50,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(51,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(52,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(53,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(54,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(55,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(56,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(57,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(58,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).
thf(59,axiom,
! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(60,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_1) ).
thf(61,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(62,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(63,axiom,
! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(64,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(65,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(66,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
thf(67,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
thf(68,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_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_0) ).
thf(69,axiom,
! [V_x: $i,V_y: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_1) ).
thf(70,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(71,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= V_m )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
thf(72,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(73,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(74,axiom,
! [T_a: $i,V_a: $i,V_r: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_r @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
thf(75,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(76,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(77,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
thf(78,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ V_n @ tc_nat )
= V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
thf(79,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(80,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
thf(81,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
thf(82,axiom,
! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(83,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_3) ).
thf(84,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__difference__nat_4) ).
thf(85,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(86,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(87,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
thf(88,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(89,axiom,
! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(90,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(91,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(92,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(93,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(94,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Ominus__class_Ominus @ 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/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff__nat_0) ).
thf(95,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(96,axiom,
! [V_m: $i,V_i: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_i @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff_0) ).
thf(97,axiom,
! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(98,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(99,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
thf(100,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
thf(101,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(102,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(103,axiom,
! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(104,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(105,axiom,
! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(106,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(107,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(108,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(109,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(110,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(111,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(112,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(113,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(114,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__if_0) ).
thf(115,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(116,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(117,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(118,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
thf(119,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
thf(120,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(121,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(122,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(123,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(124,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(125,axiom,
! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(126,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(127,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(128,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(129,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(130,axiom,
! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_l @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(131,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(132,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(133,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).
thf(134,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).
thf(135,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
thf(137,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(138,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(139,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
thf(140,axiom,
! [V_k: $i,V_n: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__le_0) ).
thf(141,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( 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_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
thf(142,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( 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_Otimes__class_Otimes @ V_c @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
thf(143,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
thf(144,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
thf(145,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
thf(146,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
thf(147,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
thf(148,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(149,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
thf(150,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
thf(151,axiom,
! [V_d: $i,V_x: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_d @ V_x @ tc_nat ) @ V_d @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
thf(152,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_5) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
thf(154,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(155,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(156,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(157,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(158,axiom,
! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(159,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(160,axiom,
! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(161,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(162,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(163,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
thf(164,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
thf(165,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/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
thf(166,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
thf(167,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
thf(168,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
thf(170,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
= V_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
thf(171,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
= V_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
thf(172,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(173,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(174,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
thf(175,axiom,
! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(176,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
thf(177,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
thf(178,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(179,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(180,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
thf(181,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
thf(182,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
thf(183,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(184,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(185,axiom,
! [V_x: $i,V_n: $i,V_xa: $i,V_y: $i,V_xb: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_xa @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_xb @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ V_y @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
thf(186,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
thf(187,axiom,
! [V_j: $i,V_k: $i,V_i: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
thf(188,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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).
thf(189,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).
thf(190,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ 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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).
thf(191,axiom,
! [V_i: $i,V_j: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_j
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).
thf(192,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
thf(193,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).
thf(194,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
thf(195,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(196,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(197,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(198,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(199,axiom,
! [V_n: $i,V_m: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).
thf(200,axiom,
! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
thf(201,axiom,
! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add2_0) ).
thf(202,axiom,
! [V_m: $i,V_x: $i] : ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_x @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__add_1) ).
thf(203,axiom,
! [V_k: $i,V_x: $i] : ( c_lessequals @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_x @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__ex__iff_1) ).
thf(204,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(205,axiom,
! [V_i: $i,V_k: $i] :
( ~ ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_i @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_i @ tc_nat ) @ V_i @ tc_nat )
= V_k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).
thf(206,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_4) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
thf(210,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/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
thf(211,axiom,
! [V_k: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).
thf(212,axiom,
! [V_k: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).
thf(213,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_y @ T_a ) @ V_x @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
thf(214,axiom,
! [V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ V_m @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__1_0) ).
thf(215,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
thf(220,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
thf(225,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/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
thf(226,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/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
thf(228,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
thf(229,axiom,
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
thf(230,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).
thf(232,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(233,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(234,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(235,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(236,axiom,
! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(237,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(238,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(239,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(240,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(241,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(242,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(243,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(244,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(245,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_c @ V_d @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
thf(246,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
thf(247,axiom,
! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
thf(248,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
thf(249,axiom,
! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
thf(250,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(251,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(252,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(253,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(254,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(255,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(256,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(257,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(258,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(259,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
thf(260,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(261,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(262,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
thf(263,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
thf(264,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
thf(265,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
thf(266,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
thf(267,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
thf(268,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_r @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
thf(269,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
thf(270,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
thf(271,axiom,
! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
thf(272,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
thf(273,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
thf(274,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(275,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(276,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(277,axiom,
! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(278,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(279,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(280,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(281,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(282,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(283,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(284,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(285,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(286,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(287,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(288,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(289,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(290,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(291,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(292,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(293,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(294,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(295,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(296,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(297,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
thf(298,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
thf(299,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
thf(300,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(301,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(302,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(303,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(304,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(305,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(306,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(307,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(308,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(309,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(310,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(311,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(312,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(313,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(314,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).
thf(316,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).
thf(317,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(318,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(319,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(320,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(321,axiom,
! [V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(322,axiom,
! [V_m: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(323,axiom,
! [V_x: $i] :
( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(324,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(325,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(326,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(327,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(328,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(329,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(330,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(331,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(332,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
thf(333,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/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
thf(334,axiom,
! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
thf(335,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
thf(336,axiom,
! [V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
| ( V_y = V_z )
| ( V_w = V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
thf(337,axiom,
! [V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) @ tc_nat ) )
| ( V_c = V_d )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
thf(338,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ V_m @ tc_nat ) ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
thf(340,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
thf(341,axiom,
! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
thf(342,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
thf(343,axiom,
! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
thf(344,axiom,
c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
thf(345,axiom,
! [V_j: $i,V_i: $i,V_k: $i] :
( ( c_lessequals @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
thf(346,axiom,
! [V_j: $i,V_k: $i,V_i: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
| ~ ( c_lessequals @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
thf(347,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_1) ).
thf(348,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_2) ).
thf(349,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(350,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
thf(351,axiom,
! [V_i: $i,V_j: $i,V_u: $i,V_n: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
thf(352,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(353,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
thf(354,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(355,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(356,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(357,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(358,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(359,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(360,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(361,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(362,axiom,
! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(363,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
thf(366,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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
thf(367,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
thf(368,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(369,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(370,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(371,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(372,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
thf(373,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
thf(376,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
thf(377,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
thf(378,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
thf(379,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
thf(380,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc_0) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
thf(383,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).
thf(385,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
thf(386,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diffD_0) ).
thf(387,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ 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_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__diffD1_0) ).
thf(388,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(389,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(390,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(391,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_d @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
thf(392,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
thf(393,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(394,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(395,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
thf(396,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
thf(397,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(398,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
thf(399,axiom,
! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(400,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(401,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(402,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(403,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
thf(404,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
thf(405,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ V_u @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a )
= V_u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(406,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(407,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(408,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(409,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).
thf(411,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(412,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(413,axiom,
( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_5) ).
thf(414,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_0) ).
thf(415,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__is__add_3) ).
thf(416,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).
thf(417,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(419,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
thf(420,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
thf(421,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
thf(422,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(423,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(424,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
thf(425,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
thf(426,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
thf(427,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
thf(428,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
thf(429,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
thf(430,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
thf(431,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
thf(435,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
thf(436,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
thf(437,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
thf(438,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
thf(439,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
thf(440,axiom,
! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).
thf(441,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).
thf(442,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).
thf(443,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).
thf(444,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
thf(445,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
thf(446,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
thf(447,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
thf(448,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
thf(449,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
thf(450,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
thf(451,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
thf(452,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
thf(453,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
thf(454,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
thf(455,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
thf(456,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
thf(457,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
thf(458,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
thf(459,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
thf(460,axiom,
! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__square_0) ).
thf(461,axiom,
! [V_m: $i] :
( ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).
thf(462,axiom,
! [V_x: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ V_x ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_1) ).
thf(463,axiom,
! [V_x: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__Suc_0) ).
thf(464,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(465,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(466,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
thf(467,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
thf(468,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).
thf(469,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
thf(470,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_3) ).
thf(471,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_0) ).
thf(472,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
thf(473,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
thf(474,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 )
= V_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
thf(475,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) )
!= V_n )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
thf(476,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
thf(477,axiom,
! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
thf(478,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__pos_0) ).
thf(479,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(480,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(481,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
thf(482,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).
thf(483,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(484,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
thf(485,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
thf(486,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(487,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
thf(488,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
thf(489,axiom,
! [V_i: $i,V_u: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
thf(490,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
thf(491,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(492,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(493,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(494,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
thf(495,axiom,
! [V_x: $i] :
( ( V_x
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
thf(496,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
thf(497,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
thf(498,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).
thf(499,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).
thf(500,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
thf(501,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
thf(502,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
thf(503,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
thf(504,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
thf(505,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
thf(506,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
thf(507,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
thf(508,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 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
thf(509,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
thf(510,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(511,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
thf(512,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
thf(513,axiom,
! [V_xa: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_xa @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
thf(514,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).
thf(515,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).
thf(516,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_1) ).
thf(517,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__leE_0) ).
thf(518,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
thf(519,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
thf(520,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
thf(521,axiom,
! [V_k: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_k @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).
thf(522,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(523,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(524,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_d @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(525,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(526,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(527,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(528,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(529,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(530,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(531,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(532,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
thf(533,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(534,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(535,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(536,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(537,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ tc_nat ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(538,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(539,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(540,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
thf(541,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/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
thf(542,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(543,axiom,
! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
thf(544,axiom,
! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
thf(545,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_Oplus__class_Oplus @ V_b @ V_c @ 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/sandbox2/benchmark/theBenchmark.p',cls_dvd__add_0) ).
thf(546,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
thf(547,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
thf(548,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(549,axiom,
! [V_n: $i,V_m: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_0) ).
thf(550,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_1) ).
thf(551,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_2) ).
thf(552,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_odd__add_3) ).
thf(553,axiom,
! [V_n: $i,V_m: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_0) ).
thf(554,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_1) ).
thf(555,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_2) ).
thf(556,axiom,
! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__add_3) ).
thf(557,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_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_0) ).
thf(558,axiom,
! [V_x: $i,V_y: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
thf(559,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_2) ).
thf(560,axiom,
! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__sum__nat_3) ).
thf(561,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
thf(562,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
thf(563,axiom,
! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__cube_0) ).
thf(564,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
thf(565,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
thf(566,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
thf(567,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
thf(568,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
thf(569,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
thf(570,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
thf(571,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(572,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(573,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(574,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(575,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
thf(576,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_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
thf(577,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
thf(578,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
thf(579,axiom,
! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
thf(580,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
thf(581,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
thf(582,axiom,
! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
thf(583,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
thf(584,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
thf(585,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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
thf(586,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
thf(587,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
thf(588,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
thf(589,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
thf(590,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/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
thf(591,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
thf(592,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
thf(593,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
thf(594,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
thf(595,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
thf(596,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
thf(597,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
thf(598,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
thf(599,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_1) ).
thf(600,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_2) ).
thf(601,axiom,
! [T_a: $i,V_d: $i,V_x: $i,V_t: $i,V_k: $i,V_D: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
thf(602,axiom,
! [T_a: $i,V_d: $i,V_x: $i,V_k: $i,V_D: $i,V_t: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
thf(603,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
thf(604,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).
thf(605,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_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(606,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
thf(607,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).
thf(608,axiom,
! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).
thf(609,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
thf(610,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
thf(611,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
thf(612,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/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
thf(613,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(614,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(615,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
thf(616,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
thf(617,axiom,
! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
thf(618,axiom,
! [V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ tc_nat ) @ tc_nat ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
thf(619,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
thf(620,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
thf(621,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
thf(622,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
thf(623,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
thf(624,axiom,
! [V_b: $i,V_q: $i,V_c: $i,V_r: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Omod @ V_q @ V_c @ tc_nat ) @ tc_nat ) @ V_r @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_r @ V_b @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_c @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
thf(625,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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).
thf(626,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/sandbox2/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).
thf(627,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(628,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
thf(629,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
thf(630,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
thf(631,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
thf(632,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(633,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(634,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/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
thf(635,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
thf(636,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
thf(637,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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
thf(638,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(639,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(640,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
thf(641,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(642,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
thf(643,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
thf(644,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) )
= V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
thf(645,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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 ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
thf(646,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(647,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
thf(648,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(649,axiom,
! [V_x: $i,V_c: $i,V_d: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).
thf(650,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).
thf(651,axiom,
! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
thf(652,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
thf(653,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
thf(654,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(655,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(656,axiom,
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__is__1_4) ).
thf(657,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/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
thf(658,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
thf(659,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
thf(660,axiom,
! [V_j: $i,V_k: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_m @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_j ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
thf(661,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(662,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(663,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
thf(664,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
thf(665,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
thf(666,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
thf(667,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
thf(668,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
thf(669,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T_a )
| ( c_lessequals @ ( 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 ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
thf(670,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(671,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(672,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
thf(673,axiom,
! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
thf(674,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
thf(675,axiom,
! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
thf(676,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
thf(677,axiom,
! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_x @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
thf(678,axiom,
! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_i @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
thf(679,axiom,
! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_m @ tc_nat ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).
thf(680,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).
thf(681,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
thf(682,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(683,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(684,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(685,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(686,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(687,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(688,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
thf(689,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
thf(690,axiom,
! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
thf(691,axiom,
! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
thf(692,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
thf(693,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
thf(694,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).
thf(695,axiom,
! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).
thf(696,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(697,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
thf(698,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
thf(699,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
thf(700,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
thf(701,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/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(702,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(703,axiom,
! [V_x: $i,V_a: $i] :
( ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ tc_nat ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(704,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(705,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
thf(706,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
thf(707,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
thf(708,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
thf(709,axiom,
! [V_j: $i,V_i: $i,V_u: $i,V_m: $i] :
( ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).
thf(710,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0R_0) ).
thf(711,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__0L_0) ).
thf(712,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(713,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(714,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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/sandbox2/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(715,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(716,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(717,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
thf(718,axiom,
! [V_xa: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_xa @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
thf(719,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat )
= V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).
thf(720,axiom,
! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_m
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).
thf(721,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/sandbox2/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
thf(722,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/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
thf(723,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/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
thf(724,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/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
thf(725,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(726,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(727,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(728,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(729,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
thf(730,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
thf(731,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
thf(732,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
thf(733,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
thf(734,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
thf(735,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
thf(736,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
thf(737,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
thf(738,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
thf(739,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
thf(740,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
thf(741,axiom,
! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
thf(742,axiom,
! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
thf(743,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/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
thf(744,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
thf(745,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
thf(746,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
thf(747,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
thf(748,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/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
thf(749,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(750,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(751,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(752,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(753,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(754,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(755,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
thf(756,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
thf(757,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
thf(758,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
thf(759,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
thf(760,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/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).
thf(761,axiom,
! [V_m: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ ( c_Suc @ V_j ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
thf(762,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
thf(763,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
thf(764,axiom,
! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).
thf(765,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__pos__nat_0) ).
thf(766,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).
thf(767,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).
thf(768,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 )
= V_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
thf(769,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(770,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).
thf(771,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(772,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).
thf(773,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).
thf(774,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/sandbox2/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).
thf(775,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).
thf(776,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).
thf(777,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/sandbox2/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).
thf(778,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(779,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(780,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(781,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
thf(782,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(783,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
thf(784,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
thf(785,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
thf(786,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/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
thf(787,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).
thf(788,axiom,
! [V_j: $i,V_i: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).
thf(789,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
thf(790,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(791,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(792,axiom,
c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).
thf(793,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
thf(794,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
thf(795,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
thf(796,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
thf(797,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
thf(798,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(799,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[798]) ).
thf(800,negated_conjecture,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ v_i @ v_k @ tc_nat ) @ v_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(801,plain,
$false = $false,
inference(unfold_def,[status(thm)],[799]) ).
thf(802,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(803,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(804,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(805,plain,
( ( class_Ring__and__Field_Odvd @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(806,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(807,plain,
( ( class_Divides_Osemiring__div @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(808,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(809,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(810,plain,
( ( class_Ring__and__Field_Omult__mono @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(811,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(812,plain,
( ( class_Ring__and__Field_Omult__mono1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(813,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(814,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(815,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(816,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(817,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(818,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(819,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(820,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(821,plain,
( ( class_Ring__and__Field_Oordered__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(822,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(823,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(824,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(825,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(826,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(827,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(828,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(829,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(830,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(831,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(832,plain,
( ( c_HOL_Oord__class_Oless @ v_i @ v_n @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(833,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(834,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(835,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(836,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(837,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(838,plain,
( ( c_HOL_Oord__class_Oless @ v_i @ v_n @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(839,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(840,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(841,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(842,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(843,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(844,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(845,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(846,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(847,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(848,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(849,plain,
( ( ! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(850,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(851,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(852,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(853,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(854,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(855,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(856,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(857,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(858,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(859,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(860,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(861,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(862,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(863,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(864,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(865,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(866,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(867,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(868,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(869,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_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(870,plain,
( ( ! [V_x: $i,V_y: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(871,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(872,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= V_m )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(873,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[72]) ).
thf(874,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(875,plain,
( ( ! [T_a: $i,V_a: $i,V_r: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_r @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(876,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(877,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(878,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(879,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(880,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(881,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( 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)],[80]) ).
thf(882,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(883,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(884,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(885,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(886,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(887,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(888,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(889,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(890,plain,
( ( ! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(891,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(892,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(893,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(894,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(895,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Ominus__class_Ominus @ 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)],[94]) ).
thf(896,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(897,plain,
( ( ! [V_m: $i,V_i: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_i @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(898,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(899,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(900,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(901,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(902,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(903,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(904,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(905,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(906,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(907,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(908,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(909,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(910,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(911,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(912,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(913,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(914,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(915,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(916,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(917,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(918,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(919,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(920,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[119]) ).
thf(921,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(922,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(923,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(924,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(925,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(926,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(927,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(928,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(929,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(930,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(931,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_l @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(932,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(933,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(934,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)],[133]) ).
thf(935,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)],[134]) ).
thf(936,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(937,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)],[136]) ).
thf(938,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(939,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(940,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(941,plain,
( ( ! [V_k: $i,V_n: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(942,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( 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_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(943,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( 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_Otimes__class_Otimes @ V_c @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(944,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[143]) ).
thf(945,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[144]) ).
thf(946,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[145]) ).
thf(947,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[146]) ).
thf(948,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(949,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(950,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(951,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(952,plain,
( ( ! [V_d: $i,V_x: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_d @ V_x @ tc_nat ) @ V_d @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(953,plain,
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(954,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)],[153]) ).
thf(955,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(956,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(957,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(958,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(959,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(960,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(961,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(962,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(963,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(964,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(965,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(966,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)],[165]) ).
thf(967,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(968,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[167]) ).
thf(969,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(970,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)],[169]) ).
thf(971,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
= V_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(972,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
= V_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(973,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(974,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(975,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(976,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(977,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(978,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(979,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(980,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(981,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(982,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(983,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(984,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(985,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(986,plain,
( ( ! [V_x: $i,V_n: $i,V_xa: $i,V_y: $i,V_xb: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_xa @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_xb @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ V_y @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(987,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(988,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(989,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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(990,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(991,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ 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)],[190]) ).
thf(992,plain,
( ( ! [V_i: $i,V_j: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_j
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(993,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(994,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(995,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(996,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(997,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(998,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(999,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(1000,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(1001,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(1002,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(1003,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_x @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(1004,plain,
( ( ! [V_k: $i,V_x: $i] : ( c_lessequals @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_x @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(1005,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(1006,plain,
( ( ! [V_i: $i,V_k: $i] :
( ~ ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_i @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_i @ tc_nat ) @ V_i @ tc_nat )
= V_k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(1007,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(1008,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)],[207]) ).
thf(1009,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)],[208]) ).
thf(1010,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)],[209]) ).
thf(1011,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)],[210]) ).
thf(1012,plain,
( ( ! [V_k: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(1013,plain,
( ( ! [V_k: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(1014,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_y @ T_a ) @ V_x @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(1015,plain,
( ( ! [V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ V_m @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(1016,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(1017,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)],[216]) ).
thf(1018,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)],[217]) ).
thf(1019,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)],[218]) ).
thf(1020,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)],[219]) ).
thf(1021,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)],[220]) ).
thf(1022,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)],[221]) ).
thf(1023,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)],[222]) ).
thf(1024,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)],[223]) ).
thf(1025,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)],[224]) ).
thf(1026,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)],[225]) ).
thf(1027,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)],[226]) ).
thf(1028,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)],[227]) ).
thf(1029,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)],[228]) ).
thf(1030,plain,
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(1031,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)],[230]) ).
thf(1032,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)],[231]) ).
thf(1033,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(1034,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(1035,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(1036,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(1037,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(1038,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(1039,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(1040,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(1041,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(1042,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(1043,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(1044,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(1045,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(1046,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_c @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(1047,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(1049,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(1050,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(1051,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(1052,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(1053,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(1055,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(1056,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(1057,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(1058,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(1059,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(1060,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(1061,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(1062,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(1063,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(1064,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(1065,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(1066,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(1067,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(1068,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(1069,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_r @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(1071,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(1072,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(1073,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(1074,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(1075,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(1076,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(1077,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(1078,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(1080,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(1081,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(1082,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(1085,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(1086,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(1087,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(1088,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(1089,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(1090,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(1091,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(1092,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(1093,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(1097,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(1098,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[297]) ).
thf(1099,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[298]) ).
thf(1100,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(1101,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(1102,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(1104,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1105,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(1106,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(1107,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1108,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(1110,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(1111,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(1113,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1114,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1116,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)],[315]) ).
thf(1117,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)],[316]) ).
thf(1118,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(1119,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(1122,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(1123,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(1124,plain,
( ( ! [V_x: $i] :
( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(1125,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(1126,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(1128,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(1131,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1134,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)],[333]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(1137,plain,
( ( ! [V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(1138,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) @ tc_nat ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(1139,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ V_m @ tc_nat ) ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1140,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)],[339]) ).
thf(1141,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1142,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(1143,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1144,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1145,plain,
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(1146,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( c_lessequals @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1147,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
| ~ ( c_lessequals @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1148,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1149,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1150,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1151,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1152,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_n: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1155,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(1156,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(1159,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1160,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1163,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(1164,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1165,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)],[364]) ).
thf(1166,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)],[365]) ).
thf(1167,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)],[366]) ).
thf(1168,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1169,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1170,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(1171,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1172,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(1174,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(1175,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)],[374]) ).
thf(1176,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)],[375]) ).
thf(1177,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( 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)],[376]) ).
thf(1178,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1179,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(1180,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1181,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(1182,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)],[381]) ).
thf(1183,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)],[382]) ).
thf(1184,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)],[383]) ).
thf(1185,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)],[384]) ).
thf(1186,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(1187,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1188,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ 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_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1189,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1190,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1191,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1192,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_d @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1193,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1195,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1196,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1197,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1198,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1199,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1200,plain,
( ( ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1201,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1202,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1203,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1204,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1205,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1206,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ V_u @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a )
= V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1207,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1208,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(1209,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(1210,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1211,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)],[410]) ).
thf(1212,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1213,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1214,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1215,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1216,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1217,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1218,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1219,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)],[418]) ).
thf(1220,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)],[419]) ).
thf(1221,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1222,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1223,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1224,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1225,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1226,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1227,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1228,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1229,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1230,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1231,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1232,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1233,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)],[432]) ).
thf(1234,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)],[433]) ).
thf(1235,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)],[434]) ).
thf(1236,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1237,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(1238,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1239,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1240,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1241,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1242,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1243,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1244,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1245,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1246,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1247,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1248,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1249,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1250,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1251,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1252,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1253,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1254,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1255,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1256,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1257,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1258,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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)],[457]) ).
thf(1259,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1260,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1261,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1262,plain,
( ( ! [V_m: $i] :
( ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1263,plain,
( ( ! [V_x: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ V_x ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1264,plain,
( ( ! [V_x: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1265,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1266,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1267,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1268,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1269,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1270,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1271,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1272,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1273,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1274,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1275,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 )
= V_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1276,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) )
!= V_n )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1277,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1278,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1279,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1280,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1281,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1282,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1283,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1284,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1285,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1286,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1287,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1288,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1289,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1290,plain,
( ( ! [V_i: $i,V_u: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1291,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1292,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1293,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1294,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1295,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1296,plain,
( ( ! [V_x: $i] :
( ( V_x
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1297,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1298,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( 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)],[497]) ).
thf(1299,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1300,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(1301,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500]) ).
thf(1302,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1303,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1304,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(1305,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( 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)],[504]) ).
thf(1306,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( 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)],[505]) ).
thf(1307,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1308,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[507]) ).
thf(1309,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 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1310,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1311,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1312,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1313,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1314,plain,
( ( ! [V_xa: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_xa @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1315,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1316,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1317,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1318,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1319,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1320,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1321,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1322,plain,
( ( ! [V_k: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_k @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1323,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1324,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1325,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1326,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1327,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1328,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1329,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1330,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1331,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1332,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1333,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1334,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1335,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1336,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1337,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1338,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ tc_nat ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1339,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1340,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1341,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1342,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)],[541]) ).
thf(1343,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1344,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1345,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1346,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_Oplus__class_Oplus @ V_b @ V_c @ 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)],[545]) ).
thf(1347,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[546]) ).
thf(1348,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[547]) ).
thf(1349,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1350,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1351,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1352,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1353,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1354,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1355,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1356,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1357,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1358,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_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1359,plain,
( ( ! [V_x: $i,V_y: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1360,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1361,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1362,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1363,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1364,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(1365,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1366,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1367,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1368,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1369,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1370,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1371,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1372,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1373,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1374,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1375,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1376,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[575]) ).
thf(1377,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_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1378,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1379,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[578]) ).
thf(1380,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1381,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1382,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1383,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1384,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[583]) ).
thf(1385,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)],[584]) ).
thf(1386,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)],[585]) ).
thf(1387,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)],[586]) ).
thf(1388,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)],[587]) ).
thf(1389,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)],[588]) ).
thf(1390,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)],[589]) ).
thf(1391,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)],[590]) ).
thf(1392,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1393,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1394,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1395,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1396,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1397,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1398,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1399,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1400,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1401,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1402,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_t: $i,V_k: $i,V_D: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1403,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_k: $i,V_D: $i,V_t: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1404,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1405,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(1406,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_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[605]) ).
thf(1407,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1408,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1409,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1410,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1411,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1412,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1413,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)],[612]) ).
thf(1414,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(1415,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1416,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1417,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1418,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(1419,plain,
( ( ! [V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ tc_nat ) @ tc_nat ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(1420,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(1421,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1422,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1423,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1424,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1425,plain,
( ( ! [V_b: $i,V_q: $i,V_c: $i,V_r: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Omod @ V_q @ V_c @ tc_nat ) @ tc_nat ) @ V_r @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_r @ V_b @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_c @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(1426,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)],[625]) ).
thf(1427,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)],[626]) ).
thf(1428,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1429,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)],[628]) ).
thf(1430,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)],[629]) ).
thf(1431,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)],[630]) ).
thf(1432,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)],[631]) ).
thf(1433,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1434,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633]) ).
thf(1435,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)],[634]) ).
thf(1436,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(1437,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)],[636]) ).
thf(1438,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)],[637]) ).
thf(1439,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[638]) ).
thf(1440,plain,
( ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[639]) ).
thf(1441,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)],[640]) ).
thf(1442,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[641]) ).
thf(1443,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1444,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(1445,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) )
= V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(1446,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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 ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(1447,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(1448,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1449,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1450,plain,
( ( ! [V_x: $i,V_c: $i,V_d: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1451,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1452,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1453,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(1454,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1455,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( 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)],[654]) ).
thf(1456,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1457,plain,
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(1458,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)],[657]) ).
thf(1459,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)],[658]) ).
thf(1460,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)],[659]) ).
thf(1461,plain,
( ( ! [V_j: $i,V_k: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_m @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_j ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1462,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(1463,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1464,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(1465,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(1466,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(1467,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(1468,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(1469,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(1470,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T_a )
| ( c_lessequals @ ( 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 ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(1471,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(1472,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(1473,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1474,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(1475,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(1476,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(1477,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1478,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_x @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1479,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_i @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(1480,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_m @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(1481,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(1482,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(1483,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(1484,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(1485,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(1486,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(1487,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(1488,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(1489,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(1490,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1491,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(1492,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(1493,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(1494,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(1495,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(1496,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(1497,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(1498,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(1499,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(1500,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(1501,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(1502,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)],[701]) ).
thf(1503,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(1504,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ tc_nat ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(1505,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(1506,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[705]) ).
thf(1507,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[706]) ).
thf(1508,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[707]) ).
thf(1509,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[708]) ).
thf(1510,plain,
( ( ! [V_j: $i,V_i: $i,V_u: $i,V_m: $i] :
( ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(1511,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[710]) ).
thf(1512,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(1513,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ 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)],[712]) ).
thf(1514,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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)],[713]) ).
thf(1515,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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)],[714]) ).
thf(1516,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(1517,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(1518,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(1519,plain,
( ( ! [V_xa: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_xa @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[718]) ).
thf(1520,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat )
= V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(1521,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_m
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(1522,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)],[721]) ).
thf(1523,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)],[722]) ).
thf(1524,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)],[723]) ).
thf(1525,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)],[724]) ).
thf(1526,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(1527,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[726]) ).
thf(1528,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[727]) ).
thf(1529,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[728]) ).
thf(1530,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[729]) ).
thf(1531,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[730]) ).
thf(1532,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[731]) ).
thf(1533,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[732]) ).
thf(1534,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[733]) ).
thf(1535,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[734]) ).
thf(1536,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[735]) ).
thf(1537,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[736]) ).
thf(1538,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[737]) ).
thf(1539,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[738]) ).
thf(1540,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[739]) ).
thf(1541,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[740]) ).
thf(1542,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[741]) ).
thf(1543,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[742]) ).
thf(1544,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)],[743]) ).
thf(1545,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[744]) ).
thf(1546,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[745]) ).
thf(1547,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[746]) ).
thf(1548,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(1549,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)],[748]) ).
thf(1550,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[749]) ).
thf(1551,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[750]) ).
thf(1552,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[751]) ).
thf(1553,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[752]) ).
thf(1554,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[753]) ).
thf(1555,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[754]) ).
thf(1556,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[755]) ).
thf(1557,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[756]) ).
thf(1558,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[757]) ).
thf(1559,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)],[758]) ).
thf(1560,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)],[759]) ).
thf(1561,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)],[760]) ).
thf(1562,plain,
( ( ! [V_m: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ ( c_Suc @ V_j ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(1563,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)],[762]) ).
thf(1564,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)],[763]) ).
thf(1565,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(1566,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(1567,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)],[766]) ).
thf(1568,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)],[767]) ).
thf(1569,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 )
= V_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(1570,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(1571,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)],[770]) ).
thf(1572,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(1573,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)],[772]) ).
thf(1574,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)],[773]) ).
thf(1575,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)],[774]) ).
thf(1576,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)],[775]) ).
thf(1577,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)],[776]) ).
thf(1578,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)],[777]) ).
thf(1579,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[778]) ).
thf(1580,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[779]) ).
thf(1581,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1582,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1583,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[782]) ).
thf(1584,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(1585,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)],[784]) ).
thf(1586,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)],[785]) ).
thf(1587,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)],[786]) ).
thf(1588,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(1589,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[788]) ).
thf(1590,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(1591,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[790]) ).
thf(1592,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[791]) ).
thf(1593,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[792]) ).
thf(1594,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[793]) ).
thf(1595,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[794]) ).
thf(1596,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[795]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[796]) ).
thf(1598,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[797]) ).
thf(1599,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ v_i @ v_k @ tc_nat ) @ v_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[800]) ).
thf(1600,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[801]) ).
thf(1601,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ v_i @ v_k @ tc_nat ) @ v_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1599]) ).
thf(1602,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(1603,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(1604,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1596]) ).
thf(1605,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1595]) ).
thf(1606,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1594]) ).
thf(1607,plain,
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1593]) ).
thf(1608,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1592]) ).
thf(1609,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1591]) ).
thf(1610,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1590]) ).
thf(1611,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(1612,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(1613,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)],[1587]) ).
thf(1614,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)],[1586]) ).
thf(1615,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)],[1585]) ).
thf(1616,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1584]) ).
thf(1617,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(1618,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1582]) ).
thf(1619,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1581]) ).
thf(1620,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1580]) ).
thf(1621,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1579]) ).
thf(1622,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)],[1578]) ).
thf(1623,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)],[1577]) ).
thf(1624,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)],[1576]) ).
thf(1625,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)],[1575]) ).
thf(1626,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)],[1574]) ).
thf(1627,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)],[1573]) ).
thf(1628,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1572]) ).
thf(1629,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)],[1571]) ).
thf(1630,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(1631,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 )
= V_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(1632,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)],[1568]) ).
thf(1633,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)],[1567]) ).
thf(1634,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1566]) ).
thf(1635,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1565]) ).
thf(1636,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)],[1564]) ).
thf(1637,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)],[1563]) ).
thf(1638,plain,
( ( ! [V_m: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ ( c_Suc @ V_j ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1562]) ).
thf(1639,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)],[1561]) ).
thf(1640,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)],[1560]) ).
thf(1641,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)],[1559]) ).
thf(1642,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(1643,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1557]) ).
thf(1644,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(1645,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1555]) ).
thf(1646,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(1647,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1553]) ).
thf(1648,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(1649,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1551]) ).
thf(1650,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1550]) ).
thf(1651,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)],[1549]) ).
thf(1652,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(1653,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1547]) ).
thf(1654,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1546]) ).
thf(1655,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ 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 ) )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(1656,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)],[1544]) ).
thf(1657,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1543]) ).
thf(1658,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1542]) ).
thf(1659,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(1660,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(1661,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1539]) ).
thf(1662,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1538]) ).
thf(1663,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1537]) ).
thf(1664,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(1665,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1535]) ).
thf(1666,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(1667,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1533]) ).
thf(1668,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(1669,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1531]) ).
thf(1670,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1530]) ).
thf(1671,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1529]) ).
thf(1672,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1528]) ).
thf(1673,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1527]) ).
thf(1674,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1526]) ).
thf(1675,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)],[1525]) ).
thf(1676,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)],[1524]) ).
thf(1677,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)],[1523]) ).
thf(1678,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)],[1522]) ).
thf(1679,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_m
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1521]) ).
thf(1680,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat )
= V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1520]) ).
thf(1681,plain,
( ( ! [V_xa: $i] : ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_xa @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1519]) ).
thf(1682,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1518]) ).
thf(1683,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1517]) ).
thf(1684,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1516]) ).
thf(1685,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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)],[1515]) ).
thf(1686,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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)],[1514]) ).
thf(1687,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ 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)],[1513]) ).
thf(1688,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(1689,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(1690,plain,
( ( ! [V_j: $i,V_i: $i,V_u: $i,V_m: $i] :
( ~ ( c_lessequals @ V_j @ V_i @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(1691,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1509]) ).
thf(1692,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1508]) ).
thf(1693,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1507]) ).
thf(1694,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1506]) ).
thf(1695,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1505]) ).
thf(1696,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_a @ tc_nat ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1504]) ).
thf(1697,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1503]) ).
thf(1698,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)],[1502]) ).
thf(1699,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1501]) ).
thf(1700,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1500]) ).
thf(1701,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1499]) ).
thf(1702,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1498]) ).
thf(1703,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(1704,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(1705,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(1706,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(1707,plain,
( ( ! [T_a: $i,V_k: $i,V_m: $i,V_n: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(1708,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1492]) ).
thf(1709,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1491]) ).
thf(1710,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1490]) ).
thf(1711,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1489]) ).
thf(1712,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1488]) ).
thf(1713,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(1714,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(1715,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1485]) ).
thf(1716,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1484]) ).
thf(1717,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1483]) ).
thf(1718,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(1719,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(1720,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_m @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1480]) ).
thf(1721,plain,
( ( ! [V_i: $i,V_m: $i] : ( c_HOL_Oord__class_Oless @ V_i @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_i @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1479]) ).
thf(1722,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_x @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1478]) ).
thf(1723,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(1724,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1476]) ).
thf(1725,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(1726,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(1727,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1473]) ).
thf(1728,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1472]) ).
thf(1729,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(1730,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ T_a )
| ( c_lessequals @ ( 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 ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(1731,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1469]) ).
thf(1732,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(1733,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(1734,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1466]) ).
thf(1735,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(1736,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1464]) ).
thf(1737,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(1738,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1462]) ).
thf(1739,plain,
( ( ! [V_j: $i,V_k: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) ) @ V_m @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_j ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1461]) ).
thf(1740,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)],[1460]) ).
thf(1741,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)],[1459]) ).
thf(1742,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)],[1458]) ).
thf(1743,plain,
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(1744,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(1745,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( 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)],[1455]) ).
thf(1746,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(1748,plain,
( ( ! [T_a: $i,V_x: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(1749,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1451]) ).
thf(1750,plain,
( ( ! [V_x: $i,V_c: $i,V_d: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_d @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_c @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(1751,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(1752,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(1753,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(1754,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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 ) @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(1755,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) )
= V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(1756,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(1757,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(1758,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[1442]) ).
thf(1759,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)],[1441]) ).
thf(1760,plain,
( ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[1440]) ).
thf(1761,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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)],[1439]) ).
thf(1762,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)],[1438]) ).
thf(1763,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)],[1437]) ).
thf(1764,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(1765,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)],[1435]) ).
thf(1766,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(1767,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(1768,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)],[1432]) ).
thf(1769,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)],[1431]) ).
thf(1770,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)],[1430]) ).
thf(1771,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)],[1429]) ).
thf(1772,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(1773,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)],[1427]) ).
thf(1774,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)],[1426]) ).
thf(1775,plain,
( ( ! [V_b: $i,V_q: $i,V_c: $i,V_r: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ ( c_Divides_Odiv__class_Omod @ V_q @ V_c @ tc_nat ) @ tc_nat ) @ V_r @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_r @ V_b @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_c @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(1776,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(1777,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(1778,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(1779,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(1780,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(1781,plain,
( ( ! [V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ tc_nat ) @ tc_nat ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(1782,plain,
( ( ! [T_a: $i,V_x: $i,V_r: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_c @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_r @ V_d @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_r
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(1783,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(1784,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(1785,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(1786,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(1787,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)],[1413]) ).
thf(1788,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1412]) ).
thf(1789,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1411]) ).
thf(1790,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1410]) ).
thf(1791,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(1792,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(1793,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(1794,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_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[1406]) ).
thf(1795,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(1796,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1404]) ).
thf(1797,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_k: $i,V_D: $i,V_t: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1403]) ).
thf(1798,plain,
( ( ! [T_a: $i,V_d: $i,V_x: $i,V_t: $i,V_k: $i,V_D: $i] :
( ~ ( class_Ring__and__Field_Odvd @ T_a )
| ~ ( class_Ring__and__Field_Ocomm__ring @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_D @ T_a ) @ T_a ) @ V_t @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_d @ V_D @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(1799,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(1800,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(1801,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1399]) ).
thf(1802,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(1803,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1397]) ).
thf(1804,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(1805,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1395]) ).
thf(1806,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1394]) ).
thf(1807,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(1808,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(1809,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)],[1391]) ).
thf(1810,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)],[1390]) ).
thf(1811,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)],[1389]) ).
thf(1812,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)],[1388]) ).
thf(1813,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)],[1387]) ).
thf(1814,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)],[1386]) ).
thf(1815,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)],[1385]) ).
thf(1816,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[1384]) ).
thf(1817,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1383]) ).
thf(1818,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(1819,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1381]) ).
thf(1820,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1380]) ).
thf(1821,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[1379]) ).
thf(1822,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1378]) ).
thf(1823,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_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(1824,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[1376]) ).
thf(1825,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(1826,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(1827,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1373]) ).
thf(1828,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(1829,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1371]) ).
thf(1830,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1370]) ).
thf(1831,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1369]) ).
thf(1832,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1368]) ).
thf(1833,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1367]) ).
thf(1834,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_m @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_m @ T_a ) @ T_a )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_m @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1366]) ).
thf(1835,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1365]) ).
thf(1836,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1364]) ).
thf(1837,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1363]) ).
thf(1838,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ T_a )
| ( c_lessequals @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(1839,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1361]) ).
thf(1840,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1360]) ).
thf(1841,plain,
( ( ! [V_x: $i,V_y: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1359]) ).
thf(1842,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_Oplus__class_Oplus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1358]) ).
thf(1843,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1357]) ).
thf(1844,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1845,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1355]) ).
thf(1846,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1354]) ).
thf(1847,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(1848,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(1849,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(1850,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_m @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1851,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1852,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1348]) ).
thf(1853,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1347]) ).
thf(1854,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_Oplus__class_Oplus @ V_b @ V_c @ 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)],[1346]) ).
thf(1855,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1345]) ).
thf(1856,plain,
( ( ! [V_x: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1857,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1858,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)],[1342]) ).
thf(1859,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1341]) ).
thf(1860,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1861,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1862,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ tc_nat ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(1863,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(1864,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(1865,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1335]) ).
thf(1866,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1867,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1868,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1869,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1331]) ).
thf(1870,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1330]) ).
thf(1871,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1329]) ).
thf(1872,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1328]) ).
thf(1873,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(1874,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(1875,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1325]) ).
thf(1876,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1324]) ).
thf(1877,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1323]) ).
thf(1878,plain,
( ( ! [V_k: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_k @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(1879,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(1880,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(1881,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1319]) ).
thf(1882,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1318]) ).
thf(1883,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1317]) ).
thf(1884,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1316]) ).
thf(1885,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1315]) ).
thf(1886,plain,
( ( ! [V_xa: $i] :
~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_xa @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1314]) ).
thf(1887,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(1888,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(1889,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1311]) ).
thf(1890,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1310]) ).
thf(1891,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 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(1892,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1308]) ).
thf(1893,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1307]) ).
thf(1894,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( 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)],[1306]) ).
thf(1895,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( 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)],[1305]) ).
thf(1896,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1304]) ).
thf(1897,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(1898,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( 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_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(1899,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1301]) ).
thf(1900,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( 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_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(1901,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1299]) ).
thf(1902,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( 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)],[1298]) ).
thf(1903,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1297]) ).
thf(1904,plain,
( ( ! [V_x: $i] :
( ( V_x
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1296]) ).
thf(1905,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_a: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_b @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1906,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(1907,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(1908,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1292]) ).
thf(1909,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_c @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1291]) ).
thf(1910,plain,
( ( ! [V_i: $i,V_u: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1911,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(1912,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(1913,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1914,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1286]) ).
thf(1915,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1285]) ).
thf(1916,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1284]) ).
thf(1917,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1283]) ).
thf(1918,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(1919,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1281]) ).
thf(1920,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1280]) ).
thf(1921,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(1922,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(1923,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(1924,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) )
!= V_n )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(1925,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 )
= V_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1275]) ).
thf(1926,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1274]) ).
thf(1927,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(1928,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(1929,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1271]) ).
thf(1930,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(1931,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_m @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ V_k ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(1932,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(1933,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_y @ T_a ) @ T_a ) @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(1934,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(1935,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(1936,plain,
( ( ! [V_x: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(1937,plain,
( ( ! [V_x: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ V_x ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1938,plain,
( ( ! [V_m: $i] :
( ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1939,plain,
( ( ! [V_m: $i] : ( c_lessequals @ V_m @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1940,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1941,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(1942,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( 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)],[1258]) ).
thf(1943,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(1944,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(1945,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1946,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(1947,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(1948,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(1949,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1950,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(1951,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1952,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1953,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1954,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1955,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1245]) ).
thf(1956,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1244]) ).
thf(1957,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1243]) ).
thf(1958,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1959,plain,
( ( ! [V_k: $i,V_i: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_i @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(1960,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(1961,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1239]) ).
thf(1962,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(1963,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Otimes__class_Otimes @ V_c @ V_b @ T_a ) @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1964,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1965,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)],[1235]) ).
thf(1966,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)],[1234]) ).
thf(1967,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)],[1233]) ).
thf(1968,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1969,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1231]) ).
thf(1970,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1230]) ).
thf(1971,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1972,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1228]) ).
thf(1973,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1974,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ T_a )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1226]) ).
thf(1975,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1225]) ).
thf(1976,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1224]) ).
thf(1977,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(1978,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1979,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1980,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)],[1220]) ).
thf(1981,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)],[1219]) ).
thf(1982,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(1983,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1217]) ).
thf(1984,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1985,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1986,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1987,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1988,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omin @ V_y @ ( c_Orderings_Oord__class_Omin @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1989,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)],[1211]) ).
thf(1990,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1991,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1992,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1993,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1994,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ V_u @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_z @ T_a )
= V_u ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1995,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1996,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1997,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1998,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1999,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(2000,plain,
( ( ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(2001,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_l @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(2002,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(2003,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(2004,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(2005,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(2006,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(2007,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(2008,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_d @ T_a ) @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ T_a ) @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_d @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(2009,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(2010,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(2011,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(2012,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ 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_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(2013,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(2014,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(2015,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)],[1185]) ).
thf(2016,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)],[1184]) ).
thf(2017,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)],[1183]) ).
thf(2018,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)],[1182]) ).
thf(2019,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(2020,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(2021,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a )
= V_d ) ) )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(2022,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) )
| ( V_c
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(2023,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( 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)],[1177]) ).
thf(2024,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)],[1176]) ).
thf(2025,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)],[1175]) ).
thf(2026,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(2027,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(2028,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(2029,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(2030,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(2031,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a )
= ( c_HOL_Oplus__class_Oplus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(2032,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(2033,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)],[1167]) ).
thf(2034,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)],[1166]) ).
thf(2035,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)],[1165]) ).
thf(2036,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_a @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(2037,plain,
( ( ! [T_a: $i,V_x: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(2038,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(2039,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(2040,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(2041,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(2042,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(2043,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omin @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(2044,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(2045,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(2046,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(2047,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(2048,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_n: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(2049,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(2050,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(2051,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(2052,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) )
| ( V_n
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( V_m
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(2053,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
| ~ ( c_lessequals @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(2054,plain,
( ( ! [V_j: $i,V_i: $i,V_k: $i] :
( ( c_lessequals @ V_j @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(2055,plain,
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(2056,plain,
( ( ! [V_i: $i,V_j: $i,V_u: $i,V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(2057,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(2058,plain,
( ( ! [V_m: $i,V_j: $i,V_i: $i,V_u: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(2059,plain,
( ( ! [V_i: $i,V_u: $i,V_m: $i,V_j: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_i @ V_u @ tc_nat ) @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_j @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_u @ tc_nat ) @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(2060,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)],[1140]) ).
thf(2061,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_k @ V_n @ tc_nat ) @ V_m @ tc_nat ) ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(2062,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_d @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ tc_nat ) @ tc_nat ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(2063,plain,
( ( ! [V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(2064,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( 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_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_d @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_c @ T_a ) @ T_a ) )
| ( V_c = V_d )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(2065,plain,
( ( ! [T_a: $i,V_w: $i,V_y: $i,V_x: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_y @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_z @ T_a ) @ T_a )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_w @ V_z @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_y @ T_a ) @ T_a ) )
| ( V_y = V_z )
| ( V_w = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(2066,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)],[1134]) ).
thf(2067,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(2068,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(2069,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(2070,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(2071,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(2072,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1128]) ).
thf(2073,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(2074,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(2075,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(2076,plain,
( ( ! [V_x: $i] :
( V_x
= ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(2077,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Oplus__class_Oplus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(2078,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(2079,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(2080,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(2081,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1119]) ).
thf(2082,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1118]) ).
thf(2083,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)],[1117]) ).
thf(2084,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)],[1116]) ).
thf(2085,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(2086,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1114]) ).
thf(2087,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(2088,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(2089,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(2090,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(2091,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(2092,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(2093,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(2094,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_a @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_c @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(2095,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(2096,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(2097,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(2098,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(2099,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1101]) ).
thf(2100,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(2101,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1099]) ).
thf(2102,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[1098]) ).
thf(2103,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(2104,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(2105,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(2106,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(2107,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(2108,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(2109,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(2110,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(2111,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(2112,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(2113,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(2114,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(2115,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1085]) ).
thf(2116,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(2117,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(2118,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(2119,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(2120,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(2121,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(2122,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(2123,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(2124,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(2125,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1075]) ).
thf(2126,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(2127,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(2128,plain,
( ( ! [T_a: $i,V_c: $i,V_b: $i,V_a: $i,V_e: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1072]) ).
thf(2129,plain,
( ( ! [T_a: $i,V_a: $i,V_e: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(2130,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_e: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_e @ T_a ) @ V_c @ T_a ) @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_e @ T_a ) @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_e @ T_a ) @ V_d @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(2131,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_r: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_r @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_r @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(2132,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_b_H: $i,V_a: $i,V_a_H: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_b_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a )
!= ( c_Divides_Odiv__class_Omod @ V_a_H @ V_c @ T_a ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a_H @ V_b_H @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(2133,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_z @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(2134,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(2135,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1065]) ).
thf(2136,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Oring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) @ ( c_Divides_Odiv__class_Omod @ V_b @ V_c @ T_a ) @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1064]) ).
thf(2137,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(2138,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(2139,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(2140,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_HOL_Ominus__class_Ominus @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(2141,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(2142,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(2143,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(2144,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(2145,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(2146,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(2147,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(2148,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(2149,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(2150,plain,
( ( ! [T_a: $i,V_xa: $i,V_x: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_xa @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_x @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_xa @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(2151,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_b_H: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_b_H @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b_H @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(2152,plain,
( ( ! [T_a: $i,V_a: $i,V_a_H: $i,V_b: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_a_H @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_a_H @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(2153,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_x @ V_ya @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(2154,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_c @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_c @ V_d @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(2155,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(2156,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1044]) ).
thf(2157,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1043]) ).
thf(2158,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(2159,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(2160,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(2161,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(2162,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(2163,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(2164,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(2165,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(2166,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(2167,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(2168,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)],[1032]) ).
thf(2169,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)],[1031]) ).
thf(2170,plain,
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(2171,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)],[1029]) ).
thf(2172,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)],[1028]) ).
thf(2173,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)],[1027]) ).
thf(2174,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)],[1026]) ).
thf(2175,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)],[1025]) ).
thf(2176,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)],[1024]) ).
thf(2177,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)],[1023]) ).
thf(2178,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)],[1022]) ).
thf(2179,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)],[1021]) ).
thf(2180,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)],[1020]) ).
thf(2181,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)],[1019]) ).
thf(2182,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)],[1018]) ).
thf(2183,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)],[1017]) ).
thf(2184,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(2185,plain,
( ( ! [V_m: $i] :
( ( c_Divides_Odiv__class_Omod @ V_m @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(2186,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ V_y @ T_a ) @ V_x @ T_a )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ V_y @ V_x @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(2187,plain,
( ( ! [V_k: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(2188,plain,
( ( ! [V_k: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(2189,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)],[1011]) ).
thf(2190,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)],[1010]) ).
thf(2191,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)],[1009]) ).
thf(2192,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)],[1008]) ).
thf(2193,plain,
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(2194,plain,
( ( ! [V_i: $i,V_k: $i] :
( ~ ( c_lessequals @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_i @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_i @ tc_nat ) @ V_i @ tc_nat )
= V_k ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(2195,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(2196,plain,
( ( ! [V_k: $i,V_x: $i] : ( c_lessequals @ V_k @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_x @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(2197,plain,
( ( ! [V_m: $i,V_x: $i] : ( c_lessequals @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_x @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(2198,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(2199,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(2200,plain,
( ( ! [V_n: $i,V_m: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_n @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(2201,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(2202,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(2203,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(2204,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(2205,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(2206,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(2207,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= V_m )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(2208,plain,
( ( ! [V_i: $i,V_j: $i] :
( ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ( V_j
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(2209,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ 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)],[991]) ).
thf(2210,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_m @ V_n @ 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(2211,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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[989]) ).
thf(2212,plain,
( ( ! [V_j: $i,V_k: $i,V_i: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ V_i @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_i @ tc_nat ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(2213,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(2214,plain,
( ( ! [V_x: $i,V_n: $i,V_xa: $i,V_y: $i,V_xb: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_x @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_xa @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_y @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_xb @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ V_x @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ V_y @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(2215,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(2216,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(2217,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(2218,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ ( 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_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(2219,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(2220,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(2221,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(2222,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(2223,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(2224,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(2225,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_Divides_Odiv__class_Omod @ V_a @ V_c @ T_a ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_c @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(2226,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(2227,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(2228,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
= V_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(2229,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ V_a @ T_a )
= V_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(2230,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)],[970]) ).
thf(2231,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(2232,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_b @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( 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)],[968]) ).
thf(2233,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(2234,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)],[966]) ).
thf(2235,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(2236,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(2237,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(2238,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(2239,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(2240,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(2241,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(2242,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_d @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(2243,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(2244,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(2245,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(2246,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)],[954]) ).
thf(2247,plain,
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(2248,plain,
( ( ! [V_d: $i,V_x: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_d @ V_x @ tc_nat ) @ V_d @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(2249,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_b @ V_a @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(2250,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ V_b @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(2251,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(2252,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(2253,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[947]) ).
thf(2254,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[946]) ).
thf(2255,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[945]) ).
thf(2256,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[944]) ).
thf(2257,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( 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_Otimes__class_Otimes @ V_c @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(2258,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ ( 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_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ V_a @ V_b @ T_a ) @ V_c @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(2259,plain,
( ( ! [V_k: $i,V_n: $i] :
( ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(2260,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oabs__class_Oabs @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(2261,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(2262,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(2263,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)],[937]) ).
thf(2264,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(2265,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)],[935]) ).
thf(2266,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)],[934]) ).
thf(2267,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(2268,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(2269,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_m @ V_l @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(2270,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(2271,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(2272,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(2273,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(2274,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(2275,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(2276,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(2277,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(2278,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(2279,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(2280,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[920]) ).
thf(2281,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(2282,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(2283,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(2284,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(2285,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(2286,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(2287,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oplus__class_Oplus @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(2288,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(2289,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(2290,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_j @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(2291,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(2292,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(2293,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(2294,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(2295,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(2296,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(2297,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(2298,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(2299,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_m @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_k @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(2300,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(2301,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(2302,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(2303,plain,
( ( ! [V_m: $i,V_i: $i,V_n: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_i @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ V_m @ V_n @ tc_nat ) @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(2304,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(2305,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_HOL_Ominus__class_Ominus @ 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)],[895]) ).
thf(2306,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(2307,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(2308,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(2309,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(2310,plain,
( ( ! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(2311,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(2312,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_i @ ( c_HOL_Oplus__class_Oplus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(2313,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(2314,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(2315,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(2316,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(2317,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(2318,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ V_n @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(2319,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Otimes__class_Otimes @ V_k @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( 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)],[881]) ).
thf(2320,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(2321,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_n @ V_m @ tc_nat ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(2322,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(2323,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(2324,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(2325,plain,
( ( ! [T_a: $i,V_a: $i,V_r: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_r @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_a @ T_a ) @ T_a ) @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(2326,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(2327,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[873]) ).
thf(2328,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= V_m )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(2329,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(2330,plain,
( ( ! [V_x: $i,V_y: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ V_x @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ V_y @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(2331,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_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(2332,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(2333,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(2334,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(2335,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(2336,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(2337,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(2338,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(2339,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_Divides_Odiv__class_Omod @ V_m @ V_n @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(2340,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(2341,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(2342,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(2343,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(2344,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(2345,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(2346,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(2347,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(2348,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(2349,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(2350,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(2351,plain,
( ( ! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(2352,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(2353,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(2354,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(2355,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(2356,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(2357,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(2358,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(2359,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(2360,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(2361,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(2362,plain,
( ( c_HOL_Oord__class_Oless @ v_i @ v_n @ tc_nat )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(2363,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(2364,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(2365,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(2366,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(2367,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(2368,plain,
( ( c_HOL_Oord__class_Oless @ v_i @ v_n @ tc_nat )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(2369,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(2370,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(2371,plain,
( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(2372,plain,
( ( class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(2373,plain,
( ( class_Ring__and__Field_Oordered__semiring__strict @ tc_nat )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(2374,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(2375,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(2376,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(2377,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(2378,plain,
( ( class_Ring__and__Field_Opordered__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(2379,plain,
( ( class_Ring__and__Field_Oordered__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(2380,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(2381,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(2382,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(2383,plain,
( ( class_OrderedGroup_Oab__semigroup__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(2384,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(2385,plain,
( ( class_Ring__and__Field_Ocomm__semiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(2386,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(2387,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(2388,plain,
( ( class_Ring__and__Field_Omult__mono1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(2389,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(2390,plain,
( ( class_Ring__and__Field_Omult__mono @ tc_nat )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(2391,plain,
( ( class_Ring__and__Field_Osemiring @ tc_nat )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(2392,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(2393,plain,
( ( class_Divides_Osemiring__div @ tc_nat )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(2394,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(2395,plain,
( ( class_Ring__and__Field_Odvd @ tc_nat )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(2396,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(2397,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(2398,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(2399,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1600]) ).
thf(2400,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX2 @ tc_nat ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1861]) ).
thf(2401,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2203]) ).
thf(2402,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1928]) ).
thf(2403,plain,
( ( ! [SX0: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SX0 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1855]) ).
thf(2404,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX0 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2304]) ).
thf(2405,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SX0 ) @ SX1 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SX0 ) @ SX2 @ tc_nat ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1793]) ).
thf(2406,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1783]) ).
thf(2407,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1863]) ).
thf(2408,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SX3 @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ SX0 @ SX1 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SX3 @ SX1 @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2214]) ).
thf(2409,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)],[2263]) ).
thf(2410,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1865]) ).
thf(2411,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1684]) ).
thf(2412,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1985]) ).
thf(2413,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX2 @ SX1 @ SX0 )
| ~ ( c_lessequals @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2139]) ).
thf(2414,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)],[1676]) ).
thf(2415,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX4 @ SX3 @ SX0 )
| ~ ( c_lessequals @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2138]) ).
thf(2416,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2147]) ).
thf(2417,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1785]) ).
thf(2418,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)],[1677]) ).
thf(2419,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1728]) ).
thf(2420,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1984]) ).
thf(2421,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX3 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2366]) ).
thf(2422,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2052]) ).
thf(2423,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2149]) ).
thf(2424,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2011]) ).
thf(2425,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1729]) ).
thf(2426,plain,
( ( ! [SX0: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SX0 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1657]) ).
thf(2427,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Oplus__class_Oplus @ SX2 @ SX3 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX2 @ SX4 @ SX0 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1994]) ).
thf(2428,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2051]) ).
thf(2429,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Divides_Osemiring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1979]) ).
thf(2430,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1683]) ).
thf(2431,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)],[1678]) ).
thf(2432,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2204]) ).
thf(2433,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2365]) ).
thf(2434,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX0 ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2064]) ).
thf(2435,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2354]) ).
thf(2436,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1687]) ).
thf(2437,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SX2 @ SX3 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SX2 @ SX1 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SX0 @ SX3 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2269]) ).
thf(2438,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Divides_Oring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ SX4 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX5 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SX5 @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2132]) ).
thf(2439,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1800]) ).
thf(2440,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)],[1698]) ).
thf(2441,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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)],[1685]) ).
thf(2442,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ 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)],[1686]) ).
thf(2443,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SX0 @ SX1 @ tc_nat ) )
!= SX1 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SX0 ) @ SX1 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1924]) ).
thf(2444,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2045]) ).
thf(2445,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)],[2033]) ).
thf(2446,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX2 @ tc_nat ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1862]) ).
thf(2447,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( SX1
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1695]) ).
thf(2448,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1929]) ).
thf(2449,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)],[1675]) ).
thf(2450,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1866]) ).
thf(2451,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX1
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1701]) ).
thf(2452,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)],[2034]) ).
thf(2453,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SX2 @ SX1 @ tc_nat ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1860]) ).
thf(2454,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ SX3 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) @ SX5 @ SX0 ) )
| ( SX3
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 ) @ SX5 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2022]) ).
thf(2455,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)],[2234]) ).
thf(2456,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1696]) ).
thf(2457,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2148]) ).
thf(2458,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1799]) ).
thf(2459,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_Orderings_Oord__class_Omin @ SX1 @ SX2 @ SX0 )
!= SX1 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1992]) ).
thf(2460,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX1 @ tc_nat ) )
| ~ ( c_lessequals @ SX1 @ SX2 @ tc_nat )
| ~ ( c_lessequals @ SX1 @ SX0 @ tc_nat )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2313]) ).
thf(2461,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2044]) ).
thf(2462,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ SX1 @ tc_nat )
!= SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1697]) ).
thf(2463,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) @ SX2 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX1 @ tc_nat ) @ SX4 @ tc_nat ) )
| ~ ( c_lessequals @ SX0 @ SX3 @ tc_nat )
| ( SX2
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX3 @ SX0 @ tc_nat ) @ SX1 @ tc_nat ) @ SX4 @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1679]) ).
thf(2464,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SX0
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1700]) ).
thf(2465,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1786]) ).
thf(2466,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2353]) ).
thf(2467,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Divides_Osemiring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ SX4 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX5 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SX5 @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2049]) ).
thf(2468,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Ring__and__Field_Oring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ SX3 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX2 @ SX0 ) @ SX5 @ SX0 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX1 @ SX4 @ SX0 ) @ SX2 @ SX0 ) @ SX3 @ SX0 )
= SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2021]) ).
thf(2469,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)],[2035]) ).
thf(2470,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 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 @ tc_nat )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1891]) ).
thf(2471,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX3 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) @ tc_nat ) )
| ( SX1 = SX3 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2062]) ).
thf(2472,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX1 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX2 @ SX0 ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1784]) ).
thf(2473,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX4 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX4 @ SX0 ) @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX2 @ SX0 ) @ SX0 ) )
| ( SX2 = SX4 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2065]) ).
thf(2474,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ~ ( class_Divides_Osemiring__div @ SX0 )
| ( ( c_Divides_Odiv__class_Omod @ SX1 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX3 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ SX4 @ SX2 @ SX0 )
!= ( c_Divides_Odiv__class_Omod @ SX5 @ SX2 @ SX0 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SX4 @ SX1 @ SX0 ) @ SX2 @ SX0 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SX5 @ SX3 @ SX0 ) @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2067]) ).
thf(2475,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX2 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SX0 @ ( c_HOL_Otimes__class_Otimes @ SX1 @ SX3 @ tc_nat ) @ tc_nat ) )
| ( SX2 = SX3 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1781]) ).
thf(2476,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1864]) ).
thf(2477,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX3 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX1 @ tc_nat ) @ tc_nat ) )
| ( SX1 = SX3 )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2063]) ).
thf(2478,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX0 @ SX1 @ tc_nat ) @ SX2 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SX3 @ SX1 @ tc_nat ) @ SX4 @ tc_nat ) )
| ~ ( c_lessequals @ SX3 @ SX0 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SX0 @ SX3 @ tc_nat ) @ SX1 @ tc_nat ) @ SX2 @ tc_nat )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1680]) ).
thf(2479,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX3 @ SX0 ) @ SX0 )
!= ( c_HOL_Oplus__class_Oplus @ SX1 @ ( c_HOL_Otimes__class_Otimes @ SX2 @ SX4 @ SX0 ) @ SX0 ) )
| ( SX3 = SX4 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1782]) ).
thf(2480,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ v_i @ v_k @ tc_nat ) @ v_n @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(2481,plain,
! [SV1: $i] :
( ( ! [SY2225: $i,SY2226: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SY2225 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SY2226 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SY2226 @ SY2225 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2482,plain,
! [SV2: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SY2227 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SY2228 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SY2227 @ SY2228 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2483,plain,
! [SV3: $i] :
( ( ! [SY2229: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV3 ) @ SY2229 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY2229 @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SY2229 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2484,plain,
! [SV4: $i] :
( ( ! [SY2230: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV4 @ ( c_Suc @ SY2230 ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV4 @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SY2230 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2485,plain,
! [SV5: $i] :
( ( ! [SY2231: $i,SY2232: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV5 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2231 @ SY2231 @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SY2232 @ SY2232 @ SV5 ) @ SV5 ) @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2486,plain,
! [SV6: $i] :
( ( ! [SY2233: $i,SY2234: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2233 @ SY2234 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_lessequals @ SY2234 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SY2233 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2487,plain,
! [SV7: $i] :
( ( ! [SY2235: $i,SY2236: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2235 @ SY2236 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SY2236 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SY2235 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2488,plain,
! [SV8: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV8 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2489,plain,
! [SV9: $i] :
( ( ! [SY2237: $i,SY2238: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV9 @ SY2237 @ tc_nat ) @ SY2238 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV9 @ SY2238 @ tc_nat ) @ SY2237 @ tc_nat ) )
| ~ ( c_lessequals @ SY2238 @ SV9 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2490,plain,
! [SV10: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV10 @ SY2239 @ tc_nat ) @ SY2240 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV10 @ ( c_HOL_Ominus__class_Ominus @ SY2239 @ SY2240 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2240 @ SY2239 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2491,plain,
! [SV11: $i] :
( ( ! [SY2241: $i,SY2242: $i,SY2243: $i,SY2244: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2241 @ SY2242 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SY2243 @ SY2244 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2241 @ SY2243 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SY2242 @ SY2244 @ SV11 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2492,plain,
! [SV12: $i] :
( ( ! [SY2245: $i,SY2246: $i,SY2247: $i,SY2248: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2245 @ SY2246 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SY2247 @ SY2248 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SY2245 @ ( c_HOL_Otimes__class_Otimes @ SY2246 @ ( c_HOL_Otimes__class_Otimes @ SY2247 @ SY2248 @ SV12 ) @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2493,plain,
! [SV13: $i] :
( ( ! [SY2249: $i,SY2250: $i,SY2251: $i,SY2252: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2249 @ SY2250 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SY2251 @ SY2252 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SY2251 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2249 @ SY2250 @ SV13 ) @ SY2252 @ SV13 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2494,plain,
! [SV14: $i] :
( ( ! [SY2253: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV14 )
| ( SY2253
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SY2253 @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2495,plain,
! [SV15: $i] :
( ( ! [SY2254: $i] :
( ~ ( class_Orderings_Olinorder @ SV15 )
| ( ( c_Orderings_Oord__class_Omin @ SY2254 @ SY2254 @ SV15 )
= SY2254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2496,plain,
! [SV16: $i] :
( ( ! [SY2255: $i,SY2256: $i,SY2257: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
| ( c_lessequals @ SY2255 @ ( c_HOL_Oplus__class_Oplus @ SY2256 @ ( c_HOL_Oabs__class_Oabs @ SY2257 @ SV16 ) @ SV16 ) @ SV16 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2255 @ SY2257 @ SV16 ) @ SY2256 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2497,plain,
! [SV17: $i] :
( ( ( SV17
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV17 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2498,plain,
! [SV18: $i] :
( ( ! [SY2258: $i,SY2259: $i] :
( ~ ( class_Orderings_Oorder @ SV18 )
| ( SY2258 = SY2259 )
| ~ ( c_lessequals @ SY2259 @ SY2258 @ SV18 )
| ~ ( c_lessequals @ SY2258 @ SY2259 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2499,plain,
! [SV19: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ~ ( class_Orderings_Oorder @ SV19 )
| ( SY2260 = SY2261 )
| ~ ( c_lessequals @ SY2261 @ SY2260 @ SV19 )
| ~ ( c_lessequals @ SY2260 @ SY2261 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2500,plain,
! [SV20: $i] :
( ( ! [SY2262: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SY2262 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2262 @ SV20 @ tc_nat )
| ( SY2262 = SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2501,plain,
! [SV21: $i] :
( ( ! [SY2263: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SY2263 @ tc_nat )
| ( SY2263 = SV21 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2263 @ SV21 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2502,plain,
! [SV22: $i] :
( ( ! [SY2264: $i] :
( ( SV22 = SY2264 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV22 @ SY2264 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2264 @ SV22 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2503,plain,
! [SV23: $i] :
( ( ! [SY2265: $i] :
( ( SV23 = SY2265 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2265 @ SV23 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV23 @ SY2265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2504,plain,
! [SV24: $i] :
( ( ! [SY2266: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV24 @ SY2266 @ tc_nat )
| ( SY2266 = SV24 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2266 @ SV24 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2505,plain,
! [SV25: $i] :
( ( ! [SY2267: $i] :
( ( SV25 = SY2267 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2267 @ SV25 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV25 @ SY2267 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2506,plain,
! [SV26: $i] :
( ( ! [SY2268: $i] :
( ( SV26 = SY2268 )
| ~ ( c_lessequals @ SY2268 @ SV26 @ tc_nat )
| ~ ( c_lessequals @ SV26 @ SY2268 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2507,plain,
! [SV27: $i] :
( ( ! [SY2269: $i] :
( ( SV27 = SY2269 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2269 @ SV27 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV27 @ SY2269 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2508,plain,
! [SV28: $i] :
( ( ! [SY2270: $i,SY2271: $i] :
( ~ ( class_Orderings_Oorder @ SV28 )
| ( SY2270 = SY2271 )
| ~ ( c_lessequals @ SY2270 @ SY2271 @ SV28 )
| ~ ( c_lessequals @ SY2271 @ SY2270 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2509,plain,
! [SV29: $i] :
( ( ! [SY2272: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV29 )
| ( ( c_HOL_Oabs__class_Oabs @ SY2272 @ SV29 )
= SY2272 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SY2272 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2510,plain,
! [SV30: $i] :
( ( ! [SY2273: $i,SY2274: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SY2273 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2274 @ SY2273 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SY2274 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2511,plain,
! [SV31: $i] :
( ( ! [SY2275: $i,SY2276: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SY2275 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2275 @ SY2276 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2276 @ SY2275 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2276 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SY2276 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2512,plain,
! [SV32: $i] :
( ( ! [SY2277: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV32 @ SY2277 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2277 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2513,plain,
! [SV33: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV33 @ SV33 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2514,plain,
! [SV34: $i] :
( ( ! [SY2278: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV34 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2278 @ SY2278 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2515,plain,
! [SV35: $i] :
( ( ! [SY2279: $i,SY2280: $i,SY2281: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2279 @ SY2280 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2281 @ SY2280 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2279 @ SY2281 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2516,plain,
! [SV36: $i] :
( ( ! [SY2282: $i,SY2283: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV36 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SY2282 @ SY2283 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SY2283 @ tc_nat ) @ ( c_Suc @ SY2282 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2283 @ SY2282 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2517,plain,
! [SV37: $i] :
( ( ! [SY2284: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV37 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2284 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2518,plain,
! [SV38: $i] :
( ( ! [SY2285: $i,SY2286: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV38 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SY2285 @ SV38 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SY2286 @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2519,plain,
! [SV39: $i] :
( ( ! [SY2287: $i,SY2288: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV39 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2287 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ ( c_HOL_Otimes__class_Otimes @ SY2288 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2520,plain,
! [SV40: $i] :
( ( ! [SY2289: $i,SY2290: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SY2289 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SY2290 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2289 @ SY2290 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2521,plain,
! [SV41: $i] :
( ( ! [SY2291: $i,SY2292: $i] :
( ( c_lessequals @ SV41 @ SY2291 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2292 @ SV41 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2292 @ SY2291 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2522,plain,
! [SV42: $i] :
( ( ! [SY2293: $i,SY2294: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV42 @ SY2293 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2294 @ SY2293 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV42 @ SY2294 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2523,plain,
! [SV43: $i] :
( ( ! [SY2295: $i,SY2296: $i,SY2297: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2295 @ SY2296 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SY2295 @ SY2297 @ SV43 ) @ SV43 )
| ~ ( c_lessequals @ SY2296 @ SY2297 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2524,plain,
! [SV44: $i] :
( ( ! [SY2298: $i,SY2299: $i,SY2300: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2298 @ SY2299 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SY2300 @ SY2299 @ SV44 ) @ SV44 )
| ~ ( c_lessequals @ SY2298 @ SY2300 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2525,plain,
! [SV45: $i] :
( ( ! [SY2301: $i,SY2302: $i,SY2303: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
| ( c_lessequals @ SY2301 @ SY2302 @ SV45 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2303 @ SY2301 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SY2303 @ SY2302 @ SV45 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2526,plain,
! [SV46: $i] :
( ( ! [SY2304: $i,SY2305: $i,SY2306: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2304 @ SY2305 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SY2304 @ SY2306 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ SY2305 @ SY2306 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2527,plain,
! [SV47: $i] :
( ( ! [SY2307: $i,SY2308: $i,SY2309: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
| ( c_lessequals @ SY2307 @ SY2308 @ SV47 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2307 @ SY2309 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SY2308 @ SY2309 @ SV47 ) @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2528,plain,
! [SV48: $i] :
( ( ! [SY2310: $i,SY2311: $i,SY2312: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2310 @ SY2311 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SY2312 @ SY2311 @ SV48 ) @ SV48 )
| ~ ( c_lessequals @ SY2310 @ SY2312 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2529,plain,
! [SV49: $i] :
( ( ! [SY2313: $i,SY2314: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV49 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY2313 @ SY2314 @ SV49 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2313 @ SV49 ) @ ( c_HOL_Oabs__class_Oabs @ SY2314 @ SV49 ) @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2530,plain,
! [SV50: $i] :
( ( ! [SY2315: $i,SY2316: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY2315 @ SY2316 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2315 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SY2316 @ SV50 ) @ SV50 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY2316 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY2315 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2531,plain,
! [SV51: $i] :
( ( ! [SY2317: $i,SY2318: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY2317 @ SY2318 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2317 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SY2318 @ SV51 ) @ SV51 ) )
| ~ ( c_lessequals @ SY2318 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SY2317 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2532,plain,
! [SV52: $i] :
( ( ! [SY2319: $i,SY2320: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY2319 @ SY2320 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2319 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SY2320 @ SV52 ) @ SV52 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SY2320 @ SV52 )
| ~ ( c_lessequals @ SY2319 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2533,plain,
! [SV53: $i] :
( ( ! [SY2321: $i,SY2322: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY2321 @ SY2322 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2321 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SY2322 @ SV53 ) @ SV53 ) )
| ~ ( c_lessequals @ SY2322 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
| ~ ( c_lessequals @ SY2321 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2534,plain,
! [SV54: $i] :
( ( ! [SY2323: $i,SY2324: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2323 @ ( c_HOL_Otimes__class_Otimes @ SY2323 @ SY2324 @ SV54 ) @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SY2323 @ SY2324 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2535,plain,
! [SV55: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV55 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV55 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2536,plain,
! [SV56: $i] :
( ( ! [SY2325: $i,SY2326: $i] :
( ~ ( class_Divides_Osemiring__div @ SV56 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2325 @ SY2326 @ SV56 ) @ SY2325 @ SV56 )
= ( c_Divides_Odiv__class_Omod @ SY2326 @ SY2325 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2537,plain,
! [SV57: $i] :
( ( ! [SY2327: $i,SY2328: $i] :
( ~ ( class_Divides_Osemiring__div @ SV57 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2327 @ SY2328 @ SV57 ) @ SY2328 @ SV57 )
= ( c_Divides_Odiv__class_Omod @ SY2327 @ SY2328 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2538,plain,
! [SV58: $i] :
( ( ! [SY2329: $i,SY2330: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
| ( c_lessequals @ SY2329 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SY2329 @ SV58 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2329 @ SY2330 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2539,plain,
! [SV59: $i] :
( ( ! [SY2331: $i,SY2332: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SY2331 @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SY2332 @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2332 @ SY2331 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2540,plain,
! [SV60: $i] :
( ( ! [SY2333: $i,SY2334: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
| ( c_lessequals @ SY2333 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ( c_lessequals @ SY2334 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2333 @ SY2334 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2541,plain,
! [SV61: $i] :
( ( ! [SY2335: $i,SY2336: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SY2335 @ SV61 )
| ( c_lessequals @ SY2335 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2336 @ SY2335 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2542,plain,
! [SV62: $i] :
( ( ! [SY2337: $i,SY2338: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2337 @ SY2338 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SY2338 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SY2337 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2543,plain,
! [SV63: $i] :
( ( ! [SY2339: $i,SY2340: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2339 @ SY2340 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY2340 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SY2339 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2544,plain,
! [SV64: $i] :
( ( ! [SY2341: $i,SY2342: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2341 @ SY2342 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SY2341 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY2342 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2545,plain,
! [SV65: $i] :
( ( ! [SY2343: $i,SY2344: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SY2343 @ SY2344 @ SV65 ) @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SY2344 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SY2343 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2546,plain,
! [SV66: $i] :
( ( ! [SY2345: $i,SY2346: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SY2345 @ SY2346 @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SY2346 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SY2345 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2547,plain,
! [SV67: $i] :
( ( ! [SY2347: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV67 @ SY2347 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2347 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV67 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2548,plain,
! [SV68: $i] :
( ( ! [SY2348: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV68 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2348 @ SY2348 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ SY2348 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2549,plain,
! [SV69: $i] :
( ( ! [SY2349: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY2349 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2349 @ SY2349 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2550,plain,
! [SV70: $i] :
( ( ! [SY2350: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV70 )
| ( c_HOL_Oord__class_Oless @ SY2350 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2350 @ SY2350 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2551,plain,
! [SV71: $i] :
( ( ! [SY2351: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV71 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2351 @ SY2351 @ SV71 ) @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
| ~ ( c_HOL_Oord__class_Oless @ SY2351 @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2552,plain,
! [SV72: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SV72 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2553,plain,
! [SV73: $i] :
( ( ! [SY2352: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV73 @ SY2352 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV73 @ SY2352 @ tc_nat ) @ SY2352 @ tc_nat ) )
| ~ ( c_lessequals @ SY2352 @ SV73 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2554,plain,
! [SV74: $i] :
( ( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV74 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2555,plain,
! [SV75: $i] :
( ( ( c_Orderings_Oord__class_Omin @ SV75 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2556,plain,
! [SV76: $i] :
( ( ! [SY2353: $i,SY2354: $i,SY2355: $i] :
( ~ ( c_lessequals @ SV76 @ SY2353 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2353 @ SY2354 @ tc_nat ) @ SY2355 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV76 @ SY2354 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2353 @ SV76 @ tc_nat ) @ SY2354 @ tc_nat ) @ SY2355 @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2557,plain,
! [SV77: $i] :
( ( ! [SY2356: $i,SY2357: $i,SY2358: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
| ( c_HOL_Oord__class_Oless @ SY2356 @ SY2357 @ SV77 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SY2358 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2356 @ SY2358 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SY2357 @ SY2358 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2558,plain,
! [SV78: $i] :
( ( ! [SY2359: $i,SY2360: $i,SY2361: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
| ( c_HOL_Oord__class_Oless @ SY2359 @ SY2360 @ SV78 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SY2361 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2361 @ SY2359 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SY2361 @ SY2360 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2559,plain,
! [SV79: $i] :
( ( ! [SY2362: $i,SY2363: $i,SY2364: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV79 )
| ( c_HOL_Oord__class_Oless @ SY2362 @ SY2363 @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SY2364 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2362 @ SY2364 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SY2363 @ SY2364 @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2560,plain,
! [SV80: $i] :
( ( ! [SY2365: $i,SY2366: $i,SY2367: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV80 )
| ( c_HOL_Oord__class_Oless @ SY2365 @ SY2366 @ SV80 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SY2367 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2367 @ SY2365 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SY2367 @ SY2366 @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2561,plain,
! [SV81: $i] :
( ( ! [SY2368: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV81 @ SY2368 @ tc_nat ) @ SY2368 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2368 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2562,plain,
! [SV82: $i] :
( ( ! [SY2369: $i,SY2370: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV82 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2369 @ SY2369 @ SV82 ) @ ( c_HOL_Otimes__class_Otimes @ SY2370 @ SY2370 @ SV82 ) @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2563,plain,
! [SV83: $i] :
( ( ! [SY2371: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV83 ) @ SY2371 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV83 @ SY2371 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY2371 @ SV83 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2564,plain,
! [SV84: $i] :
( ( ! [SY2372: $i,SY2373: $i,SY2374: $i] :
( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2372 @ SY2373 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2372 @ SY2374 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2372 @ ( c_Divides_Odiv__class_Omod @ SY2373 @ SY2374 @ SV84 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2565,plain,
! [SV85: $i] :
( ( ! [SY2375: $i,SY2376: $i,SY2377: $i] :
( ~ ( class_Divides_Osemiring__div @ SV85 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2375 @ ( c_Divides_Odiv__class_Omod @ SY2376 @ SY2377 @ SV85 ) @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2375 @ SY2376 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2375 @ SY2377 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2566,plain,
! [SV86: $i] :
( ( ! [SY2378: $i,SY2379: $i,SY2380: $i] :
( ~ ( class_Divides_Osemiring__div @ SV86 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2378 @ SY2379 @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2378 @ ( c_Divides_Odiv__class_Omod @ SY2379 @ SY2380 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2378 @ SY2380 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2567,plain,
! [SV87: $i] :
( ( ! [SY2381: $i,SY2382: $i,SY2383: $i] :
( ~ ( class_Divides_Osemiring__div @ SV87 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2381 @ ( c_Divides_Odiv__class_Omod @ SY2382 @ SY2383 @ SV87 ) @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2381 @ SY2383 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2381 @ SY2382 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2568,plain,
! [SV88: $i] :
( ( ! [SY2384: $i,SY2385: $i,SY2386: $i,SY2387: $i,SY2388: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2384 @ SY2385 @ SV88 ) @ SY2386 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2387 @ SY2385 @ SV88 ) @ SY2388 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SY2386 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2387 @ SY2384 @ SV88 ) @ SY2385 @ SV88 ) @ SY2388 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2569,plain,
! [SV89: $i] :
( ( ! [SY2389: $i,SY2390: $i,SY2391: $i,SY2392: $i,SY2393: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 )
| ( c_lessequals @ SY2389 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2390 @ SY2391 @ SV89 ) @ SY2392 @ SV89 ) @ SY2393 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2391 @ SY2392 @ SV89 ) @ SY2389 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2390 @ SY2392 @ SV89 ) @ SY2393 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2570,plain,
! [SV90: $i] :
( ( ! [SY2394: $i,SY2395: $i,SY2396: $i,SY2397: $i,SY2398: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2394 @ SY2395 @ SV90 ) @ SY2396 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2397 @ SY2395 @ SV90 ) @ SY2398 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2394 @ SY2397 @ SV90 ) @ SY2395 @ SV90 ) @ SY2396 @ SV90 ) @ SY2398 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2571,plain,
! [SV91: $i] :
( ( ! [SY2399: $i,SY2400: $i,SY2401: $i,SY2402: $i,SY2403: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2399 @ SY2400 @ SV91 ) @ SY2401 @ SV91 ) @ SY2402 @ SV91 ) @ SY2403 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2399 @ SY2401 @ SV91 ) @ SY2402 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2400 @ SY2401 @ SV91 ) @ SY2403 @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2572,plain,
! [SV92: $i] :
( ( ! [SY2404: $i] :
( ( c_lessequals @ ( c_Suc @ SV92 ) @ SY2404 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV92 @ SY2404 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2573,plain,
! [SV93: $i] :
( ( ! [SY2405: $i] :
( ( c_HOL_Oord__class_Oless @ SV93 @ SY2405 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV93 ) @ SY2405 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2574,plain,
! [SV94: $i] :
( ( ! [SY2406: $i] :
( ( c_lessequals @ ( c_Suc @ SV94 ) @ SY2406 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SY2406 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2575,plain,
! [SV95: $i] :
( ( ! [SY2407: $i] :
( ( c_HOL_Oord__class_Oless @ SV95 @ SY2407 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV95 ) @ SY2407 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2576,plain,
! [SV96: $i] :
( ( ! [SY2408: $i,SY2409: $i,SY2410: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_lessequals @ SY2408 @ ( c_HOL_Oplus__class_Oplus @ SY2409 @ SY2410 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SY2408 @ SY2409 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SY2410 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2577,plain,
! [SV97: $i] :
( ( ! [SY2411: $i,SY2412: $i,SY2413: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
| ( c_lessequals @ SY2411 @ ( c_HOL_Oplus__class_Oplus @ SY2412 @ SY2413 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SY2411 @ SY2413 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SY2412 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2578,plain,
! [SV98: $i] :
( ( ! [SY2414: $i,SY2415: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SY2414 @ tc_nat ) @ SY2415 @ tc_nat )
| ~ ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SY2415 @ SY2414 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2414 @ SY2415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2579,plain,
! [SV99: $i] :
( ( ! [SY2416: $i,SY2417: $i] :
( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SY2416 @ SY2417 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SY2417 @ tc_nat ) @ SY2416 @ tc_nat )
| ~ ( c_lessequals @ SY2417 @ SY2416 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2580,plain,
! [SV100: $i] :
( ( ! [SY2418: $i] : ( c_HOL_Oord__class_Oless @ SV100 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV100 @ SY2418 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2581,plain,
! [SV101: $i] :
( ( ! [SY2419: $i] : ( c_HOL_Oord__class_Oless @ SV101 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SY2419 @ SV101 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2582,plain,
! [SV102: $i] :
( ( ! [SY2420: $i] : ( c_HOL_Oord__class_Oless @ SV102 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV102 @ SY2420 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2583,plain,
! [SV103: $i] :
( ( ! [SY2421: $i,SY2422: $i,SY2423: $i,SY2424: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SY2421 @ tc_nat ) @ SY2422 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2423 @ SY2421 @ tc_nat ) @ SY2424 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2422 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2423 @ SV103 @ tc_nat ) @ SY2421 @ tc_nat ) @ SY2424 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV103 @ SY2423 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2584,plain,
! [SV104: $i] :
( ( ! [SY2425: $i,SY2426: $i,SY2427: $i,SY2428: $i] :
( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2425 @ SY2426 @ tc_nat ) @ SY2427 @ tc_nat ) @ SY2428 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2426 @ SY2427 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2425 @ SY2427 @ tc_nat ) @ SY2428 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2426 @ SY2425 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2585,plain,
! [SV105: $i] :
( ( ! [SY2429: $i,SY2430: $i,SY2431: $i,SY2432: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SY2429 @ tc_nat ) @ SY2430 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2431 @ SY2429 @ tc_nat ) @ SY2432 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SY2431 @ tc_nat ) @ SY2429 @ tc_nat ) @ SY2430 @ tc_nat ) @ SY2432 @ tc_nat )
| ~ ( c_lessequals @ SY2431 @ SV105 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2586,plain,
! [SV106: $i] :
( ( ! [SY2433: $i,SY2434: $i,SY2435: $i,SY2436: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SY2433 @ tc_nat ) @ SY2434 @ tc_nat ) @ SY2435 @ tc_nat ) @ SY2436 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SY2434 @ tc_nat ) @ SY2435 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2433 @ SY2434 @ tc_nat ) @ SY2436 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2433 @ SV106 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2587,plain,
! [SV107: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i,SY2440: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV107 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2437 @ SY2438 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2439 @ SY2437 @ SV107 ) @ SY2438 @ SV107 ) @ SY2440 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2439 @ SY2438 @ SV107 ) @ SY2440 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2588,plain,
! [SV108: $i] :
( ( ! [SY2441: $i,SY2442: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ SV108 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY2441 @ SY2442 @ SV108 ) @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2441 @ SV108 ) @ ( c_HOL_Oabs__class_Oabs @ SY2442 @ SV108 ) @ SV108 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2589,plain,
! [SV109: $i] :
( ( ! [SY2443: $i,SY2444: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 )
| ( c_lessequals @ SY2443 @ SY2444 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SY2443 @ SV109 ) @ SY2444 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2590,plain,
! [SV110: $i] :
( ( ! [SY2445: $i,SY2446: $i,SY2447: $i,SY2448: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2445 @ SY2446 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SY2447 @ SY2448 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SY2446 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SY2447 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SY2446 @ SY2448 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SY2445 @ SY2447 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2591,plain,
! [SV111: $i] :
( ( ! [SY2449: $i,SY2450: $i,SY2451: $i] :
( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY2449 @ SY2450 @ SV111 ) @ SY2451 @ SV111 ) @ SY2450 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2449 @ SY2451 @ SV111 ) @ SY2450 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2592,plain,
! [SV112: $i] :
( ( ! [SY2452: $i,SY2453: $i,SY2454: $i] :
( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ SY2452 @ ( c_Orderings_Oord__class_Omin @ SY2453 @ SY2454 @ SV112 ) @ SV112 )
| ~ ( c_lessequals @ SY2452 @ SY2454 @ SV112 )
| ~ ( c_lessequals @ SY2452 @ SY2453 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2593,plain,
! [SV113: $i] :
( ( ! [SY2455: $i,SY2456: $i,SY2457: $i] :
( ~ ( class_Orderings_Olinorder @ SV113 )
| ( c_lessequals @ SY2455 @ ( c_Orderings_Oord__class_Omin @ SY2456 @ SY2457 @ SV113 ) @ SV113 )
| ~ ( c_lessequals @ SY2455 @ SY2457 @ SV113 )
| ~ ( c_lessequals @ SY2455 @ SY2456 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2594,plain,
! [SV114: $i] :
( ( ! [SY2458: $i,SY2459: $i,SY2460: $i] :
( ~ ( class_Orderings_Olinorder @ SV114 )
| ( c_lessequals @ SY2458 @ ( c_Orderings_Oord__class_Omin @ SY2459 @ SY2460 @ SV114 ) @ SV114 )
| ~ ( c_lessequals @ SY2458 @ SY2460 @ SV114 )
| ~ ( c_lessequals @ SY2458 @ SY2459 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2595,plain,
! [SV115: $i] :
( ( ! [SY2461: $i,SY2462: $i] :
( ~ ( class_Orderings_Olinorder @ SV115 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY2461 @ SY2462 @ SV115 ) @ SY2462 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2596,plain,
! [SV116: $i] :
( ( ! [SY2463: $i,SY2464: $i] :
( ~ ( class_Orderings_Olinorder @ SV116 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY2463 @ SY2464 @ SV116 ) @ SY2463 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2597,plain,
! [SV117: $i] :
( ( ! [SY2465: $i,SY2466: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SY2465 @ tc_nat ) ) @ SY2466 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV117 ) @ ( c_HOL_Oplus__class_Oplus @ SY2465 @ SY2466 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2465 @ SV117 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2598,plain,
! [SV118: $i] :
( ( ! [SY2467: $i,SY2468: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2467 @ ( c_HOL_Otimes__class_Otimes @ SY2468 @ SY2467 @ SV118 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2599,plain,
! [SV119: $i] :
( ( ! [SY2469: $i,SY2470: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV119 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2469 @ ( c_HOL_Otimes__class_Otimes @ SY2469 @ SY2470 @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2600,plain,
! [SV120: $i] :
( ( ! [SY2471: $i,SY2472: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV120 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2471 @ ( c_HOL_Otimes__class_Otimes @ SY2471 @ SY2472 @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2601,plain,
! [SV121: $i] :
( ( ! [SY2473: $i,SY2474: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV121 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2473 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2474 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ SY2473 @ SY2474 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2602,plain,
! [SV122: $i] :
( ( ! [SY2475: $i,SY2476: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV122 )
| ( c_lessequals @ SY2475 @ SY2476 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2475 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2476 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2603,plain,
! [SV123: $i] :
( ( ! [SY2477: $i] :
( ~ ( class_Divides_Osemiring__div @ SV123 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SY2477 @ SV123 )
= ( c_HOL_Ozero__class_Ozero @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2604,plain,
! [SV124: $i] :
( ( ! [SY2478: $i,SY2479: $i,SY2480: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV124 )
| ~ ( class_Int_Onumber__ring @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2478 @ SY2479 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SY2478 @ SY2480 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2478 @ SY2480 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SY2478 @ SY2479 @ SV124 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2605,plain,
! [SV125: $i] :
( ( ! [SY2481: $i,SY2482: $i,SY2483: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV125 )
| ~ ( class_Int_Onumber__ring @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2481 @ SY2482 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SY2481 @ SY2483 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2481 @ SY2483 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SY2481 @ SY2482 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2606,plain,
! [SV126: $i] :
( ( ! [SY2484: $i,SY2485: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SY2484 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SY2485 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SY2485 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SY2484 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2607,plain,
! [SV127: $i] :
( ( ! [SY2486: $i,SY2487: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SY2486 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SY2487 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SY2487 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SY2486 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2608,plain,
! [SV128: $i] :
( ( ( SV128
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV128 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2609,plain,
! [SV129: $i] :
( ( ! [SY2488: $i,SY2489: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV129 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SY2488 @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ SY2489 @ SV129 ) @ SV129 ) @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY2488 @ SY2489 @ SV129 ) @ SV129 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2610,plain,
! [SV130: $i] :
( ( ! [SY2490: $i,SY2491: $i] :
( ~ ( class_Orderings_Olinorder @ SV130 )
| ( ( c_Orderings_Oord__class_Omin @ SY2490 @ ( c_Orderings_Oord__class_Omin @ SY2490 @ SY2491 @ SV130 ) @ SV130 )
= ( c_Orderings_Oord__class_Omin @ SY2490 @ SY2491 @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2611,plain,
! [SV131: $i] :
( ( ! [SY2492: $i,SY2493: $i,SY2494: $i,SY2495: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV131 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY2492 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SY2493 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SY2494 @ SY2495 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SY2493 @ SV131 ) @ SY2495 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SY2492 @ SV131 ) @ SY2494 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2612,plain,
! [SV132: $i] :
( ( ! [SY2496: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV132 ) @ SY2496 @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV132 @ SY2496 @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV132 @ SY2496 @ tc_nat ) )
= SY2496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2613,plain,
! [SV133: $i] :
( ( ! [SY2497: $i,SY2498: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SY2497 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SY2498 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV133 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2614,plain,
! [SV134: $i] :
( ( ! [SY2499: $i,SY2500: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV134 @ SY2499 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2500 @ SY2499 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2499 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2615,plain,
! [SV135: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2616,plain,
! [SV136: $i] :
( ( ! [SY2501: $i,SY2502: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2501 @ SY2502 @ SV136 )
= ( c_HOL_Otimes__class_Otimes @ SY2502 @ SY2501 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2617,plain,
! [SV137: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV137 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV137 ) @ ( c_HOL_Ozero__class_Ozero @ SV137 ) @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2618,plain,
! [SV138: $i] :
( ( ! [SY2503: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV138 @ SY2503 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SY2503 @ SV138 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2619,plain,
! [SV139: $i] :
( ( ! [SY2504: $i,SY2505: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV139 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2504 @ SY2505 @ SV139 )
= ( c_HOL_Otimes__class_Otimes @ SY2505 @ SY2504 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2620,plain,
! [SV140: $i] :
( ( ! [SY2506: $i,SY2507: $i,SY2508: $i] :
( ~ ( class_Divides_Osemiring__div @ SV140 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2506 @ SY2507 @ SV140 ) @ SY2508 @ SV140 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY2506 @ SY2508 @ SV140 ) @ ( c_Divides_Odiv__class_Omod @ SY2507 @ SY2508 @ SV140 ) @ SV140 ) @ SY2508 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2621,plain,
! [SV141: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV141 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2622,plain,
! [SV142: $i] :
( ( ! [SY2509: $i,SY2510: $i,SY2511: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV142 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2509 @ ( c_HOL_Oplus__class_Oplus @ SY2510 @ SY2511 @ SV142 ) @ SV142 )
= ( c_HOL_Oplus__class_Oplus @ SY2510 @ ( c_HOL_Oplus__class_Oplus @ SY2509 @ SY2511 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2623,plain,
! [SV143: $i] :
( ( ! [SY2512: $i,SY2513: $i,SY2514: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV143 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2512 @ SY2513 @ SV143 ) @ SY2514 @ SV143 )
= ( c_HOL_Oplus__class_Oplus @ SY2512 @ ( c_HOL_Oplus__class_Oplus @ SY2513 @ SY2514 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2624,plain,
! [SV144: $i] :
( ( ! [SY2515: $i,SY2516: $i,SY2517: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2515 @ ( c_HOL_Otimes__class_Otimes @ SY2516 @ SY2517 @ SV144 ) @ SV144 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2515 @ SY2517 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2625,plain,
! [SV145: $i] :
( ( ! [SY2518: $i,SY2519: $i,SY2520: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2518 @ ( c_HOL_Otimes__class_Otimes @ SY2519 @ SY2520 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2518 @ SY2519 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2626,plain,
! [SV146: $i] :
( ( ! [SY2521: $i,SY2522: $i,SY2523: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2521 @ SY2522 @ SV146 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2521 @ SY2523 @ SV146 ) @ SY2522 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2627,plain,
! [SV147: $i] :
( ( ! [SY2524: $i,SY2525: $i,SY2526: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2524 @ SY2525 @ SV147 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2526 @ SY2524 @ SV147 ) @ SY2525 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2628,plain,
! [SV148: $i] :
( ( ! [SY2527: $i,SY2528: $i,SY2529: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 )
| ( c_HOL_Oord__class_Oless @ SY2527 @ ( c_HOL_Oplus__class_Oplus @ SY2528 @ SY2529 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ SY2527 @ SY2529 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SY2528 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2629,plain,
! [SV149: $i] :
( ( ! [SY2530: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV149 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SY2530 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2630,plain,
! [SV150: $i] :
( ( ! [SY2531: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV150 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2531 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2631,plain,
! [SV151: $i] :
( ( ! [SY2532: $i,SY2533: $i,SY2534: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SY2532 @ SY2533 @ tc_nat ) @ tc_nat ) @ SY2534 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SY2533 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2534 @ SV151 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2533 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2632,plain,
! [SV152: $i] :
( ( ! [SY2535: $i,SY2536: $i,SY2537: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ SV152 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2535 @ SY2536 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SY2535 @ SY2537 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SY2535 @ SV152 )
| ~ ( c_lessequals @ SY2536 @ SY2537 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2633,plain,
! [SV153: $i] :
( ( ! [SY2538: $i,SY2539: $i,SY2540: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV153 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2538 @ SY2539 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SY2538 @ SY2540 @ SV153 ) @ SV153 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SY2538 @ SV153 )
| ~ ( c_lessequals @ SY2539 @ SY2540 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2634,plain,
! [SV154: $i] :
( ( ! [SY2541: $i,SY2542: $i,SY2543: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV154 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2541 @ SY2542 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SY2543 @ SY2542 @ SV154 ) @ SV154 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SY2542 @ SV154 )
| ~ ( c_lessequals @ SY2541 @ SY2543 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2635,plain,
! [SV155: $i] :
( ( ! [SY2544: $i,SY2545: $i,SY2546: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV155 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2544 @ SY2545 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SY2544 @ SY2546 @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SY2544 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SY2546 @ SY2545 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2636,plain,
! [SV156: $i] :
( ( ! [SY2547: $i,SY2548: $i,SY2549: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV156 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2547 @ SY2548 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SY2549 @ SY2548 @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SY2548 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SY2549 @ SY2547 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2637,plain,
! [SV157: $i] :
( ( ! [SY2550: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV157 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2550 @ SY2550 @ SV157 )
= SY2550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2638,plain,
! [SV158: $i] :
( ( ! [SY2551: $i,SY2552: $i,SY2553: $i,SY2554: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2551 @ SY2552 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SY2553 @ SY2554 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SY2552 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SY2551 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SY2552 @ SY2554 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SY2551 @ SY2553 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2639,plain,
! [SV159: $i] :
( ( ! [SY2555: $i,SY2556: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV159 @ SY2555 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2556 @ SY2555 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV159 @ SY2556 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2640,plain,
! [SV160: $i] :
( ( ! [SY2557: $i,SY2558: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SY2557 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SY2558 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2557 @ SY2558 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2641,plain,
! [SV161: $i] :
( ( ! [SY2559: $i,SY2560: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SY2559 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SY2560 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2559 @ SY2560 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2642,plain,
! [SV162: $i] :
( ( ! [SY2561: $i,SY2562: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV162 @ SY2561 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2562 @ SY2561 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV162 @ SY2562 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2643,plain,
! [SV163: $i] :
( ( ! [SY2563: $i,SY2564: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV163 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SY2563 @ SY2564 @ tc_nat ) @ SV163 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2563 @ SV163 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2564 @ SV163 ) @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2644,plain,
! [SV164: $i] :
( ( ! [SY2565: $i,SY2566: $i,SY2567: $i] :
( ~ ( class_Divides_Osemiring__div @ SV164 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2565 @ ( c_Divides_Odiv__class_Omod @ SY2566 @ SY2567 @ SV164 ) @ SV164 ) @ SY2567 @ SV164 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2565 @ SY2566 @ SV164 ) @ SY2567 @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2645,plain,
! [SV165: $i] :
( ( ! [SY2568: $i,SY2569: $i,SY2570: $i] :
( ~ ( class_Divides_Osemiring__div @ SV165 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY2568 @ SY2569 @ SV165 ) @ SY2570 @ SV165 ) @ SY2569 @ SV165 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2568 @ SY2570 @ SV165 ) @ SY2569 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2646,plain,
! [SV166: $i] :
( ( ! [SY2571: $i,SY2572: $i,SY2573: $i,SY2574: $i,SY2575: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV166 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2571 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2572 @ ( c_HOL_Otimes__class_Otimes @ SY2573 @ SY2574 @ SV166 ) @ SV166 ) @ SY2575 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2571 @ ( c_HOL_Oplus__class_Oplus @ SY2572 @ SY2575 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2571 @ SY2574 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2647,plain,
! [SV167: $i] :
( ( ! [SY2576: $i,SY2577: $i,SY2578: $i,SY2579: $i,SY2580: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV167 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2576 @ ( c_HOL_Oplus__class_Oplus @ SY2577 @ SY2578 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2576 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2577 @ ( c_HOL_Otimes__class_Otimes @ SY2579 @ SY2580 @ SV167 ) @ SV167 ) @ SY2578 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2576 @ SY2580 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2648,plain,
! [SV168: $i] :
( ( ! [SY2581: $i,SY2582: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV168 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SY2581 @ SY2582 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SY2582 @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SY2581 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2649,plain,
! [SV169: $i] :
( ( ! [SY2583: $i,SY2584: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV169 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SY2583 @ SY2584 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SY2584 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SY2583 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2650,plain,
! [SV170: $i] :
( ( ! [SY2585: $i,SY2586: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV170 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SY2585 @ SY2586 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SY2586 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SY2585 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2651,plain,
! [SV171: $i] :
( ( ! [SY2587: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV171 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV171 ) @ ( c_HOL_Otimes__class_Otimes @ SY2587 @ SY2587 @ SV171 ) @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2652,plain,
! [SV172: $i] :
( ( ! [SY2588: $i,SY2589: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SY2588 @ SY2589 @ SV172 ) @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SY2589 @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SY2588 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2653,plain,
! [SV173: $i] :
( ( ! [SY2590: $i,SY2591: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SY2590 @ SY2591 @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SY2591 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SY2590 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2654,plain,
! [SV174: $i] :
( ( ! [SY2592: $i,SY2593: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SY2592 @ SY2593 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SY2593 @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SY2592 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2655,plain,
! [SV175: $i] :
( ( ! [SY2594: $i,SY2595: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV175 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SY2594 @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ SY2595 @ SV175 ) @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY2594 @ SY2595 @ SV175 ) @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2656,plain,
! [SV176: $i] :
( ( ! [SY2596: $i,SY2597: $i,SY2598: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV176 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2596 @ SY2597 @ SV176 ) @ SY2598 @ SV176 )
= ( c_HOL_Otimes__class_Otimes @ SY2596 @ ( c_HOL_Otimes__class_Otimes @ SY2597 @ SY2598 @ SV176 ) @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2657,plain,
! [SV177: $i] :
( ( ! [SY2599: $i,SY2600: $i,SY2601: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV177 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2599 @ SY2600 @ SV177 ) @ SY2601 @ SV177 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2599 @ SY2601 @ SV177 ) @ SY2600 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2658,plain,
! [SV178: $i] :
( ( ! [SY2602: $i,SY2603: $i,SY2604: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV178 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2602 @ SY2603 @ SV178 ) @ SY2604 @ SV178 )
= ( c_HOL_Otimes__class_Otimes @ SY2602 @ ( c_HOL_Otimes__class_Otimes @ SY2603 @ SY2604 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2659,plain,
! [SV179: $i] :
( ( ! [SY2605: $i,SY2606: $i,SY2607: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV179 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2605 @ ( c_HOL_Otimes__class_Otimes @ SY2606 @ SY2607 @ SV179 ) @ SV179 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2605 @ SY2606 @ SV179 ) @ SY2607 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2660,plain,
! [SV180: $i] :
( ( ! [SY2608: $i,SY2609: $i,SY2610: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV180 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2608 @ ( c_HOL_Otimes__class_Otimes @ SY2609 @ SY2610 @ SV180 ) @ SV180 )
= ( c_HOL_Otimes__class_Otimes @ SY2609 @ ( c_HOL_Otimes__class_Otimes @ SY2608 @ SY2610 @ SV180 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2661,plain,
! [SV181: $i] :
( ( ! [SY2611: $i,SY2612: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV181 @ SY2611 @ tc_nat ) @ SY2612 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV181 @ ( c_HOL_Otimes__class_Otimes @ SY2611 @ SY2612 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2662,plain,
! [SV182: $i] :
( ( ! [SY2613: $i,SY2614: $i,SY2615: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV182 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2613 @ ( c_HOL_Otimes__class_Otimes @ SY2614 @ SY2615 @ SV182 ) @ SV182 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SY2613 @ SY2614 @ SV182 ) @ SY2615 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2663,plain,
! [SV183: $i] :
( ( ! [SY2616: $i,SY2617: $i,SY2618: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2616 @ SY2617 @ SV183 ) @ SY2618 @ SV183 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2616 @ SY2618 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SY2617 @ SY2618 @ SV183 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2664,plain,
! [SV184: $i] :
( ( ! [SY2619: $i,SY2620: $i,SY2621: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV184 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2619 @ ( c_HOL_Oplus__class_Oplus @ SY2620 @ SY2621 @ SV184 ) @ SV184 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2619 @ SY2620 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SY2619 @ SY2621 @ SV184 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2665,plain,
! [SV185: $i] :
( ( ! [SY2622: $i,SY2623: $i,SY2624: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV185 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2622 @ ( c_HOL_Oplus__class_Oplus @ SY2623 @ SY2624 @ SV185 ) @ SV185 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2622 @ SY2623 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SY2622 @ SY2624 @ SV185 ) @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2666,plain,
! [SV186: $i] :
( ( ! [SY2625: $i,SY2626: $i,SY2627: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2625 @ SY2626 @ SV186 ) @ SY2627 @ SV186 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2625 @ SY2627 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SY2626 @ SY2627 @ SV186 ) @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2667,plain,
! [SV187: $i] :
( ( ! [SY2628: $i,SY2629: $i,SY2630: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV187 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2628 @ SY2629 @ SV187 ) @ SY2630 @ SV187 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2628 @ SY2630 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SY2629 @ SY2630 @ SV187 ) @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2668,plain,
! [SV188: $i] :
( ( ! [SY2631: $i,SY2632: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV188 @ ( c_HOL_Oplus__class_Oplus @ SY2631 @ SY2632 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV188 @ SY2631 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV188 @ SY2632 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2669,plain,
! [SV189: $i] :
( ( ! [SY2633: $i,SY2634: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV189 @ SY2633 @ tc_nat ) @ SY2634 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV189 @ SY2634 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2633 @ SY2634 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2670,plain,
! [SV190: $i] :
( ( ! [SY2635: $i,SY2636: $i,SY2637: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV190 )
| ( ( c_HOL_Otimes__class_Otimes @ SY2635 @ ( c_HOL_Oplus__class_Oplus @ SY2636 @ SY2637 @ SV190 ) @ SV190 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2635 @ SY2636 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SY2635 @ SY2637 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2671,plain,
! [SV191: $i] :
( ( ! [SY2638: $i,SY2639: $i,SY2640: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2638 @ SY2639 @ SV191 ) @ SY2640 @ SV191 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2638 @ SY2640 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SY2639 @ SY2640 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2672,plain,
! [SV192: $i] :
( ( ! [SY2641: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV192 @ SY2641 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2641 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2673,plain,
! [SV193: $i] :
( ( ! [SY2642: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV193 @ SY2642 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV193 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2674,plain,
! [SV194: $i] :
( ( ! [SY2643: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY2643 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( c_HOL_Oplus__class_Oplus @ SY2643 @ SY2643 @ SV194 ) @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2675,plain,
! [SV195: $i] :
( ( ! [SY2644: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV195 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ SY2644 @ SY2644 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SY2644 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2676,plain,
! [SV196: $i] :
( ( ! [SY2645: $i,SY2646: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
| ( c_lessequals @ SY2645 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SY2645 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SY2645 @ SY2646 @ SV196 ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2677,plain,
! [SV197: $i] :
( ( ! [SY2647: $i,SY2648: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
| ( c_lessequals @ SY2647 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY2648 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SY2648 @ SY2647 @ SV197 ) @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2678,plain,
! [SV198: $i] :
( ( ! [SY2649: $i,SY2650: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
| ( c_lessequals @ SY2649 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SY2650 @ SV198 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SY2649 @ SY2650 @ SV198 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2679,plain,
! [SV199: $i] :
( ( ! [SY2651: $i,SY2652: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
| ( c_lessequals @ SY2651 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SY2651 @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SY2652 @ SY2651 @ SV199 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2680,plain,
! [SV200: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ SV200 ) @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2681,plain,
! [SV201: $i] :
( ( ! [SY2653: $i,SY2654: $i,SY2655: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2653 @ SY2654 @ SV201 ) @ ( c_HOL_Otimes__class_Otimes @ SY2655 @ SY2654 @ SV201 ) @ SV201 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2653 @ SY2655 @ SV201 ) @ SY2654 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2682,plain,
! [SV202: $i] :
( ( ! [SY2656: $i,SY2657: $i,SY2658: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SY2656 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2657 @ SY2658 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2656 @ SY2658 @ tc_nat )
| ~ ( c_lessequals @ SV202 @ SY2657 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2683,plain,
! [SV203: $i] :
( ( c_lessequals @ SV203 @ ( c_HOL_Otimes__class_Otimes @ SV203 @ ( c_HOL_Otimes__class_Otimes @ SV203 @ SV203 @ tc_nat ) @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2684,plain,
! [SV204: $i] :
( ( ! [SY2659: $i,SY2660: $i,SY2661: $i,SY2662: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV204 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2659 @ SY2660 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SY2661 @ SY2662 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY2660 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY2661 @ SV204 )
| ~ ( c_lessequals @ SY2660 @ SY2662 @ SV204 )
| ~ ( c_lessequals @ SY2659 @ SY2661 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2685,plain,
! [SV205: $i] :
( ( ! [SY2663: $i,SY2664: $i,SY2665: $i,SY2666: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV205 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2663 @ SY2664 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SY2665 @ SY2666 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SY2664 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SY2663 @ SV205 )
| ~ ( c_lessequals @ SY2664 @ SY2666 @ SV205 )
| ~ ( c_lessequals @ SY2663 @ SY2665 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2686,plain,
! [SV206: $i] :
( ( ! [SY2667: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV206 @ SY2667 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY2667 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV206 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2687,plain,
! [SV207: $i] :
( ( ! [SY2668: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV207 @ SY2668 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2668 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV207 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2688,plain,
! [SV208: $i] :
( ( ! [SY2669: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV208 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY2669 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV208 @ SY2669 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2689,plain,
! [SV209: $i] :
( ( ! [SY2670: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV209 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY2670 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SY2670 @ SV209 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2690,plain,
! [SV210: $i] :
( ( ! [SY2671: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SY2671 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2671 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV210 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2691,plain,
! [SV211: $i] :
( ( ! [SY2672: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV211 @ SY2672 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY2672 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV211 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2692,plain,
! [SV212: $i] :
( ( ! [SY2673: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ SV212 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2673 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV212 @ SY2673 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2693,plain,
! [SV213: $i] :
( ( ! [SY2674: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ SV213 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2674 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SY2674 @ SV213 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2694,plain,
! [SV214: $i] :
( ( ! [SY2675: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV214 @ SY2675 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY2675 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV214 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2695,plain,
! [SV215: $i] :
( ( ! [SY2676: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV215 @ SY2676 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2676 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV215 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2696,plain,
! [SV216: $i] :
( ( ! [SY2677: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ SV216 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY2677 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV216 @ SY2677 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2697,plain,
! [SV217: $i] :
( ( ! [SY2678: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV217 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2678 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SY2678 @ SV217 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2698,plain,
! [SV218: $i] :
( ( ! [SY2679: $i] :
( ( SV218
= ( c_Suc @ SY2679 ) )
| ( c_lessequals @ SV218 @ SY2679 @ tc_nat )
| ~ ( c_lessequals @ SV218 @ ( c_Suc @ SY2679 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2699,plain,
! [SV219: $i] :
( ( ! [SY2680: $i,SY2681: $i,SY2682: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
| ( c_HOL_Oord__class_Oless @ SY2680 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SY2680 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2680 @ SY2681 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SY2680 @ SY2682 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2700,plain,
! [SV220: $i] :
( ( ! [SY2683: $i,SY2684: $i,SY2685: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
| ( c_HOL_Oord__class_Oless @ SY2683 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SY2683 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2684 @ SY2683 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SY2685 @ SY2683 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2701,plain,
! [SV221: $i] :
( ( ! [SY2686: $i,SY2687: $i,SY2688: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2686 @ ( c_HOL_Oplus__class_Oplus @ SY2687 @ SY2688 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2686 @ SY2688 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2686 @ SY2687 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2702,plain,
! [SV222: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV222 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( c_Parity_Oeven__odd__class_Oeven @ SV222 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2703,plain,
! [SV223: $i] :
( ( ! [SY2689: $i,SY2690: $i,SY2691: $i,SY2692: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2689 @ SY2690 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SY2691 @ SY2692 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2689 @ SY2691 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SY2690 @ SY2692 @ SV223 ) @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2704,plain,
! [SV224: $i] :
( ( ! [SY2693: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV224 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2693 @ SV224 ) @ SV224 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SY2693 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2705,plain,
! [SV225: $i] :
( ( ! [SY2694: $i,SY2695: $i,SY2696: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ SY2694 @ SY2695 @ SV225 ) @ SY2696 @ SV225 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ SY2694 @ SY2696 @ SV225 ) @ ( c_HOL_Oplus__class_Oplus @ SY2695 @ SY2696 @ SV225 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2706,plain,
! [SV226: $i] :
( ( ! [SY2697: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2697 @ SY2697 @ SV226 ) @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2707,plain,
! [SV227: $i] :
( ( ! [SY2698: $i,SY2699: $i,SY2700: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2698 @ ( c_HOL_Oplus__class_Oplus @ SY2699 @ SY2700 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2698 @ SY2699 @ SV227 ) @ SY2700 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2708,plain,
! [SV228: $i] :
( ( ! [SY2701: $i,SY2702: $i,SY2703: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2701 @ ( c_HOL_Oplus__class_Oplus @ SY2702 @ SY2703 @ SV228 ) @ SV228 )
= ( c_HOL_Oplus__class_Oplus @ SY2702 @ ( c_HOL_Oplus__class_Oplus @ SY2701 @ SY2703 @ SV228 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2709,plain,
! [SV229: $i] :
( ( ! [SY2704: $i,SY2705: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV229 @ SY2704 @ tc_nat ) @ SY2705 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV229 @ ( c_HOL_Oplus__class_Oplus @ SY2704 @ SY2705 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2710,plain,
! [SV230: $i] :
( ( ! [SY2706: $i,SY2707: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV230 @ ( c_HOL_Oplus__class_Oplus @ SY2706 @ SY2707 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY2706 @ ( c_HOL_Oplus__class_Oplus @ SV230 @ SY2707 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2711,plain,
! [SV231: $i] :
( ( ! [SY2708: $i,SY2709: $i,SY2710: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2708 @ SY2709 @ SV231 ) @ SY2710 @ SV231 )
= ( c_HOL_Oplus__class_Oplus @ SY2708 @ ( c_HOL_Oplus__class_Oplus @ SY2709 @ SY2710 @ SV231 ) @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2712,plain,
! [SV232: $i] :
( ( ! [SY2711: $i,SY2712: $i,SY2713: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2711 @ ( c_HOL_Oplus__class_Oplus @ SY2712 @ SY2713 @ SV232 ) @ SV232 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2711 @ SY2712 @ SV232 ) @ SY2713 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2713,plain,
! [SV233: $i] :
( ( ! [SY2714: $i,SY2715: $i,SY2716: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2714 @ SY2715 @ SV233 ) @ SY2716 @ SV233 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2714 @ SY2716 @ SV233 ) @ SY2715 @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2714,plain,
! [SV234: $i] :
( ( ! [SY2717: $i,SY2718: $i,SY2719: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2717 @ ( c_HOL_Oplus__class_Oplus @ SY2718 @ SY2719 @ SV234 ) @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SY2718 @ ( c_HOL_Oplus__class_Oplus @ SY2717 @ SY2719 @ SV234 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2715,plain,
! [SV235: $i] :
( ( ! [SY2720: $i,SY2721: $i,SY2722: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2720 @ SY2721 @ SV235 ) @ SY2722 @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SY2720 @ ( c_HOL_Oplus__class_Oplus @ SY2721 @ SY2722 @ SV235 ) @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2716,plain,
! [SV236: $i] :
( ( ! [SY2723: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV236 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2723 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2723 @ SV236 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2717,plain,
! [SV237: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV237 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2718,plain,
! [SV238: $i] :
( ( ! [SY2724: $i,SY2725: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV238 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ SY2724 @ SY2725 @ SV238 ) @ SV238 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SY2724 @ SV238 ) @ ( c_HOL_Oabs__class_Oabs @ SY2725 @ SV238 ) @ SV238 ) @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2719,plain,
! [SV239: $i] :
( ( ! [SY2726: $i,SY2727: $i] :
( ( c_lessequals @ SV239 @ ( c_HOL_Oplus__class_Oplus @ SY2726 @ SY2727 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV239 @ SY2726 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2720,plain,
! [SV240: $i] :
( ( ! [SY2728: $i,SY2729: $i] :
( ( c_lessequals @ SV240 @ ( c_HOL_Oplus__class_Oplus @ SY2728 @ SY2729 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV240 @ SY2729 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2721,plain,
! [SV241: $i] :
( ( ! [SY2730: $i,SY2731: $i] :
( ( c_lessequals @ SV241 @ SY2730 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SY2731 @ tc_nat ) @ SY2730 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2722,plain,
! [SV242: $i] :
( ( ! [SY2732: $i,SY2733: $i] :
( ( c_lessequals @ SV242 @ SY2732 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2733 @ SV242 @ tc_nat ) @ SY2732 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2723,plain,
! [SV243: $i] :
( ( ! [SY2734: $i,SY2735: $i] :
( ( c_lessequals @ SV243 @ ( c_HOL_Oplus__class_Oplus @ SY2734 @ SY2735 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV243 @ SY2734 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2724,plain,
! [SV244: $i] :
( ( ! [SY2736: $i,SY2737: $i] :
( ( c_lessequals @ SV244 @ ( c_HOL_Oplus__class_Oplus @ SY2736 @ SY2737 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV244 @ SY2737 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2725,plain,
! [SV245: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SV245 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2726,plain,
! [SV246: $i] :
( ( ! [SY2738: $i,SY2739: $i,SY2740: $i] :
( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2738 @ SY2739 @ SV246 ) @ SY2740 @ SV246 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2738 @ ( c_Divides_Odiv__class_Omod @ SY2739 @ SY2740 @ SV246 ) @ SV246 ) @ SY2740 @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2727,plain,
! [SV247: $i] :
( ( ! [SY2741: $i,SY2742: $i,SY2743: $i] :
( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2741 @ SY2742 @ SV247 ) @ SY2743 @ SV247 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY2741 @ SY2743 @ SV247 ) @ SY2742 @ SV247 ) @ SY2743 @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2728,plain,
! [SV248: $i] :
( ( ! [SY2744: $i,SY2745: $i,SY2746: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
| ( c_HOL_Oord__class_Oless @ SY2744 @ ( c_HOL_Oplus__class_Oplus @ SY2745 @ SY2746 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SY2744 @ SY2746 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SY2745 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2729,plain,
! [SV249: $i] :
( ( ! [SY2747: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV249 @ ( c_HOL_Oplus__class_Oplus @ SV249 @ SY2747 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2730,plain,
! [SV250: $i] :
( ( ! [SY2748: $i,SY2749: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV250 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SY2748 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SY2749 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2731,plain,
! [SV251: $i] :
( ( ! [SY2750: $i,SY2751: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV251 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2750 @ SV251 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2751 @ SV251 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2732,plain,
! [SV252: $i] :
( ( ! [SY2752: $i,SY2753: $i,SY2754: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
| ( c_lessequals @ SY2752 @ SY2753 @ SV252 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SY2754 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2752 @ SY2754 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SY2753 @ SY2754 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2733,plain,
! [SV253: $i] :
( ( ! [SY2755: $i,SY2756: $i,SY2757: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
| ( c_lessequals @ SY2755 @ SY2756 @ SV253 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SY2757 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2757 @ SY2755 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SY2757 @ SY2756 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2734,plain,
! [SV254: $i] :
( ( ! [SY2758: $i,SY2759: $i,SY2760: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2758 @ SY2759 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SY2758 @ SY2760 @ SV254 ) @ SV254 )
| ~ ( c_lessequals @ SY2759 @ SY2760 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SY2758 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2735,plain,
! [SV255: $i] :
( ( ! [SY2761: $i,SY2762: $i,SY2763: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
| ( c_lessequals @ SY2761 @ SY2762 @ SV255 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2763 @ SY2761 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SY2763 @ SY2762 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SY2763 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2736,plain,
! [SV256: $i] :
( ( ! [SY2764: $i,SY2765: $i,SY2766: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2764 @ SY2765 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SY2764 @ SY2766 @ SV256 ) @ SV256 )
| ~ ( c_lessequals @ SY2766 @ SY2765 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SY2764 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2737,plain,
! [SV257: $i] :
( ( ! [SY2767: $i,SY2768: $i,SY2769: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
| ( c_lessequals @ SY2767 @ SY2768 @ SV257 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2769 @ SY2768 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SY2769 @ SY2767 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY2769 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2738,plain,
! [SV258: $i] :
( ( ! [SY2770: $i,SY2771: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SY2770 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SY2771 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2770 @ SY2771 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2739,plain,
! [SV259: $i] :
( ( ! [SY2772: $i,SY2773: $i] :
( ( c_lessequals @ SV259 @ SY2772 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2773 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2773 @ SY2772 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2773 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2740,plain,
! [SV260: $i] :
( ( ! [SY2774: $i,SY2775: $i] :
( ( c_lessequals @ SV260 @ SY2774 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2775 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2775 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2775 @ SY2774 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2741,plain,
! [SV261: $i] :
( ( ! [SY2776: $i,SY2777: $i] :
( ( c_lessequals @ SV261 @ SY2776 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2777 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SY2777 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2776 @ SY2777 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2742,plain,
! [SV262: $i] :
( ( ( SV262
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV262
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV262 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2743,plain,
! [SV263: $i] :
( ( ! [SY2778: $i,SY2779: $i,SY2780: $i,SY2781: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV263 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY2778 @ SY2779 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SY2780 @ SY2781 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2778 @ SY2780 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SY2779 @ SY2781 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2778 @ SY2780 @ SV263 ) @ SY2781 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SY2780 @ ( c_HOL_Ominus__class_Ominus @ SY2779 @ SY2781 @ SV263 ) @ SV263 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2744,plain,
! [SV264: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV264 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2745,plain,
! [SV265: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV265 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2746,plain,
! [SV266: $i] :
( ( ! [SY2782: $i,SY2783: $i] :
( ~ ( class_Orderings_Olinorder @ SV266 )
| ( ( c_Orderings_Oord__class_Omin @ SY2782 @ SY2783 @ SV266 )
= ( c_Orderings_Oord__class_Omin @ SY2783 @ SY2782 @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2747,plain,
! [SV267: $i] :
( ( ! [SY2784: $i,SY2785: $i,SY2786: $i,SY2787: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV267 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2784 @ SY2785 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2786 @ SY2785 @ SV267 ) @ SY2787 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SY2784 @ SY2786 @ SV267 ) @ SY2785 @ SV267 ) @ SY2787 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2748,plain,
! [SV268: $i] :
( ( ! [SY2788: $i,SY2789: $i,SY2790: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SY2788 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2789 @ SY2788 @ tc_nat ) @ SY2790 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV268 @ SY2789 @ tc_nat ) @ SY2788 @ tc_nat ) @ SY2790 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2749,plain,
! [SV269: $i] :
( ( ! [SY2791: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV269 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV269 @ SY2791 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2750,plain,
! [SV270: $i] :
( ( ! [SY2792: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV270 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2792 @ SV270 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2751,plain,
! [SV271: $i] :
( ( ! [SY2793: $i,SY2794: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2793 @ SY2794 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SY2794 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SY2793 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2752,plain,
! [SV272: $i] :
( ( ! [SY2795: $i,SY2796: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV272 )
| ( SY2795
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2796 @ SY2796 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SY2795 @ SY2795 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2753,plain,
! [SV273: $i] :
( ( ! [SY2797: $i,SY2798: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV273 )
| ( SY2797
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2797 @ SY2797 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SY2798 @ SY2798 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2754,plain,
! [SV274: $i] :
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV274 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2755,plain,
! [SV275: $i] :
( ( ! [SY2799: $i,SY2800: $i] :
( ( c_HOL_Oord__class_Oless @ SV275 @ SY2799 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY2800 ) @ SV275 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY2800 ) @ SY2799 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2756,plain,
! [SV276: $i] :
( ( ! [SY2801: $i,SY2802: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SY2801 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SY2802 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2801 @ SY2802 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2757,plain,
! [SV277: $i] :
( ( ! [SY2803: $i] :
( ( c_lessequals @ ( c_Suc @ SV277 ) @ SY2803 @ tc_nat )
| ( c_lessequals @ SY2803 @ SV277 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2758,plain,
! [SV278: $i] :
( ( ! [SY2804: $i] :
( ~ ( c_lessequals @ SV278 @ SY2804 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SY2804 ) @ SV278 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2759,plain,
! [SV279: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV279 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV279 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2760,plain,
! [SV280: $i] :
( ( ! [SY2805: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV280 @ SY2805 @ tc_nat ) @ SV280 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2761,plain,
! [SV281: $i] :
( ( ! [SY2806: $i,SY2807: $i] :
( ( c_lessequals @ SV281 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY2806 @ SV281 @ tc_nat ) @ SY2807 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2807 @ SY2806 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2762,plain,
! [SV282: $i] :
( ( ! [SY2808: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV282 )
| ( ( c_HOL_Oabs__class_Oabs @ SY2808 @ SV282 )
= SY2808 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SY2808 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2763,plain,
! [SV283: $i] :
( ( ! [SY2809: $i,SY2810: $i,SY2811: $i] :
( ~ ( class_Divides_Osemiring__div @ SV283 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2809 @ SY2810 @ SV283 ) @ SY2811 @ SV283 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2809 @ ( c_Divides_Odiv__class_Omod @ SY2810 @ SY2811 @ SV283 ) @ SV283 ) @ SY2811 @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2764,plain,
! [SV284: $i] :
( ( ! [SY2812: $i,SY2813: $i,SY2814: $i] :
( ~ ( class_Divides_Osemiring__div @ SV284 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2812 @ SY2813 @ SV284 ) @ SY2814 @ SV284 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY2812 @ SY2814 @ SV284 ) @ SY2813 @ SV284 ) @ SY2814 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2765,plain,
! [SV285: $i] :
( ( ! [SY2815: $i,SY2816: $i] :
( ( c_lessequals @ SV285 @ SY2815 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY2816 ) @ SV285 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY2816 ) @ SY2815 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2766,plain,
! [SV286: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SY2817 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SY2818 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2817 @ SY2818 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2767,plain,
! [SV287: $i] :
( ( ! [SY2819: $i,SY2820: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV287 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV287 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2819 @ SY2819 @ SV287 ) @ ( c_HOL_Otimes__class_Otimes @ SY2820 @ SY2820 @ SV287 ) @ SV287 ) @ SV287 )
| ( SY2820
= ( c_HOL_Ozero__class_Ozero @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2768,plain,
! [SV288: $i] :
( ( ! [SY2821: $i,SY2822: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV288 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV288 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2821 @ SY2821 @ SV288 ) @ ( c_HOL_Otimes__class_Otimes @ SY2822 @ SY2822 @ SV288 ) @ SV288 ) @ SV288 )
| ( SY2821
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2769,plain,
! [SV289: $i] :
( ( ! [SY2823: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV289 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2823 @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV289 ) @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2770,plain,
! [SV290: $i] :
( ( c_lessequals @ ( c_Suc @ SV290 ) @ ( c_Suc @ SV290 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2771,plain,
! [SV291: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV291 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ SV291 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2772,plain,
! [SV292: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ SV292 ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV292 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2773,plain,
! [SV293: $i] :
( ( ( SV293
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV293 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2774,plain,
! [SV294: $i] :
( ( c_lessequals @ SV294 @ ( c_HOL_Otimes__class_Otimes @ SV294 @ SV294 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2775,plain,
! [SV295: $i] :
( ( ! [SY2824: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ SV295 ) @ ( c_Suc @ SY2824 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ SV295 @ SY2824 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2776,plain,
! [SV296: $i] :
( ( ! [SY2825: $i,SY2826: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV296 @ SY2825 @ tc_nat ) @ SY2826 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV296 @ SY2826 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2825 @ SY2826 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2777,plain,
! [SV297: $i] :
( ( ! [SY2827: $i,SY2828: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV297 @ ( c_Divides_Odiv__class_Omod @ SY2827 @ SY2828 @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV297 @ SY2827 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV297 @ SY2828 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2778,plain,
! [SV298: $i] :
( ( ! [SY2829: $i,SY2830: $i,SY2831: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2829 @ SY2830 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SY2829 @ SY2831 @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SY2829 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SY2830 @ SY2831 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2779,plain,
! [SV299: $i] :
( ( ! [SY2832: $i,SY2833: $i,SY2834: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2832 @ SY2833 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SY2834 @ SY2833 @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SY2834 @ SY2832 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SY2833 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2780,plain,
! [SV300: $i] :
( ( ! [SY2835: $i,SY2836: $i,SY2837: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2835 @ SY2836 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SY2837 @ SY2836 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SY2835 @ SY2837 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SY2836 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2781,plain,
! [SV301: $i] :
( ( ! [SY2838: $i,SY2839: $i,SY2840: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2838 @ SY2839 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SY2840 @ SY2839 @ SV301 ) @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SY2839 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SY2838 @ SY2840 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2782,plain,
! [SV302: $i] :
( ( ! [SY2841: $i,SY2842: $i,SY2843: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2841 @ SY2842 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SY2843 @ SY2842 @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SY2842 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SY2843 @ SY2841 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2783,plain,
! [SV303: $i] :
( ( ! [SY2844: $i,SY2845: $i,SY2846: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2844 @ SY2845 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SY2844 @ SY2846 @ SV303 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SY2846 @ SY2845 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SY2844 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2784,plain,
! [SV304: $i] :
( ( ! [SY2847: $i,SY2848: $i,SY2849: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2847 @ SY2848 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SY2847 @ SY2849 @ SV304 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SY2848 @ SY2849 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SY2847 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2785,plain,
! [SV305: $i] :
( ( ! [SY2850: $i,SY2851: $i,SY2852: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2850 @ SY2851 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SY2850 @ SY2852 @ SV305 ) @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SY2850 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SY2851 @ SY2852 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2786,plain,
! [SV306: $i] :
( ( ! [SY2853: $i,SY2854: $i,SY2855: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2853 @ SY2854 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SY2853 @ SY2855 @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SY2853 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SY2855 @ SY2854 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2787,plain,
! [SV307: $i] :
( ( ! [SY2856: $i,SY2857: $i,SY2858: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2856 @ SY2857 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SY2856 @ SY2858 @ SV307 ) @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SY2857 @ SY2858 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SY2856 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2788,plain,
! [SV308: $i] :
( ( ! [SY2859: $i,SY2860: $i,SY2861: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
| ( c_HOL_Oord__class_Oless @ SY2859 @ SY2860 @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2861 @ SY2859 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SY2861 @ SY2860 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SY2861 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2789,plain,
! [SV309: $i] :
( ( ! [SY2862: $i,SY2863: $i,SY2864: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2862 @ SY2863 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SY2862 @ SY2864 @ SV309 ) @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SY2864 @ SY2863 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SY2862 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2790,plain,
! [SV310: $i] :
( ( ! [SY2865: $i,SY2866: $i,SY2867: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
| ( c_HOL_Oord__class_Oless @ SY2865 @ SY2866 @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2867 @ SY2866 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SY2867 @ SY2865 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SY2867 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2791,plain,
! [SV311: $i] :
( ( ! [SY2868: $i,SY2869: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SY2868 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SY2869 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2868 @ SY2869 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2792,plain,
! [SV312: $i] :
( ( ! [SY2870: $i,SY2871: $i] :
( ( c_HOL_Oord__class_Oless @ SV312 @ SY2870 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY2871 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2871 @ SY2870 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2871 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2793,plain,
! [SV313: $i] :
( ( ! [SY2872: $i,SY2873: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SY2872 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2873 @ SY2872 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2872 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SY2873 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2794,plain,
! [SV314: $i] :
( ( ! [SY2874: $i,SY2875: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SY2874 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SY2875 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2874 @ SY2875 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2795,plain,
! [SV315: $i] :
( ( ! [SY2876: $i,SY2877: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SY2876 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SY2877 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2876 @ SY2877 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2796,plain,
! [SV316: $i] :
( ( ! [SY2878: $i,SY2879: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SY2878 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2879 @ SY2878 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV316 @ SY2879 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2878 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2797,plain,
! [SV317: $i] :
( ( ! [SY2880: $i,SY2881: $i,SY2882: $i] :
( ~ ( class_Divides_Osemiring__div @ SV317 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2880 @ ( c_HOL_Otimes__class_Otimes @ SY2881 @ SY2882 @ SV317 ) @ SV317 ) @ SY2881 @ SV317 )
= ( c_Divides_Odiv__class_Omod @ SY2880 @ SY2881 @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2798,plain,
! [SV318: $i] :
( ( ! [SY2883: $i,SY2884: $i,SY2885: $i] :
( ~ ( class_Divides_Osemiring__div @ SV318 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2883 @ ( c_HOL_Otimes__class_Otimes @ SY2884 @ SY2885 @ SV318 ) @ SV318 ) @ SY2885 @ SV318 )
= ( c_Divides_Odiv__class_Omod @ SY2883 @ SY2885 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2799,plain,
! [SV319: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV319 @ SY2886 @ tc_nat ) @ SY2887 @ tc_nat ) @ SY2886 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SY2887 @ SY2886 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2800,plain,
! [SV320: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV320 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2888 @ SY2889 @ SV320 )
| ( SY2890
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2888 @ SY2890 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SY2889 @ SY2890 @ SV320 ) @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2801,plain,
! [SV321: $i] :
( ( ! [SY2891: $i,SY2892: $i,SY2893: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV321 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2891 @ SY2892 @ SV321 )
| ( SY2893
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2893 @ SY2891 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SY2893 @ SY2892 @ SV321 ) @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2802,plain,
! [SV322: $i] :
( ( ! [SY2894: $i,SY2895: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV322 @ SY2894 @ tc_nat )
| ( SY2895
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2895 @ SV322 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY2895 @ SY2894 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2803,plain,
! [SV323: $i] :
( ( ! [SY2896: $i,SY2897: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2896 @ SY2897 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ SY2897 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SY2896 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2804,plain,
! [SV324: $i] :
( ( ! [SY2898: $i,SY2899: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2898 @ SY2899 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SY2899 @ SV324 )
| ~ ( c_lessequals @ SY2898 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2805,plain,
! [SV325: $i] :
( ( ! [SY2900: $i,SY2901: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2900 @ SY2901 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ SY2901 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SY2900 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2806,plain,
! [SV326: $i] :
( ( ! [SY2902: $i,SY2903: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2902 @ SY2903 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SY2903 @ SV326 )
| ~ ( c_lessequals @ SY2902 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2807,plain,
! [SV327: $i] :
( ( ! [SY2904: $i,SY2905: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2904 @ SY2905 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ SY2905 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SY2904 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2808,plain,
! [SV328: $i] :
( ( ! [SY2906: $i,SY2907: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2906 @ SY2907 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SY2907 @ SV328 )
| ~ ( c_lessequals @ SY2906 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2809,plain,
! [SV329: $i] :
( ( ! [SY2908: $i,SY2909: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY2908 @ SY2909 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ SY2908 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SY2909 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2810,plain,
! [SV330: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV330 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV330 ) @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2811,plain,
! [SV331: $i] :
( ( ! [SY2910: $i,SY2911: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SY2910 @ SY2911 @ SV331 ) @ SV331 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SY2911 @ SV331 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SY2910 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2812,plain,
! [SV332: $i] :
( ( ! [SY2912: $i,SY2913: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SY2912 @ SY2913 @ SV332 ) @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SY2913 @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SY2912 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2813,plain,
! [SV333: $i] :
( ( ! [SY2914: $i,SY2915: $i] :
( ~ ( class_Divides_Osemiring__div @ SV333 )
| ( ( c_Divides_Odiv__class_Omod @ SY2914 @ SY2915 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2915 @ SY2914 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2814,plain,
! [SV334: $i] :
( ( ! [SY2916: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 )
| ( SY2916
= ( c_HOL_Ozero__class_Ozero @ SV334 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV334 ) @ SY2916 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2815,plain,
! [SV335: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV335 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV335 )
= ( c_HOL_Ozero__class_Ozero @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2816,plain,
! [SV336: $i] :
( ( ! [SY2917: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SY2917 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV336 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2917 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2817,plain,
! [SV337: $i] :
( ( ! [SY2918: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV337 ) @ SY2918 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV337 @ ( c_Suc @ SY2918 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2818,plain,
! [SV338: $i] :
( ( ! [SY2919: $i,SY2920: $i,SY2921: $i] :
( ~ ( class_Orderings_Olinorder @ SV338 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SY2919 @ SY2920 @ SV338 ) @ SY2921 @ SV338 )
= ( c_Orderings_Oord__class_Omin @ SY2919 @ ( c_Orderings_Oord__class_Omin @ SY2920 @ SY2921 @ SV338 ) @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2819,plain,
! [SV339: $i] :
( ( ! [SY2922: $i,SY2923: $i,SY2924: $i] :
( ~ ( class_Orderings_Olinorder @ SV339 )
| ( ( c_Orderings_Oord__class_Omin @ SY2922 @ ( c_Orderings_Oord__class_Omin @ SY2923 @ SY2924 @ SV339 ) @ SV339 )
= ( c_Orderings_Oord__class_Omin @ SY2923 @ ( c_Orderings_Oord__class_Omin @ SY2922 @ SY2924 @ SV339 ) @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2820,plain,
! [SV340: $i] :
( ( ! [SY2925: $i,SY2926: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SY2925 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SY2926 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2926 @ SV340 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2926 @ SY2925 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2925 @ SY2926 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2821,plain,
! [SV341: $i] :
( ( ! [SY2927: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV341 @ SY2927 @ tc_nat ) @ SY2927 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2927 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2822,plain,
! [SV342: $i] :
( ( ! [SY2928: $i,SY2929: $i] :
( ~ ( class_Orderings_Olinorder @ SV342 )
| ( ( c_Orderings_Oord__class_Omin @ SY2928 @ SY2929 @ SV342 )
= SY2928 )
| ~ ( c_lessequals @ SY2928 @ SY2929 @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2823,plain,
! [SV343: $i] :
( ( ! [SY2930: $i,SY2931: $i] :
( ~ ( class_Orderings_Olinorder @ SV343 )
| ( ( c_Orderings_Oord__class_Omin @ SY2930 @ SY2931 @ SV343 )
= SY2931 )
| ~ ( c_lessequals @ SY2931 @ SY2930 @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2824,plain,
! [SV344: $i] :
( ( ! [SY2932: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV344 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SY2932 @ SV344 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2825,plain,
! [SV345: $i] :
( ( ! [SY2933: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV345 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SY2933 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2826,plain,
! [SV346: $i] :
( ( ! [SY2934: $i,SY2935: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SY2934 @ SY2935 @ SV346 ) @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SY2935 @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SY2934 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2827,plain,
! [SV347: $i] :
( ( ! [SY2936: $i] :
( ( c_HOL_Oord__class_Oless @ SV347 @ ( c_Suc @ SY2936 ) @ tc_nat )
| ~ ( c_lessequals @ SV347 @ SY2936 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2828,plain,
! [SV348: $i] :
( ( ! [SY2937: $i] :
( ( c_lessequals @ SV348 @ SY2937 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV348 @ ( c_Suc @ SY2937 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2829,plain,
! [SV349: $i] :
( ( ~ ( c_lessequals @ SV349 @ SV349 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Suc @ SV349 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2830,plain,
! [SV350: $i] :
( ( ! [SY2938: $i,SY2939: $i,SY2940: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SY2938 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2939 @ SY2940 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2938 @ SY2940 @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SY2939 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2831,plain,
! [SV351: $i] :
( ( ! [SY2941: $i,SY2942: $i,SY2943: $i,SY2944: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2941 @ SY2942 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SY2943 @ SY2944 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SY2942 @ SY2944 @ SV351 )
| ~ ( c_lessequals @ SY2941 @ SY2943 @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2832,plain,
! [SV352: $i] :
( ( ! [SY2945: $i,SY2946: $i,SY2947: $i,SY2948: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SY2945 @ tc_nat ) @ SY2946 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2947 @ SY2945 @ tc_nat ) @ SY2948 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SY2947 @ tc_nat ) @ SY2945 @ tc_nat ) @ SY2946 @ tc_nat ) @ SY2948 @ tc_nat ) )
| ~ ( c_lessequals @ SY2947 @ SV352 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2833,plain,
! [SV353: $i] :
( ( ! [SY2949: $i,SY2950: $i,SY2951: $i,SY2952: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SY2949 @ tc_nat ) @ SY2950 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2951 @ SY2949 @ tc_nat ) @ SY2952 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY2950 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2951 @ SV353 @ tc_nat ) @ SY2949 @ tc_nat ) @ SY2952 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV353 @ SY2951 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2834,plain,
! [SV354: $i] :
( ( ! [SY2953: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV354 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SY2953 @ SV354 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ ( c_HOL_Oplus__class_Oplus @ SY2953 @ SY2953 @ SV354 ) @ SV354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2835,plain,
! [SV355: $i] :
( ( ! [SY2954: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV355 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ ( c_HOL_Oplus__class_Oplus @ SY2954 @ SY2954 @ SV355 ) @ SV355 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ SY2954 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2836,plain,
! [SV356: $i] :
( ( ! [SY2955: $i,SY2956: $i] :
( ~ ( class_Divides_Osemiring__div @ SV356 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SY2955 @ SY2956 @ SV356 ) @ SY2956 @ SV356 )
= ( c_Divides_Odiv__class_Omod @ SY2955 @ SY2956 @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2837,plain,
! [SV357: $i] :
( ( ! [SY2957: $i,SY2958: $i,SY2959: $i,SY2960: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY2957 @ SY2958 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SY2959 @ SY2960 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY2957 @ SY2959 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY2958 @ SY2960 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2838,plain,
! [SV358: $i] :
( ( ! [SY2961: $i,SY2962: $i,SY2963: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
| ( c_HOL_Oord__class_Oless @ SY2961 @ ( c_HOL_Oplus__class_Oplus @ SY2962 @ SY2963 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SY2961 @ SY2963 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SY2962 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2839,plain,
! [SV359: $i] :
( ( ! [SY2964: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SY2964 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV359 @ SY2964 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2840,plain,
! [SV360: $i] :
( ( ! [SY2965: $i,SY2966: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SY2965 @ tc_nat )
| ~ ( c_lessequals @ SY2965 @ SY2966 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SY2966 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SY2966 @ SY2965 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2841,plain,
! [SV361: $i] :
( ( ! [SY2967: $i,SY2968: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SY2967 @ tc_nat )
| ~ ( c_lessequals @ SY2968 @ SY2967 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SY2968 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SY2967 @ SY2968 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2842,plain,
! [SV362: $i] :
( ( ! [SY2969: $i,SY2970: $i,SY2971: $i,SY2972: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV362 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2969 @ SY2970 @ SV362 ) @ SY2971 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY2972 @ SY2970 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY2969 @ SY2972 @ SV362 ) @ SY2970 @ SV362 ) @ SY2971 @ SV362 ) @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2843,plain,
! [SV363: $i] :
( ( ! [SY2973: $i,SY2974: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SY2973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SY2974 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2973 @ SY2974 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2844,plain,
! [SV364: $i] :
( ( ! [SY2975: $i,SY2976: $i,SY2977: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV364 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2975 @ SY2976 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SY2975 @ SY2977 @ SV364 ) @ SV364 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2976 @ SY2977 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2845,plain,
! [SV365: $i] :
( ( ! [SY2978: $i,SY2979: $i,SY2980: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV365 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY2978 @ SY2979 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SY2980 @ SY2979 @ SV365 ) @ SV365 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2978 @ SY2980 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2846,plain,
! [SV366: $i] :
( ( ! [SY2981: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV366 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SY2981 @ SV366 ) @ SV366 )
= ( c_HOL_Oabs__class_Oabs @ SY2981 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2847,plain,
! [SV367: $i] :
( ( ! [SY2982: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV367 ) @ SY2982 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV367 @ SY2982 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2848,plain,
! [SV368: $i] :
( ( ! [SY2983: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV368 @ ( c_Suc @ SY2983 ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV368 @ SY2983 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2849,plain,
! [SV369: $i] :
( ( ! [SY2984: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV369 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oabs__class_Oabs @ SY2984 @ SV369 ) @ SV369 )
| ( SY2984
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2850,plain,
! [SV370: $i] :
( ( ! [SY2985: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV370 @ SY2985 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY2985 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2851,plain,
! [SV371: $i] :
( ( ! [SY2986: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV371 @ SY2986 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV371 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2852,plain,
! [SV372: $i] :
( ( ! [SY2987: $i] :
( ~ ( class_Divides_Osemiring__div @ SV372 )
| ( ( c_Divides_Odiv__class_Omod @ SY2987 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 )
= SY2987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2853,plain,
! [SV373: $i] :
( ( ! [SY2988: $i] :
( ~ ( class_Divides_Osemiring__div @ SV373 )
| ( ( c_Divides_Odiv__class_Omod @ SY2988 @ SY2988 @ SV373 )
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2854,plain,
! [SV374: $i] :
( ( ! [SY2989: $i,SY2990: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2989 @ SY2990 @ SV374 )
= ( c_HOL_Oplus__class_Oplus @ SY2990 @ SY2989 @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2855,plain,
! [SV375: $i] :
( ( ! [SY2991: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV375 @ SY2991 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY2991 @ SV375 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2856,plain,
! [SV376: $i] :
( ( ! [SY2992: $i,SY2993: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV376 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2992 @ SY2993 @ SV376 )
= ( c_HOL_Oplus__class_Oplus @ SY2993 @ SY2992 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2857,plain,
! [SV377: $i] :
( ( ! [SY2994: $i,SY2995: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2994 @ SY2995 @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ SY2995 @ SY2994 @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2858,plain,
! [SV378: $i] :
( ( ! [SY2996: $i,SY2997: $i,SY2998: $i] :
( ~ ( class_Divides_Osemiring__div @ SV378 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY2996 @ SY2997 @ SV378 ) @ SY2998 @ SV378 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY2996 @ SY2998 @ SV378 ) @ ( c_Divides_Odiv__class_Omod @ SY2997 @ SY2998 @ SV378 ) @ SV378 ) @ SY2998 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2859,plain,
! [SV379: $i] :
( ( ! [SY2999: $i,SY3000: $i,SY3001: $i] :
( ~ ( class_Orderings_Olinorder @ SV379 )
| ( c_lessequals @ SY2999 @ SY3000 @ SV379 )
| ~ ( c_lessequals @ SY2999 @ ( c_Orderings_Oord__class_Omin @ SY3000 @ SY3001 @ SV379 ) @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2860,plain,
! [SV380: $i] :
( ( ! [SY3002: $i,SY3003: $i,SY3004: $i] :
( ~ ( class_Orderings_Olinorder @ SV380 )
| ( c_lessequals @ SY3002 @ SY3003 @ SV380 )
| ~ ( c_lessequals @ SY3002 @ ( c_Orderings_Oord__class_Omin @ SY3004 @ SY3003 @ SV380 ) @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2861,plain,
! [SV381: $i] :
( ( ! [SY3005: $i,SY3006: $i,SY3007: $i] :
( ~ ( class_Orderings_Olinorder @ SV381 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3005 @ SY3006 @ SV381 ) @ SY3007 @ SV381 )
| ~ ( c_lessequals @ SY3005 @ SY3007 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2862,plain,
! [SV382: $i] :
( ( ! [SY3008: $i,SY3009: $i,SY3010: $i] :
( ~ ( class_Orderings_Olinorder @ SV382 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3008 @ SY3009 @ SV382 ) @ SY3010 @ SV382 )
| ~ ( c_lessequals @ SY3009 @ SY3010 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2863,plain,
! [SV383: $i] :
( ( ! [SY3011: $i,SY3012: $i,SY3013: $i] :
( ~ ( class_Orderings_Olinorder @ SV383 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3011 @ SY3012 @ SV383 ) @ SY3013 @ SV383 )
| ~ ( c_lessequals @ SY3011 @ SY3013 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2864,plain,
! [SV384: $i] :
( ( ! [SY3014: $i,SY3015: $i,SY3016: $i] :
( ~ ( class_Orderings_Olinorder @ SV384 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3014 @ SY3015 @ SV384 ) @ SY3016 @ SV384 )
| ~ ( c_lessequals @ SY3015 @ SY3016 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2865,plain,
! [SV385: $i] :
( ( ! [SY3017: $i,SY3018: $i,SY3019: $i] :
( ~ ( class_Orderings_Olinorder @ SV385 )
| ( c_lessequals @ SY3017 @ SY3018 @ SV385 )
| ~ ( c_lessequals @ SY3017 @ ( c_Orderings_Oord__class_Omin @ SY3018 @ SY3019 @ SV385 ) @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2866,plain,
! [SV386: $i] :
( ( ! [SY3020: $i,SY3021: $i,SY3022: $i] :
( ~ ( class_Orderings_Olinorder @ SV386 )
| ( c_lessequals @ SY3020 @ SY3021 @ SV386 )
| ~ ( c_lessequals @ SY3020 @ ( c_Orderings_Oord__class_Omin @ SY3022 @ SY3021 @ SV386 ) @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2867,plain,
! [SV387: $i] :
( ( ! [SY3023: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV387 )
| ( c_lessequals @ SY3023 @ ( c_HOL_Oabs__class_Oabs @ SY3023 @ SV387 ) @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2868,plain,
! [SV388: $i] :
( ( ! [SY3024: $i,SY3025: $i,SY3026: $i] :
( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_lessequals @ SY3024 @ SY3025 @ SV388 )
| ( c_lessequals @ SY3026 @ SY3025 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY3026 @ SY3024 @ SV388 ) @ SY3025 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2869,plain,
! [SV389: $i] :
( ( ! [SY3027: $i,SY3028: $i,SY3029: $i] :
( ~ ( c_lessequals @ SV389 @ SY3027 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV389 @ SY3028 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3027 @ SV389 @ tc_nat ) @ SY3028 @ tc_nat ) @ SY3029 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3027 @ SY3028 @ tc_nat ) @ SY3029 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2870,plain,
! [SV390: $i] :
( ( ! [SY3030: $i,SY3031: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV390 @ SY3030 @ tc_nat ) @ SY3031 @ tc_nat )
| ~ ( c_lessequals @ SV390 @ ( c_HOL_Oplus__class_Oplus @ SY3031 @ SY3030 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2871,plain,
! [SV391: $i] :
( ( ! [SY3032: $i,SY3033: $i] :
( ( c_lessequals @ SV391 @ ( c_HOL_Oplus__class_Oplus @ SY3032 @ SY3033 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV391 @ SY3033 @ tc_nat ) @ SY3032 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2872,plain,
! [SV392: $i] :
( ( ! [SY3034: $i,SY3035: $i,SY3036: $i,SY3037: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SY3034 @ tc_nat ) @ SY3035 @ tc_nat ) @ SY3036 @ tc_nat ) @ SY3037 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SY3035 @ tc_nat ) @ SY3036 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3034 @ SY3035 @ tc_nat ) @ SY3037 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3034 @ SV392 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2873,plain,
! [SV393: $i] :
( ( ! [SY3038: $i,SY3039: $i,SY3040: $i,SY3041: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SY3038 @ tc_nat ) @ SY3039 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3040 @ SY3038 @ tc_nat ) @ SY3041 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SY3040 @ tc_nat ) @ SY3038 @ tc_nat ) @ SY3039 @ tc_nat ) @ SY3041 @ tc_nat )
| ~ ( c_lessequals @ SY3040 @ SV393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2874,plain,
! [SV394: $i] :
( ( ! [SY3042: $i,SY3043: $i,SY3044: $i,SY3045: $i] :
( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3042 @ SY3043 @ tc_nat ) @ SY3044 @ tc_nat ) @ SY3045 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3043 @ SY3044 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3042 @ SY3044 @ tc_nat ) @ SY3045 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3043 @ SY3042 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2875,plain,
! [SV395: $i] :
( ( ! [SY3046: $i,SY3047: $i,SY3048: $i,SY3049: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SY3046 @ tc_nat ) @ SY3047 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3048 @ SY3046 @ tc_nat ) @ SY3049 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3047 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3048 @ SV395 @ tc_nat ) @ SY3046 @ tc_nat ) @ SY3049 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV395 @ SY3048 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2876,plain,
! [SV396: $i] :
( ( ! [SY3050: $i,SY3051: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV396 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SY3050 @ SY3051 @ tc_nat ) @ SV396 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3050 @ SV396 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3051 @ SV396 ) @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2877,plain,
! [SV397: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SY3052 @ tc_nat ) @ SY3053 @ tc_nat ) ) @ SY3052 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SY3053 ) @ SY3052 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2878,plain,
! [SV398: $i] :
( ( ! [SY3054: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV398 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY3054 @ SV398 ) @ ( c_HOL_Oabs__class_Oabs @ SY3054 @ SV398 ) @ SV398 )
= ( c_HOL_Otimes__class_Otimes @ SY3054 @ SY3054 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2879,plain,
! [SV399: $i] :
( ( ! [SY3055: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV399 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV399 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3055 @ SV399 ) @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2880,plain,
! [SV400: $i] :
( ( ! [SY3056: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV400 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV400 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3056 @ SV400 ) @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2881,plain,
! [SV401: $i] :
( ( ! [SY3057: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV401 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3057 @ ( c_HOL_Ozero__class_Ozero @ SV401 ) @ SV401 )
= SY3057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2882,plain,
! [SV402: $i] :
( ( ! [SY3058: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV402 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV402 ) @ SY3058 @ SV402 )
= SY3058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2883,plain,
! [SV403: $i] :
( ( ! [SY3059: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV403 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3059 @ ( c_HOL_Ozero__class_Ozero @ SV403 ) @ SV403 )
= SY3059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2884,plain,
! [SV404: $i] :
( ( ! [SY3060: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV404 )
| ~ ( class_Int_Onumber__ring @ SV404 )
| ( SY3060
= ( c_HOL_Oplus__class_Oplus @ SY3060 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2885,plain,
! [SV405: $i] :
( ( ! [SY3061: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV405 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SY3061 @ SV405 )
= SY3061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2886,plain,
! [SV406: $i] :
( ( ! [SY3062: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV406 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SY3062 @ SV406 )
= SY3062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2887,plain,
! [SV407: $i] :
( ( SV407
= ( c_HOL_Oplus__class_Oplus @ SV407 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2888,plain,
! [SV408: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV408 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV408 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2889,plain,
! [SV409: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV409 @ tc_nat )
= SV409 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2890,plain,
! [SV410: $i] :
( ( ! [SY3063: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV410 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3063 @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV410 )
= SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2891,plain,
! [SV411: $i] :
( ( ! [SY3064: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV411 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV411 ) @ SY3064 @ SV411 )
= SY3064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2892,plain,
! [SV412: $i] :
( ( ! [SY3065: $i,SY3066: $i,SY3067: $i,SY3068: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3065 @ SY3066 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SY3067 @ SY3068 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SY3066 @ SY3068 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SY3065 @ SY3067 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2893,plain,
! [SV413: $i] :
( ( ! [SY3069: $i,SY3070: $i,SY3071: $i,SY3072: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3069 @ SY3070 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SY3071 @ SY3072 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SY3070 @ SY3072 @ SV413 )
| ~ ( c_lessequals @ SY3069 @ SY3071 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2894,plain,
! [SV414: $i] :
( ( ! [SY3073: $i,SY3074: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SY3073 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SY3074 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3074 @ SV414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3073 @ SY3074 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2895,plain,
! [SV415: $i] :
( ( ! [SY3075: $i,SY3076: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SY3075 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3076 @ SV415 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3076 @ SY3075 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3075 @ SY3076 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2896,plain,
! [SV416: $i] :
( ( ! [SY3077: $i,SY3078: $i,SY3079: $i] :
( ~ ( class_Orderings_Oorder @ SV416 )
| ( c_HOL_Oord__class_Oless @ SY3077 @ SY3078 @ SV416 )
| ~ ( c_lessequals @ SY3077 @ SY3079 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SY3079 @ SY3078 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2897,plain,
! [SV417: $i] :
( ( ! [SY3080: $i,SY3081: $i,SY3082: $i] :
( ~ ( class_Orderings_Oorder @ SV417 )
| ( c_HOL_Oord__class_Oless @ SY3080 @ SY3081 @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SY3080 @ SY3082 @ SV417 )
| ~ ( c_lessequals @ SY3082 @ SY3081 @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2898,plain,
! [SV418: $i] :
( ( ! [SY3083: $i,SY3084: $i,SY3085: $i] :
( ~ ( class_Orderings_Opreorder @ SV418 )
| ( c_HOL_Oord__class_Oless @ SY3083 @ SY3084 @ SV418 )
| ~ ( c_lessequals @ SY3085 @ SY3084 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SY3083 @ SY3085 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2899,plain,
! [SV419: $i] :
( ( ! [SY3086: $i,SY3087: $i,SY3088: $i] :
( ~ ( class_Orderings_Opreorder @ SV419 )
| ( c_HOL_Oord__class_Oless @ SY3086 @ SY3087 @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SY3088 @ SY3087 @ SV419 )
| ~ ( c_lessequals @ SY3086 @ SY3088 @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2900,plain,
! [SV420: $i] :
( ( ! [SY3089: $i,SY3090: $i,SY3091: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3089 @ SY3090 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SY3091 @ SY3090 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SY3089 @ SY3091 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2901,plain,
! [SV421: $i] :
( ( ! [SY3092: $i,SY3093: $i,SY3094: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3092 @ SY3093 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SY3094 @ SY3093 @ SV421 ) @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SY3092 @ SY3094 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2902,plain,
! [SV422: $i] :
( ( ! [SY3095: $i,SY3096: $i,SY3097: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_HOL_Oord__class_Oless @ SY3095 @ SY3096 @ SV422 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3095 @ SY3097 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SY3096 @ SY3097 @ SV422 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2903,plain,
! [SV423: $i] :
( ( ! [SY3098: $i,SY3099: $i,SY3100: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3098 @ SY3099 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SY3098 @ SY3100 @ SV423 ) @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SY3099 @ SY3100 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2904,plain,
! [SV424: $i] :
( ( ! [SY3101: $i,SY3102: $i,SY3103: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3101 @ SY3102 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SY3101 @ SY3103 @ SV424 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ SY3102 @ SY3103 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2905,plain,
! [SV425: $i] :
( ( ! [SY3104: $i,SY3105: $i,SY3106: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
| ( c_HOL_Oord__class_Oless @ SY3104 @ SY3105 @ SV425 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3106 @ SY3104 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SY3106 @ SY3105 @ SV425 ) @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2906,plain,
! [SV426: $i] :
( ( ! [SY3107: $i,SY3108: $i] :
( ~ ( class_Orderings_Opreorder @ SV426 )
| ( c_lessequals @ SY3107 @ SY3108 @ SV426 )
| ~ ( c_HOL_Oord__class_Oless @ SY3107 @ SY3108 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2907,plain,
! [SV427: $i] :
( ( ! [SY3109: $i,SY3110: $i] :
( ~ ( class_Orderings_Oorder @ SV427 )
| ( c_lessequals @ SY3109 @ SY3110 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SY3109 @ SY3110 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2908,plain,
! [SV428: $i] :
( ( ! [SY3111: $i,SY3112: $i,SY3113: $i,SY3114: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3111 @ SY3112 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SY3113 @ SY3114 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SY3112 @ SY3114 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SY3111 @ SY3113 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2909,plain,
! [SV429: $i] :
( ( ! [SY3115: $i,SY3116: $i] :
( ~ ( class_Orderings_Opreorder @ SV429 )
| ( c_HOL_Oord__class_Oless @ SY3115 @ SY3116 @ SV429 )
| ( c_lessequals @ SY3116 @ SY3115 @ SV429 )
| ~ ( c_lessequals @ SY3115 @ SY3116 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2910,plain,
! [SV430: $i] :
( ( ! [SY3117: $i,SY3118: $i,SY3119: $i] :
( ~ ( class_Orderings_Olinorder @ SV430 )
| ( c_HOL_Oord__class_Oless @ SY3117 @ SY3118 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SY3119 @ SY3118 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3119 @ SY3117 @ SV430 ) @ SY3118 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2911,plain,
! [SV431: $i] :
( ( ! [SY3120: $i,SY3121: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV431 )
| ( c_HOL_Oord__class_Oless @ SY3120 @ SY3121 @ SV431 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SY3120 @ SV431 ) @ SY3121 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2912,plain,
! [SV432: $i] :
( ( ! [SY3122: $i,SY3123: $i,SY3124: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
| ( c_HOL_Oord__class_Oless @ SY3122 @ SY3123 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SY3123 @ SY3122 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3123 @ SY3124 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SY3122 @ SY3124 @ SV432 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2913,plain,
! [SV433: $i] :
( ( ! [SY3125: $i,SY3126: $i,SY3127: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
| ( c_HOL_Oord__class_Oless @ SY3125 @ SY3126 @ SV433 )
| ( c_HOL_Oord__class_Oless @ SY3126 @ SY3125 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3127 @ SY3126 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SY3127 @ SY3125 @ SV433 ) @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2914,plain,
! [SV434: $i] :
( ( ! [SY3128: $i,SY3129: $i] :
( ~ ( class_Orderings_Oorder @ SV434 )
| ( c_HOL_Oord__class_Oless @ SY3128 @ SY3129 @ SV434 )
| ( SY3129 = SY3128 )
| ~ ( c_lessequals @ SY3128 @ SY3129 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2915,plain,
! [SV435: $i] :
( ( ! [SY3130: $i,SY3131: $i] :
( ~ ( class_Orderings_Oorder @ SV435 )
| ( c_HOL_Oord__class_Oless @ SY3130 @ SY3131 @ SV435 )
| ~ ( c_lessequals @ SY3130 @ SY3131 @ SV435 )
| ( SY3131 = SY3130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2916,plain,
! [SV436: $i] :
( ( ! [SY3132: $i,SY3133: $i] :
( ~ ( class_Orderings_Olinorder @ SV436 )
| ( SY3132 = SY3133 )
| ( c_HOL_Oord__class_Oless @ SY3132 @ SY3133 @ SV436 )
| ~ ( c_lessequals @ SY3132 @ SY3133 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2917,plain,
! [SV437: $i] :
( ( ! [SY3134: $i,SY3135: $i] :
( ~ ( class_Orderings_Olinorder @ SV437 )
| ( SY3134 = SY3135 )
| ~ ( c_lessequals @ SY3134 @ SY3135 @ SV437 )
| ( c_HOL_Oord__class_Oless @ SY3134 @ SY3135 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2918,plain,
! [SV438: $i] :
( ( ! [SY3136: $i,SY3137: $i] :
( ~ ( class_Orderings_Oorder @ SV438 )
| ( c_HOL_Oord__class_Oless @ SY3136 @ SY3137 @ SV438 )
| ~ ( c_lessequals @ SY3136 @ SY3137 @ SV438 )
| ( SY3136 = SY3137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2919,plain,
! [SV439: $i] :
( ( ! [SY3138: $i,SY3139: $i] :
( ~ ( class_Orderings_Oorder @ SV439 )
| ( c_HOL_Oord__class_Oless @ SY3138 @ SY3139 @ SV439 )
| ( SY3138 = SY3139 )
| ~ ( c_lessequals @ SY3138 @ SY3139 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2920,plain,
! [SV440: $i] :
( ( ! [SY3140: $i,SY3141: $i] :
( ~ ( class_Orderings_Oorder @ SV440 )
| ( SY3140 = SY3141 )
| ( c_HOL_Oord__class_Oless @ SY3140 @ SY3141 @ SV440 )
| ~ ( c_lessequals @ SY3140 @ SY3141 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2921,plain,
! [SV441: $i] :
( ( ! [SY3142: $i,SY3143: $i] :
( ~ ( class_Orderings_Oorder @ SV441 )
| ( c_HOL_Oord__class_Oless @ SY3142 @ SY3143 @ SV441 )
| ( SY3142 = SY3143 )
| ~ ( c_lessequals @ SY3142 @ SY3143 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2922,plain,
! [SV442: $i] :
( ( ! [SY3144: $i,SY3145: $i,SY3146: $i] :
( ~ ( class_Orderings_Olinorder @ SV442 )
| ( c_HOL_Oord__class_Oless @ SY3144 @ ( c_Orderings_Oord__class_Omin @ SY3145 @ SY3146 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SY3144 @ SY3146 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SY3144 @ SY3145 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2923,plain,
! [SV443: $i] :
( ( ! [SY3147: $i,SY3148: $i] :
( ~ ( class_Orderings_Opreorder @ SV443 )
| ~ ( c_lessequals @ SY3147 @ SY3148 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ SY3148 @ SY3147 @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2924,plain,
! [SV444: $i] :
( ( ! [SY3149: $i,SY3150: $i] :
( ~ ( class_Orderings_Olinorder @ SV444 )
| ( c_HOL_Oord__class_Oless @ SY3149 @ SY3150 @ SV444 )
| ( c_lessequals @ SY3150 @ SY3149 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2925,plain,
! [SV445: $i] :
( ( ! [SY3151: $i] :
( ~ ( class_Orderings_Olinorder @ SV445 )
| ~ ( c_lessequals @ SY3151 @ SY3151 @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SY3151 @ SY3151 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2926,plain,
! [SV446: $i] :
( ( ! [SY3152: $i] :
( ~ ( class_Orderings_Olinorder @ SV446 )
| ( c_HOL_Oord__class_Oless @ SY3152 @ SY3152 @ SV446 )
| ( c_lessequals @ SY3152 @ SY3152 @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2927,plain,
! [SV447: $i] :
( ( ! [SY3153: $i,SY3154: $i] :
( ~ ( class_Orderings_Olinorder @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SY3153 @ SY3154 @ SV447 )
| ~ ( c_lessequals @ SY3154 @ SY3153 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2928,plain,
! [SV448: $i] :
( ( ! [SY3155: $i,SY3156: $i] :
( ~ ( class_Orderings_Olinorder @ SV448 )
| ( c_lessequals @ SY3155 @ SY3156 @ SV448 )
| ( c_HOL_Oord__class_Oless @ SY3156 @ SY3155 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2929,plain,
! [SV449: $i] :
( ( ! [SY3157: $i,SY3158: $i] :
( ~ ( class_Orderings_Olinorder @ SV449 )
| ( c_HOL_Oord__class_Oless @ SY3157 @ SY3158 @ SV449 )
| ( c_lessequals @ SY3158 @ SY3157 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2930,plain,
! [SV450: $i] :
( ( ! [SY3159: $i,SY3160: $i] :
( ~ ( class_Orderings_Olinorder @ SV450 )
| ~ ( c_lessequals @ SY3159 @ SY3160 @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ SY3160 @ SY3159 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2931,plain,
! [SV451: $i] :
( ( ! [SY3161: $i,SY3162: $i,SY3163: $i] :
( ~ ( class_Orderings_Olinorder @ SV451 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3161 @ SY3162 @ SV451 ) @ SY3163 @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ SY3162 @ SY3163 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2932,plain,
! [SV452: $i] :
( ( ! [SY3164: $i,SY3165: $i,SY3166: $i] :
( ~ ( class_Orderings_Olinorder @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3164 @ SY3165 @ SV452 ) @ SY3166 @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SY3164 @ SY3166 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2933,plain,
! [SV453: $i] :
( ( ! [SY3167: $i,SY3168: $i,SY3169: $i] :
( ~ ( class_Orderings_Olinorder @ SV453 )
| ( c_HOL_Oord__class_Oless @ SY3167 @ SY3168 @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SY3167 @ ( c_Orderings_Oord__class_Omin @ SY3169 @ SY3168 @ SV453 ) @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2934,plain,
! [SV454: $i] :
( ( ! [SY3170: $i,SY3171: $i,SY3172: $i] :
( ~ ( class_Orderings_Olinorder @ SV454 )
| ( c_HOL_Oord__class_Oless @ SY3170 @ SY3171 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ SY3170 @ ( c_Orderings_Oord__class_Omin @ SY3171 @ SY3172 @ SV454 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2935,plain,
! [SV455: $i] :
( ( ! [SY3173: $i,SY3174: $i,SY3175: $i] :
( ~ ( class_Orderings_Olinorder @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3173 @ SY3174 @ SV455 ) @ SY3175 @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SY3174 @ SY3175 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2936,plain,
! [SV456: $i] :
( ( ! [SY3176: $i,SY3177: $i,SY3178: $i] :
( ~ ( class_Orderings_Olinorder @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY3176 @ SY3177 @ SV456 ) @ SY3178 @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SY3176 @ SY3178 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2937,plain,
! [SV457: $i] :
( ( ! [SY3179: $i,SY3180: $i,SY3181: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV457 )
| ( c_HOL_Oord__class_Oless @ SY3179 @ ( c_HOL_Oplus__class_Oplus @ SY3180 @ SY3181 @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY3179 @ SY3180 @ SV457 ) @ SV457 ) @ SY3181 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2938,plain,
! [SV458: $i] :
( ( ! [SY3182: $i,SY3183: $i,SY3184: $i,SY3185: $i,SY3186: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3182 @ SY3183 @ SV458 ) @ SY3184 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3185 @ SY3183 @ SV458 ) @ SY3186 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SY3184 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3185 @ SY3182 @ SV458 ) @ SY3183 @ SV458 ) @ SY3186 @ SV458 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2939,plain,
! [SV459: $i] :
( ( ! [SY3187: $i,SY3188: $i,SY3189: $i,SY3190: $i,SY3191: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 )
| ( c_HOL_Oord__class_Oless @ SY3187 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3188 @ SY3189 @ SV459 ) @ SY3190 @ SV459 ) @ SY3191 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3189 @ SY3190 @ SV459 ) @ SY3187 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3188 @ SY3190 @ SV459 ) @ SY3191 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2940,plain,
! [SV460: $i] :
( ( ! [SY3192: $i,SY3193: $i,SY3194: $i,SY3195: $i,SY3196: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3192 @ SY3193 @ SV460 ) @ SY3194 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3195 @ SY3193 @ SV460 ) @ SY3196 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3192 @ SY3195 @ SV460 ) @ SY3193 @ SV460 ) @ SY3194 @ SV460 ) @ SY3196 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2941,plain,
! [SV461: $i] :
( ( ! [SY3197: $i,SY3198: $i,SY3199: $i,SY3200: $i,SY3201: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3197 @ SY3198 @ SV461 ) @ SY3199 @ SV461 ) @ SY3200 @ SV461 ) @ SY3201 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3197 @ SY3199 @ SV461 ) @ SY3200 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3198 @ SY3199 @ SV461 ) @ SY3201 @ SV461 ) @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2942,plain,
! [SV462: $i] :
( ( ! [SY3202: $i,SY3203: $i,SY3204: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV462 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY3202 @ SY3203 @ SV462 ) @ SV462 ) @ SY3204 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SY3202 @ ( c_HOL_Oplus__class_Oplus @ SY3203 @ SY3204 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3203 @ SY3204 @ SV462 ) @ SY3202 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2943,plain,
! [SV463: $i] :
( ( ! [SY3205: $i,SY3206: $i,SY3207: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV463 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SY3205 @ SY3206 @ SV463 ) @ SY3207 @ SV463 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SY3205 @ SY3207 @ SV463 ) @ ( c_HOL_Ominus__class_Ominus @ SY3206 @ SY3207 @ SV463 ) @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2944,plain,
! [SV464: $i] :
( ( ! [SY3208: $i,SY3209: $i,SY3210: $i] :
( ~ ( class_Divides_Oring__div @ SV464 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3208 @ SY3209 @ SV464 ) @ SY3210 @ SV464 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3208 @ ( c_Divides_Odiv__class_Omod @ SY3209 @ SY3210 @ SV464 ) @ SV464 ) @ SY3210 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2945,plain,
! [SV465: $i] :
( ( ! [SY3211: $i,SY3212: $i,SY3213: $i] :
( ~ ( class_Divides_Oring__div @ SV465 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3211 @ SY3212 @ SV465 ) @ SY3213 @ SV465 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SY3211 @ SY3213 @ SV465 ) @ SY3212 @ SV465 ) @ SY3213 @ SV465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2946,plain,
! [SV466: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i] :
( ~ ( class_Divides_Oring__div @ SV466 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3214 @ SY3215 @ SV466 ) @ SY3216 @ SV466 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SY3214 @ SY3216 @ SV466 ) @ ( c_Divides_Odiv__class_Omod @ SY3215 @ SY3216 @ SV466 ) @ SV466 ) @ SY3216 @ SV466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2947,plain,
! [SV467: $i] :
( ( ! [SY3217: $i,SY3218: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV467 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY3217 @ SY3218 @ SV467 ) @ SV467 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY3218 @ SY3217 @ SV467 ) @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2948,plain,
! [SV468: $i] :
( ( ! [SY3219: $i,SY3220: $i,SY3221: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3219 @ ( c_HOL_Ominus__class_Ominus @ SY3220 @ SY3221 @ SV468 ) @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3219 @ SY3221 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3219 @ SY3220 @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2949,plain,
! [SV469: $i] :
( ( ! [SY3222: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV469 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3222 @ SY3222 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2950,plain,
! [SV470: $i] :
( ( ! [SY3223: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV470 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3223 @ SY3223 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2951,plain,
! [SV471: $i] :
( ( ! [SY3224: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV471 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3224 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= SY3224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2952,plain,
! [SV472: $i] :
( ( ! [SY3225: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV472 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3225 @ SY3225 @ SV472 )
= ( c_HOL_Ozero__class_Ozero @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2953,plain,
! [SV473: $i] :
( ( ! [SY3226: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV473 )
| ~ ( class_Int_Onumber__ring @ SV473 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3226 @ SY3226 @ SV473 )
= ( c_HOL_Ozero__class_Ozero @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2954,plain,
! [SV474: $i] :
( ( ! [SY3227: $i,SY3228: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV474 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY3227 @ SY3228 @ SV474 ) @ SY3228 @ SV474 )
= SY3227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2955,plain,
! [SV475: $i] :
( ( ! [SY3229: $i,SY3230: $i,SY3231: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV475 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3229 @ ( c_HOL_Ominus__class_Ominus @ SY3230 @ SY3231 @ SV475 ) @ SV475 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY3229 @ SY3230 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SY3229 @ SY3231 @ SV475 ) @ SV475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2956,plain,
! [SV476: $i] :
( ( ! [SY3232: $i,SY3233: $i,SY3234: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV476 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3232 @ ( c_HOL_Ominus__class_Ominus @ SY3233 @ SY3234 @ SV476 ) @ SV476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY3232 @ SY3233 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SY3232 @ SY3234 @ SV476 ) @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2957,plain,
! [SV477: $i] :
( ( ! [SY3235: $i,SY3236: $i,SY3237: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV477 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3235 @ SY3236 @ SV477 ) @ SY3237 @ SV477 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY3235 @ SY3237 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SY3236 @ SY3237 @ SV477 ) @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2958,plain,
! [SV478: $i] :
( ( ! [SY3238: $i,SY3239: $i,SY3240: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV478 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3238 @ SY3239 @ SV478 ) @ SY3240 @ SV478 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SY3238 @ SY3240 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SY3239 @ SY3240 @ SV478 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2959,plain,
! [SV479: $i] :
( ( ! [SY3241: $i,SY3242: $i,SY3243: $i,SY3244: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV479 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY3241 @ SY3242 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SY3243 @ SY3244 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY3241 @ SY3243 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SY3242 @ SY3244 @ SV479 ) @ SV479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2960,plain,
! [SV480: $i] :
( ( ! [SY3245: $i,SY3246: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV480 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY3245 @ SY3246 @ SV480 ) @ SY3246 @ SV480 )
= SY3245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2961,plain,
! [SV481: $i] :
( ( ! [SY3247: $i,SY3248: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SY3247 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SY3248 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3247 @ SY3248 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2962,plain,
! [SV482: $i] :
( ( ! [SY3249: $i,SY3250: $i] :
( ( c_HOL_Oord__class_Oless @ SV482 @ SY3249 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3250 @ SV482 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3250 @ SY3249 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2963,plain,
! [SV483: $i] :
( ( ! [SY3251: $i,SY3252: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV483 @ SY3251 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3252 @ SY3251 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SY3252 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2964,plain,
! [SV484: $i] :
( ( ! [SY3253: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV484 @ SY3253 @ tc_nat ) @ SV484 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2965,plain,
! [SV485: $i] :
( ( ! [SY3254: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV485 @ SY3254 @ tc_nat ) @ SY3254 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2966,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2967,plain,
! [SV486: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV486 @ tc_nat )
| ( SV486
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2968,plain,
! [SV487: $i] :
( ( ! [SY3255: $i] :
( ( c_lessequals @ SV487 @ SY3255 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV487 @ SY3255 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2969,plain,
! [SV488: $i] :
( ( ! [SY3256: $i] :
( ( c_lessequals @ SV488 @ SY3256 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV488 @ SY3256 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2970,plain,
! [SV489: $i] :
( ( ! [SY3257: $i,SY3258: $i,SY3259: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SY3257 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3258 @ SY3259 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3257 @ SY3259 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SY3258 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2971,plain,
! [SV490: $i] :
( ( ! [SY3260: $i] :
( ( SV490 = SY3260 )
| ( c_HOL_Oord__class_Oless @ SV490 @ SY3260 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV490 @ ( c_Suc @ SY3260 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2972,plain,
! [SV491: $i] :
( ( ! [SY3261: $i] :
( ( SV491 = SY3261 )
| ~ ( c_HOL_Oord__class_Oless @ SY3261 @ ( c_Suc @ SV491 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3261 @ SV491 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2973,plain,
! [SV492: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV492 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2974,plain,
! [SV493: $i] :
( ( ! [SY3262: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV493 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3262 @ ( c_HOL_Ozero__class_Ozero @ SV493 ) @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2975,plain,
! [SV494: $i] :
( ( ! [SY3263: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV494 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV494 ) @ SY3263 @ SV494 )
= ( c_HOL_Ozero__class_Ozero @ SV494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2976,plain,
! [SV495: $i] :
( ( ! [SY3264: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV495 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3264 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= ( c_HOL_Ozero__class_Ozero @ SV495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2977,plain,
! [SV496: $i] :
( ( ! [SY3265: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV496 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV496 ) @ SY3265 @ SV496 )
= ( c_HOL_Ozero__class_Ozero @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2978,plain,
! [SV497: $i] :
( ( ! [SY3266: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV497 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV497 ) @ SY3266 @ SV497 )
= ( c_HOL_Ozero__class_Ozero @ SV497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2979,plain,
! [SV498: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV498 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2980,plain,
! [SV499: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV499 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2981,plain,
! [SV500: $i] :
( ( ! [SY3267: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV500 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3267 @ ( c_HOL_Ozero__class_Ozero @ SV500 ) @ SV500 )
= ( c_HOL_Ozero__class_Ozero @ SV500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2982,plain,
! [SV501: $i] :
( ( ! [SY3268: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV501 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3268 @ ( c_HOL_Ozero__class_Ozero @ SV501 ) @ SV501 )
= ( c_HOL_Ozero__class_Ozero @ SV501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2983,plain,
! [SV502: $i] :
( ( ! [SY3269: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV502 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV502 ) @ SY3269 @ SV502 )
= ( c_HOL_Ozero__class_Ozero @ SV502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2984,plain,
! [SV503: $i] :
( ( ! [SY3270: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV503 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV503 ) @ SY3270 @ SV503 )
= ( c_HOL_Ozero__class_Ozero @ SV503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2985,plain,
! [SV504: $i] :
( ( ! [SY3271: $i] :
( ~ ( class_Ring__and__Field_Omult__zero @ SV504 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3271 @ ( c_HOL_Ozero__class_Ozero @ SV504 ) @ SV504 )
= ( c_HOL_Ozero__class_Ozero @ SV504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2986,plain,
! [SV505: $i] :
( ( ! [SY3272: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV505 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SY3272 @ SV505 )
= ( c_HOL_Ozero__class_Ozero @ SV505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2987,plain,
! [SV506: $i] :
( ( ! [SY3273: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV506 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3273 @ ( c_HOL_Ozero__class_Ozero @ SV506 ) @ SV506 )
= ( c_HOL_Ozero__class_Ozero @ SV506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2988,plain,
! [SV507: $i] :
( ( ! [SY3274: $i,SY3275: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV507 @ ( c_HOL_Ominus__class_Ominus @ SY3274 @ SY3275 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV507 @ SY3275 @ tc_nat ) @ SY3274 @ tc_nat ) )
| ~ ( c_lessequals @ SY3275 @ SY3274 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2989,plain,
! [SV508: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV508 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2990,plain,
! [SV509: $i] :
( ( ! [SY3276: $i,SY3277: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV509 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SY3276 @ SV509 ) @ SY3277 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SY3276 @ SY3277 @ SV509 ) @ SV509 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SY3277 @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2991,plain,
! [SV510: $i] :
( ( ! [SY3278: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ ( c_HOL_Oplus__class_Oplus @ SY3278 @ SV510 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ SY3278 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2992,plain,
! [SV511: $i] :
( ( ! [SY3279: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ SY3279 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ ( c_HOL_Oplus__class_Oplus @ SY3279 @ SV511 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2993,plain,
! [SV512: $i] :
( ( ! [SY3280: $i,SY3281: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV512 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3280 @ SY3281 @ SV512 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SY3280 @ SV512 ) @ SY3281 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2994,plain,
! [SV513: $i] :
( ( ! [SY3282: $i,SY3283: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV513 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SY3282 @ SV513 ) @ SY3283 @ SV513 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3282 @ SY3283 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2995,plain,
! [SV514: $i] :
( ( ! [SY3284: $i,SY3285: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV514 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3284 @ SY3285 @ SV514 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3284 @ ( c_HOL_Oabs__class_Oabs @ SY3285 @ SV514 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2996,plain,
! [SV515: $i] :
( ( ! [SY3286: $i,SY3287: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV515 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3286 @ ( c_HOL_Oabs__class_Oabs @ SY3287 @ SV515 ) @ SV515 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3286 @ SY3287 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2997,plain,
! [SV516: $i] :
( ( ! [SY3288: $i] :
( ~ ( c_lessequals @ SV516 @ ( c_HOL_Oplus__class_Oplus @ SY3288 @ SV516 @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY3288 @ SV516 @ tc_nat ) @ SV516 @ tc_nat )
= SY3288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2998,plain,
! [SV517: $i] :
( ( ! [SY3289: $i,SY3290: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SY3289 @ SY3290 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SY3290 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SY3289 @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2999,plain,
! [SV518: $i] :
( ( ! [SY3291: $i] : ( c_lessequals @ SV518 @ ( c_HOL_Oplus__class_Oplus @ SV518 @ SY3291 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(3000,plain,
! [SV519: $i] :
( ( ! [SY3292: $i] : ( c_lessequals @ SV519 @ ( c_HOL_Oplus__class_Oplus @ SV519 @ SY3292 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(3001,plain,
! [SV520: $i] :
( ( ! [SY3293: $i] : ( c_lessequals @ SV520 @ ( c_HOL_Oplus__class_Oplus @ SY3293 @ SV520 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(3002,plain,
! [SV521: $i] :
( ( ! [SY3294: $i] : ( c_lessequals @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SY3294 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(3003,plain,
! [SV522: $i] :
( ( ! [SY3295: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SY3295 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3295 @ SV522 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3295 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(3004,plain,
! [SV523: $i] :
( ( ! [SY3296: $i,SY3297: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV523 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY3296 @ SY3297 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SY3296 @ SY3297 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(3005,plain,
! [SV524: $i] :
( ( ! [SY3298: $i,SY3299: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV524 )
| ( c_lessequals @ SY3298 @ SY3299 @ SV524 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY3298 @ SY3299 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(3006,plain,
! [SV525: $i] :
( ( ! [SY3300: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SY3300 @ SV525 ) @ ( c_HOL_Ozero__class_Ozero @ SV525 ) @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(3007,plain,
! [SV526: $i] :
( ( ! [SY3301: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV526 @ SY3301 @ tc_nat ) @ SY3301 @ tc_nat )
= SV526 )
| ~ ( c_lessequals @ SY3301 @ SV526 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(3008,plain,
! [SV527: $i] :
( ( ! [SY3302: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV527 @ ( c_HOL_Ominus__class_Ominus @ SY3302 @ SV527 @ tc_nat ) @ tc_nat )
= SY3302 )
| ~ ( c_lessequals @ SV527 @ SY3302 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(3009,plain,
! [SV528: $i] :
( ( ! [SY3303: $i] :
( ~ ( c_lessequals @ SV528 @ SY3303 @ tc_nat )
| ( SY3303
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY3303 @ SV528 @ tc_nat ) @ SV528 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(3010,plain,
! [SV529: $i] :
( ( ! [SY3304: $i,SY3305: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SY3304 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3305 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY3305 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3305 @ SY3304 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(3011,plain,
! [SV530: $i] :
( ( ! [SY3306: $i,SY3307: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SY3306 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY3307 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3307 @ SY3306 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3307 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(3012,plain,
! [SV531: $i] :
( ( ! [SY3308: $i,SY3309: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SY3308 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SY3309 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3308 @ SY3309 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(3013,plain,
! [SV532: $i] :
( ( ! [SY3310: $i,SY3311: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV532 @ SY3310 @ tc_nat ) @ SY3311 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SY3311 @ tc_nat ) @ SY3310 @ tc_nat ) )
| ~ ( c_lessequals @ SY3310 @ SV532 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(3014,plain,
! [SV533: $i] :
( ( ! [SY3312: $i,SY3313: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV533 @ ( c_HOL_Ominus__class_Ominus @ SY3312 @ SY3313 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SY3312 @ tc_nat ) @ SY3313 @ tc_nat ) )
| ~ ( c_lessequals @ SY3313 @ SY3312 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(3015,plain,
! [SV534: $i] :
( ( ! [SY3314: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV534 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV534 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3314 @ SV534 ) @ SV534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(3016,plain,
! [SV535: $i] :
( ( ! [SY3315: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV535 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3315 @ SV535 ) @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3315 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(3017,plain,
! [SV536: $i] :
( ( ! [SY3316: $i,SY3317: $i,SY3318: $i,SY3319: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3316 @ SY3317 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SY3318 @ SY3319 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SY3317 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SY3316 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SY3317 @ SY3319 @ SV536 )
| ~ ( c_lessequals @ SY3316 @ SY3318 @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(3018,plain,
! [SV537: $i] :
( ( ! [SY3320: $i,SY3321: $i,SY3322: $i,SY3323: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3320 @ SY3321 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SY3322 @ SY3323 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SY3321 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SY3320 @ SV537 )
| ~ ( c_lessequals @ SY3321 @ SY3323 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SY3320 @ SY3322 @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(3019,plain,
! [SV538: $i] :
( ( ! [SY3324: $i,SY3325: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV538 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY3324 @ SY3325 @ SV538 ) @ SV538 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SY3324 @ SV538 ) @ ( c_HOL_Oabs__class_Oabs @ SY3325 @ SV538 ) @ SV538 ) @ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(3020,plain,
! [SV539: $i] :
( ( ! [SY3326: $i] :
( ( c_lessequals @ SV539 @ ( c_Suc @ SY3326 ) @ tc_nat )
| ~ ( c_lessequals @ SV539 @ SY3326 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(3021,plain,
! [SV540: $i] :
( ( ! [SY3327: $i] :
( ( c_lessequals @ SV540 @ SY3327 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV540 ) @ SY3327 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(3022,plain,
! [SV541: $i] :
( ( ! [SY3328: $i] :
( ( c_HOL_Oord__class_Oless @ SV541 @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SY3328 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3328 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV541 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(3023,plain,
! [SV542: $i] :
( ( ! [SY3329: $i] :
( ( c_HOL_Oord__class_Oless @ SV542 @ ( c_HOL_Otimes__class_Otimes @ SY3329 @ SV542 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3329 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV542 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(3024,plain,
! [SV543: $i] :
( ( ~ ( c_lessequals @ ( c_Suc @ SV543 ) @ SV543 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(3025,plain,
! [SV544: $i] :
( ( ! [SY3330: $i,SY3331: $i,SY3332: $i] :
( ~ ( class_Divides_Osemiring__div @ SV544 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SY3330 @ SY3331 @ SV544 ) @ SY3332 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SY3330 @ SY3332 @ SV544 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3332 @ SY3331 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(3026,plain,
! [SV545: $i] :
( ( ! [SY3333: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV545 )
| ( c_lessequals @ SY3333 @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3333 @ SY3333 @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(3027,plain,
! [SV546: $i] :
( ( ! [SY3334: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV546 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3334 @ SY3334 @ SV546 ) @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
| ~ ( c_lessequals @ SY3334 @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(3028,plain,
! [SV547: $i] :
( ( ! [SY3335: $i] :
( ~ ( class_Orderings_Olinorder @ SV547 )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 )
| ( ( c_HOL_Oabs__class_Oabs @ SY3335 @ SV547 )
= SY3335 )
| ( c_HOL_Oord__class_Oless @ SY3335 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(3029,plain,
! [SV548: $i] :
( ( ! [SY3336: $i] :
( ~ ( class_Ring__and__Field_Oabs__if @ SV548 )
| ( ( c_HOL_Oabs__class_Oabs @ SY3336 @ SV548 )
= SY3336 )
| ( c_HOL_Oord__class_Oless @ SY3336 @ ( c_HOL_Ozero__class_Ozero @ SV548 ) @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(3030,plain,
! [SV549: $i] :
( ( ! [SY3337: $i,SY3338: $i,SY3339: $i,SY3340: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY3337 @ SY3338 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SY3339 @ SY3340 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3338 @ SY3340 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3337 @ SY3339 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(3031,plain,
! [SV550: $i] :
( ( ! [SY3341: $i,SY3342: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV550 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SY3341 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SY3342 @ SV550 ) @ SV550 ) @ SV550 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SY3341 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SY3342 @ SV550 ) @ SV550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(3032,plain,
! [SV551: $i] :
( ( ! [SY3343: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV551 ) @ SY3343 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV551 @ SY3343 @ tc_nat ) ) @ SY3343 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(3033,plain,
! [SV552: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ SV552 ) @ SV552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(3034,plain,
! [SV553: $i] :
( ( ! [SY3344: $i] :
( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV553 @ SY3344 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3344 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV553 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(3035,plain,
! [SV554: $i] :
( ( ! [SY3345: $i] :
( ~ ( class_Orderings_Opreorder @ SV554 )
| ( c_lessequals @ SY3345 @ SY3345 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(3036,plain,
! [SV555: $i] :
( ( ! [SY3346: $i] :
( ~ ( class_Orderings_Oorder @ SV555 )
| ( c_lessequals @ SY3346 @ SY3346 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(3037,plain,
! [SV556: $i] :
( ( c_lessequals @ SV556 @ SV556 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(3038,plain,
! [SV557: $i] :
( ( ! [SY3347: $i,SY3348: $i] :
( ( c_lessequals @ SV557 @ SY3347 @ tc_nat )
| ~ ( c_lessequals @ SY3348 @ SY3347 @ tc_nat )
| ~ ( c_lessequals @ SV557 @ SY3348 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(3039,plain,
! [SV558: $i] :
( ( c_lessequals @ SV558 @ SV558 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(3040,plain,
! [SV559: $i] :
( ( ! [SY3349: $i,SY3350: $i,SY3351: $i,SY3352: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
| ( c_lessequals @ SY3349 @ ( c_HOL_Oplus__class_Oplus @ SY3350 @ SY3351 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SY3352 @ SY3351 @ SV559 )
| ~ ( c_lessequals @ SY3349 @ ( c_HOL_Oplus__class_Oplus @ SY3350 @ SY3352 @ SV559 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(3041,plain,
! [SV560: $i] :
( ( ! [SY3353: $i,SY3354: $i,SY3355: $i] :
( ~ ( class_Orderings_Opreorder @ SV560 )
| ( c_lessequals @ SY3353 @ SY3354 @ SV560 )
| ~ ( c_lessequals @ SY3355 @ SY3354 @ SV560 )
| ~ ( c_lessequals @ SY3353 @ SY3355 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(3042,plain,
! [SV561: $i] :
( ( ! [SY3356: $i,SY3357: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3356 @ SY3357 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SY3357 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SY3356 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(3043,plain,
! [SV562: $i] :
( ( ! [SY3358: $i,SY3359: $i,SY3360: $i] :
( ~ ( class_Orderings_Oorder @ SV562 )
| ( c_lessequals @ SY3358 @ SY3359 @ SV562 )
| ~ ( c_lessequals @ SY3358 @ SY3360 @ SV562 )
| ~ ( c_lessequals @ SY3360 @ SY3359 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(3044,plain,
! [SV563: $i] :
( ( ! [SY3361: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ SV563 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY3361 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SY3361 @ SV563 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(3045,plain,
! [SV564: $i] :
( ( ! [SY3362: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV564 @ SY3362 @ tc_nat ) @ SV564 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(3046,plain,
! [SV565: $i] :
( ( ! [SY3363: $i,SY3364: $i] :
( ~ ( class_Divides_Osemiring__div @ SV565 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY3363 @ SY3364 @ SV565 ) @ SY3363 @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(3047,plain,
! [SV566: $i] :
( ( ! [SY3365: $i,SY3366: $i] :
( ~ ( class_Divides_Osemiring__div @ SV566 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY3365 @ SY3366 @ SV566 ) @ SY3366 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(3048,plain,
! [SV567: $i] :
( ( ! [SY3367: $i] :
( ( SV567 = SY3367 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ ( c_Suc @ SY3367 ) @ tc_nat )
| ~ ( c_lessequals @ SY3367 @ SV567 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(3049,plain,
! [SV568: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV568 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ SV568 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ SV568 ) @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(3050,plain,
! [SV569: $i] :
( ( ! [SY3368: $i,SY3369: $i,SY3370: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
| ( c_HOL_Oord__class_Oless @ SY3368 @ SY3369 @ SV569 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SY3370 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3370 @ SY3369 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SY3370 @ SY3368 @ SV569 ) @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(3051,plain,
! [SV570: $i] :
( ( ! [SY3371: $i,SY3372: $i,SY3373: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
| ( c_HOL_Oord__class_Oless @ SY3371 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
| ( c_HOL_Oord__class_Oless @ SY3372 @ SY3373 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3371 @ SY3372 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SY3371 @ SY3373 @ SV570 ) @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(3052,plain,
! [SV571: $i] :
( ( ! [SY3374: $i,SY3375: $i,SY3376: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
| ( c_HOL_Oord__class_Oless @ SY3374 @ SY3375 @ SV571 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SY3376 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3375 @ SY3376 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SY3374 @ SY3376 @ SV571 ) @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(3053,plain,
! [SV572: $i] :
( ( ! [SY3377: $i,SY3378: $i,SY3379: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
| ( c_HOL_Oord__class_Oless @ SY3377 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
| ( c_HOL_Oord__class_Oless @ SY3378 @ SY3379 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3378 @ SY3377 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SY3379 @ SY3377 @ SV572 ) @ SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(3054,plain,
! [SV573: $i] :
( ( ! [SY3380: $i,SY3381: $i,SY3382: $i] :
( ~ ( class_Divides_Osemiring__div @ SV573 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY3380 @ SY3381 @ SV573 ) @ ( c_HOL_Otimes__class_Otimes @ SY3380 @ SY3382 @ SV573 ) @ SV573 )
= ( c_HOL_Otimes__class_Otimes @ SY3380 @ ( c_Divides_Odiv__class_Omod @ SY3381 @ SY3382 @ SV573 ) @ SV573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(3055,plain,
! [SV574: $i] :
( ( ! [SY3383: $i,SY3384: $i,SY3385: $i] :
( ~ ( class_Divides_Osemiring__div @ SV574 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY3383 @ SY3384 @ SV574 ) @ ( c_HOL_Otimes__class_Otimes @ SY3385 @ SY3384 @ SV574 ) @ SV574 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SY3383 @ SY3385 @ SV574 ) @ SY3384 @ SV574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(3056,plain,
! [SV575: $i] :
( ( ! [SY3386: $i] :
( ( c_lessequals @ SV575 @ SY3386 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3386 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV575 @ SY3386 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(3057,plain,
! [SV576: $i] :
( ( ! [SY3387: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV576 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ ( c_HOL_Oabs__class_Oabs @ SY3387 @ SV576 ) @ SV576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(3058,plain,
! [SV577: $i] :
( ( ! [SY3388: $i] :
( ( c_lessequals @ ( c_Suc @ SV577 ) @ ( c_Suc @ SY3388 ) @ tc_nat )
| ~ ( c_lessequals @ SV577 @ SY3388 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(3059,plain,
! [SV578: $i] :
( ( ! [SY3389: $i] :
( ( c_lessequals @ SV578 @ SY3389 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV578 ) @ ( c_Suc @ SY3389 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(3060,plain,
! [SV579: $i] :
( ( ! [SY3390: $i,SY3391: $i] :
( ~ ( class_Orderings_Olinorder @ SV579 )
| ( c_lessequals @ SY3390 @ SY3391 @ SV579 )
| ( c_lessequals @ SY3391 @ SY3390 @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(3061,plain,
! [SV580: $i] :
( ( ! [SY3392: $i,SY3393: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SY3392 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3393 @ SY3392 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3393 @ SV580 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SY3393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(3062,plain,
! [SV581: $i] :
( ( ! [SY3394: $i,SY3395: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SY3394 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3394 @ SY3395 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3395 @ SY3394 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SY3395 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(3063,plain,
! [SV582: $i] :
( ( ! [SY3396: $i] :
( ( c_lessequals @ SV582 @ SY3396 @ tc_nat )
| ( c_lessequals @ SY3396 @ SV582 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(3064,plain,
! [SV583: $i] :
( ( ! [SY3397: $i] :
( ( SV583 = SY3397 )
| ~ ( c_HOL_Oord__class_Oless @ SV583 @ ( c_Suc @ SY3397 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV583 @ SY3397 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(3065,plain,
! [SV584: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV584 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(3066,plain,
! [SV585: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV585 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(3067,plain,
! [SV586: $i] :
( ( ! [SY3398: $i] :
( ( c_HOL_Oord__class_Oless @ SV586 @ ( c_Suc @ SY3398 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3398 @ SV586 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(3068,plain,
! [SV587: $i] :
( ( ! [SY3399: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV587 @ SY3399 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3399 @ ( c_Suc @ SV587 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(3069,plain,
! [SV588: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV588 @ SV588 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV588 @ ( c_Suc @ SV588 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(3070,plain,
! [SV589: $i] :
( ( ! [SY3400: $i] :
( ( c_HOL_Oord__class_Oless @ SV589 @ SY3400 @ tc_nat )
| ( SV589 = SY3400 )
| ~ ( c_lessequals @ SV589 @ SY3400 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(3071,plain,
! [SV590: $i] :
( ( ! [SY3401: $i] :
( ( SV590 = SY3401 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SY3401 @ tc_nat )
| ~ ( c_lessequals @ SV590 @ SY3401 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(3072,plain,
! [SV591: $i] :
( ( ! [SY3402: $i] :
( ( c_HOL_Oord__class_Oless @ SV591 @ SY3402 @ tc_nat )
| ( SV591 = SY3402 )
| ~ ( c_lessequals @ SV591 @ SY3402 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(3073,plain,
! [SV592: $i] :
( ( ! [SY3403: $i] :
( ( c_HOL_Oord__class_Oless @ SV592 @ SY3403 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV592 ) @ SY3403 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(3074,plain,
! [SV593: $i] :
( ( ! [SY3404: $i] :
( ( c_HOL_Oord__class_Oless @ SV593 @ ( c_Suc @ SY3404 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV593 @ SY3404 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(3075,plain,
! [SV594: $i] :
( ( ! [SY3405: $i,SY3406: $i] :
( ( c_HOL_Oord__class_Oless @ SV594 @ SY3405 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3406 @ SV594 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3406 @ SY3405 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(3076,plain,
! [SV595: $i] :
( ( ! [SY3407: $i,SY3408: $i] :
( ( c_HOL_Oord__class_Oless @ SV595 @ SY3407 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV595 @ SY3408 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3407 @ SY3408 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(3077,plain,
! [SV596: $i] :
( ( c_HOL_Oord__class_Oless @ SV596 @ ( c_Suc @ SV596 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(3078,plain,
! [SV597: $i] :
( ( c_HOL_Oord__class_Oless @ SV597 @ ( c_Suc @ SV597 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(3079,plain,
! [SV598: $i] :
( ( ! [SY3409: $i,SY3410: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SY3409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3410 @ SY3409 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV598 @ SY3410 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(3080,plain,
! [SV599: $i] :
( ( ! [SY3411: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV599 @ SY3411 @ tc_nat )
= SV599 )
| ~ ( c_HOL_Oord__class_Oless @ SV599 @ SY3411 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(3081,plain,
! [SV600: $i] :
( ( ! [SY3412: $i,SY3413: $i] :
( ( c_HOL_Oord__class_Oless @ SV600 @ ( c_HOL_Oplus__class_Oplus @ SY3412 @ SY3413 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV600 @ SY3412 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(3082,plain,
! [SV601: $i] :
( ( ! [SY3414: $i,SY3415: $i] :
( ( c_HOL_Oord__class_Oless @ SV601 @ ( c_HOL_Oplus__class_Oplus @ SY3414 @ SY3415 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV601 @ SY3415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(3083,plain,
! [SV602: $i] :
( ( ! [SY3416: $i,SY3417: $i] :
( ( c_HOL_Oord__class_Oless @ SV602 @ SY3416 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV602 @ SY3417 @ tc_nat ) @ SY3416 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(3084,plain,
! [SV603: $i] :
( ( ! [SY3418: $i,SY3419: $i] :
( ( c_HOL_Oord__class_Oless @ SV603 @ ( c_HOL_Oplus__class_Oplus @ SY3418 @ SY3419 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV603 @ SY3418 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(3085,plain,
! [SV604: $i] :
( ( ! [SY3420: $i,SY3421: $i] :
( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Oplus__class_Oplus @ SY3420 @ SY3421 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ SY3421 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(3086,plain,
! [SV605: $i] :
( ( ! [SY3422: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV605 ) @ SY3422 @ tc_nat )
| ( ( c_Suc @ SV605 )
= SY3422 )
| ~ ( c_HOL_Oord__class_Oless @ SV605 @ SY3422 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(3087,plain,
! [SV606: $i] :
( ( ! [SY3423: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV606 ) @ ( c_Suc @ SY3423 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV606 @ SY3423 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(3088,plain,
! [SV607: $i] :
( ( ! [SY3424: $i] :
( ( c_HOL_Oord__class_Oless @ SV607 @ SY3424 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV607 ) @ ( c_Suc @ SY3424 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(3089,plain,
! [SV608: $i] :
( ( ! [SY3425: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV608 ) @ ( c_Suc @ SY3425 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV608 @ SY3425 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(3090,plain,
! [SV609: $i] :
( ( ! [SY3426: $i,SY3427: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV609 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SY3426 @ SY3427 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3426 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3427 @ SV609 ) @ SV609 ) )
| ~ ( c_lessequals @ SY3427 @ SY3426 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(3091,plain,
! [SV610: $i] :
( ( ! [SY3428: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV610 @ ( c_Suc @ SY3428 ) @ tc_nat ) @ SV610 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV610 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(3092,plain,
! [SV611: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV611 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV611 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV611 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(3093,plain,
! [SV612: $i] :
( ( ! [SY3429: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV612 ) @ ( c_Suc @ SY3429 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV612 @ SY3429 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(3094,plain,
! [SV613: $i] :
( ( ! [SY3430: $i,SY3431: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV613 @ SY3430 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV613 @ SY3431 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY3430 @ SY3431 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(3095,plain,
! [SV614: $i] :
( ( ! [SY3432: $i,SY3433: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV614 @ SY3432 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3433 @ SY3432 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV614 @ SY3433 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(3096,plain,
! [SV615: $i] :
( ( ! [SY3434: $i,SY3435: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV615 ) @ SY3434 @ tc_nat ) @ ( c_Suc @ SY3435 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV615 @ SY3434 @ tc_nat ) @ SY3435 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(3097,plain,
! [SV616: $i] :
( ( ! [SY3436: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_HOL_Ominus__class_Ominus @ SV616 @ SY3436 @ tc_nat ) @ tc_nat )
= SY3436 )
| ~ ( c_lessequals @ SY3436 @ SV616 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(3098,plain,
! [SV617: $i] :
( ( ! [SY3437: $i,SY3438: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV617 @ SY3437 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3438 @ SY3437 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV617 @ SY3438 @ tc_nat ) @ SY3437 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(3099,plain,
! [SV618: $i] :
( ( ! [SY3439: $i,SY3440: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SY3439 @ SY3440 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SY3440 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SY3439 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(3100,plain,
! [SV619: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV619 @ SV619 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(3101,plain,
! [SV620: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV620 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV620 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(3102,plain,
! [SV621: $i] :
( ( ! [SY3441: $i,SY3442: $i] :
( ( c_lessequals @ SV621 @ SY3441 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SY3442 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3441 @ SY3442 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3442 @ SY3441 @ tc_nat )
| ~ ( c_lessequals @ SY3442 @ SV621 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(3103,plain,
! [SV622: $i] :
( ( ! [SY3443: $i,SY3444: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SY3443 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3444 @ SY3443 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV622 @ SY3444 @ tc_nat )
| ~ ( c_lessequals @ SY3443 @ SY3444 @ tc_nat )
| ~ ( c_lessequals @ SY3443 @ SV622 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(3104,plain,
! [SV623: $i] :
( ( ! [SY3445: $i,SY3446: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV623 @ SY3445 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3446 @ SY3445 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV623 @ SY3446 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(3105,plain,
! [SV624: $i] :
( ( ! [SY3447: $i,SY3448: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SY3447 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SY3448 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3448 @ SY3447 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(3106,plain,
! [SV625: $i] :
( ( ! [SY3449: $i,SY3450: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV625 @ SY3449 @ tc_nat ) @ SY3450 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV625 @ ( c_HOL_Oplus__class_Oplus @ SY3449 @ SY3450 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(3107,plain,
! [SV626: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV626 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(3108,plain,
! [SV627: $i] :
( ( ! [SY3451: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV627 @ SY3451 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY3451 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV627 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(3109,plain,
! [SV628: $i] :
( ( ! [SY3452: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV628 @ SY3452 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SY3452 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV628 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(3110,plain,
! [SV629: $i] :
( ( ! [SY3453: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV629 @ SY3453 @ tc_nat ) @ SV629 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(3111,plain,
! [SV630: $i] :
( ( ! [SY3454: $i,SY3455: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV630 @ SY3454 @ tc_nat ) @ SY3455 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV630 @ SY3455 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3454 @ SY3455 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(3112,plain,
! [SV631: $i] :
( ( ! [SY3456: $i,SY3457: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Ominus__class_Ominus @ SY3456 @ SY3457 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV631 @ SY3456 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV631 @ SY3457 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(3113,plain,
! [SV632: $i] :
( ( ! [SY3458: $i,SY3459: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SY3458 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3459 @ SY3458 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SY3459 @ tc_nat ) )
| ~ ( c_lessequals @ SY3458 @ SY3459 @ tc_nat )
| ~ ( c_lessequals @ SY3458 @ SV632 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(3114,plain,
! [SV633: $i] :
( ( ! [SY3460: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV633 @ SY3460 @ tc_nat ) @ SV633 @ tc_nat )
= SY3460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(3115,plain,
! [SV634: $i] :
( ( ! [SY3461: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV634 @ SY3461 @ tc_nat ) @ SY3461 @ tc_nat )
= SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(3116,plain,
! [SV635: $i] :
( ( ! [SY3462: $i,SY3463: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV635 )
| ( c_HOL_Oord__class_Oless @ SY3462 @ SY3463 @ SV635 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3462 @ SY3463 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(3117,plain,
! [SV636: $i] :
( ( ! [SY3464: $i,SY3465: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV636 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3464 @ SY3465 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
| ~ ( c_HOL_Oord__class_Oless @ SY3464 @ SY3465 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(3118,plain,
! [SV637: $i] :
( ( ! [SY3466: $i,SY3467: $i,SY3468: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV637 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY3466 @ SY3467 @ SV637 ) @ SY3468 @ SV637 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY3468 @ SY3466 @ SV637 ) @ SV637 ) @ SY3467 @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(3119,plain,
! [SV638: $i] :
( ( ! [SY3469: $i,SY3470: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV638 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3469 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3470 @ SV638 ) @ SV638 )
| ~ ( c_HOL_Oord__class_Oless @ SY3469 @ SY3470 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(3120,plain,
! [SV639: $i] :
( ( ! [SY3471: $i,SY3472: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( c_HOL_Oord__class_Oless @ SY3471 @ SY3472 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3471 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3472 @ SV639 ) @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(3121,plain,
! [SV640: $i] :
( ( ! [SY3473: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV640 @ ( c_HOL_Ominus__class_Ominus @ SY3473 @ SV640 @ tc_nat ) @ tc_nat )
= SY3473 )
| ( c_HOL_Oord__class_Oless @ SY3473 @ SV640 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(3122,plain,
! [SV641: $i] :
( ( ! [SY3474: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SY3474 @ tc_nat ) @ SV641 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV641 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3474 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(3123,plain,
! [SV642: $i] :
( ( ! [SY3475: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY3475 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV642 @ SY3475 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SY3475 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(3124,plain,
! [SV643: $i] :
( ( ! [SY3476: $i] :
( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SY3476 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3476 @ SV643 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SY3476 @ SV643 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(3125,plain,
! [SV644: $i] :
( ( ! [SY3477: $i,SY3478: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV644 @ SY3477 @ tc_nat ) @ SY3478 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV644 @ ( c_HOL_Ominus__class_Ominus @ SY3478 @ SY3477 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(3126,plain,
! [SV645: $i] :
( ( ! [SY3479: $i,SY3480: $i] :
( ( c_HOL_Oord__class_Oless @ SV645 @ ( c_HOL_Ominus__class_Ominus @ SY3479 @ SY3480 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV645 @ SY3480 @ tc_nat ) @ SY3479 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(3127,plain,
! [SV646: $i] :
( ( ! [SY3481: $i,SY3482: $i] :
( ( c_HOL_Oord__class_Oless @ SV646 @ SY3481 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SY3482 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3481 @ SY3482 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3482 @ SY3481 @ tc_nat )
| ~ ( c_lessequals @ SY3482 @ SV646 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(3128,plain,
! [SV647: $i] :
( ( ! [SY3483: $i,SY3484: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SY3483 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3484 @ SY3483 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV647 @ SY3484 @ tc_nat )
| ~ ( c_lessequals @ SY3483 @ SY3484 @ tc_nat )
| ~ ( c_lessequals @ SY3483 @ SV647 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(3129,plain,
! [SV648: $i] :
( ( ! [SY3485: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SY3485 @ tc_nat ) @ ( c_Suc @ SV648 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(3130,plain,
! [SV649: $i] :
( ( ! [SY3486: $i] :
( ( c_HOL_Oord__class_Oless @ SV649 @ SY3486 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3486 @ SV649 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(3131,plain,
! [SV650: $i] :
( ( ! [SY3487: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV650 @ SY3487 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3487 @ SV650 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(3132,plain,
! [SV651: $i] :
( ( ! [SY3488: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV651 @ SY3488 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV651 @ SY3488 @ tc_nat ) @ SY3488 @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ SV651 @ SY3488 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(3133,plain,
! [SV652: $i] :
( ( ! [SY3489: $i,SY3490: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SY3489 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3490 @ SY3489 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3489 @ SV652 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV652 @ SY3490 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(3134,plain,
! [SV653: $i] :
( ( ! [SY3491: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV653 @ SY3491 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV653 @ SY3491 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(3135,plain,
! [SV654: $i] :
( ( ! [SY3492: $i,SY3493: $i] :
( ~ ( class_Orderings_Oorder @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SY3492 @ SY3493 @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SY3493 @ SY3492 @ SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(3136,plain,
! [SV655: $i] :
( ( ! [SY3494: $i,SY3495: $i] :
( ~ ( class_Orderings_Olinorder @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SY3494 @ SY3495 @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SY3495 @ SY3494 @ SV655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(3137,plain,
! [SV656: $i] :
( ( ! [SY3496: $i,SY3497: $i] :
( ~ ( class_Orderings_Opreorder @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SY3496 @ SY3497 @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SY3497 @ SY3496 @ SV656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(3138,plain,
! [SV657: $i] :
( ( ! [SY3498: $i,SY3499: $i] :
( ~ ( class_Orderings_Opreorder @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SY3498 @ SY3499 @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SY3499 @ SY3498 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(3139,plain,
! [SV658: $i] :
( ( ! [SY3500: $i] :
( ~ ( class_Orderings_Opreorder @ SV658 )
| ~ ( c_HOL_Oord__class_Oless @ SY3500 @ SY3500 @ SV658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(3140,plain,
! [SV659: $i] :
( ( ! [SY3501: $i] :
( ~ ( class_Orderings_Olinorder @ SV659 )
| ~ ( c_HOL_Oord__class_Oless @ SY3501 @ SY3501 @ SV659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(3141,plain,
! [SV660: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV660 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(3142,plain,
! [SV661: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV661 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(3143,plain,
! [SV662: $i] :
( ( ! [SY3502: $i] :
( ~ ( class_Orderings_Oorder @ SV662 )
| ~ ( c_HOL_Oord__class_Oless @ SY3502 @ SY3502 @ SV662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(3144,plain,
! [SV663: $i] :
( ( ! [SY3503: $i,SY3504: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV663 @ SY3503 @ tc_nat ) @ SY3504 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV663 @ SY3504 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(3145,plain,
! [SV664: $i] :
( ( ! [SY3505: $i,SY3506: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SY3505 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SY3506 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3506 @ SV664 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3506 @ SY3505 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(3146,plain,
! [SV665: $i] :
( ( ! [SY3507: $i,SY3508: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV665 )
| ( c_HOL_Oord__class_Oless @ SY3507 @ SY3508 @ SV665 )
| ( c_HOL_Oord__class_Oless @ SY3508 @ SY3507 @ SV665 )
| ( SY3508 = SY3507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(3147,plain,
! [SV666: $i] :
( ( ! [SY3509: $i,SY3510: $i] :
( ~ ( class_Orderings_Olinorder @ SV666 )
| ( SY3509 = SY3510 )
| ( c_HOL_Oord__class_Oless @ SY3510 @ SY3509 @ SV666 )
| ( c_HOL_Oord__class_Oless @ SY3509 @ SY3510 @ SV666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(3148,plain,
! [SV667: $i] :
( ( ! [SY3511: $i,SY3512: $i] :
( ~ ( class_Orderings_Olinorder @ SV667 )
| ( SY3511 = SY3512 )
| ( c_HOL_Oord__class_Oless @ SY3511 @ SY3512 @ SV667 )
| ( c_HOL_Oord__class_Oless @ SY3512 @ SY3511 @ SV667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3149,plain,
! [SV668: $i] :
( ( ! [SY3513: $i,SY3514: $i] :
( ~ ( class_Orderings_Olinorder @ SV668 )
| ( c_HOL_Oord__class_Oless @ SY3513 @ SY3514 @ SV668 )
| ( SY3514 = SY3513 )
| ( c_HOL_Oord__class_Oless @ SY3514 @ SY3513 @ SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3150,plain,
! [SV669: $i] :
( ( ! [SY3515: $i] :
( ( c_HOL_Oord__class_Oless @ SV669 @ SY3515 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3515 @ SV669 @ tc_nat )
| ( SY3515 = SV669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(3151,plain,
! [SV670: $i] :
( ( ! [SY3516: $i] :
( ( c_HOL_Oord__class_Oless @ SV670 @ SY3516 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY3516 @ SV670 @ tc_nat )
| ( SY3516 = SV670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(3152,plain,
! [SV671: $i] :
( ( ! [SY3517: $i,SY3518: $i] :
( ~ ( class_Orderings_Olinorder @ SV671 )
| ( c_HOL_Oord__class_Oless @ SY3517 @ SY3518 @ SV671 )
| ( c_HOL_Oord__class_Oless @ SY3518 @ SY3517 @ SV671 )
| ( SY3518 = SY3517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(3153,plain,
! [SV672: $i] :
( ( ! [SY3519: $i,SY3520: $i,SY3521: $i] :
( ~ ( class_Orderings_Oorder @ SV672 )
| ( c_HOL_Oord__class_Oless @ SY3519 @ SY3520 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SY3519 @ SY3521 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SY3521 @ SY3520 @ SV672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3154,plain,
! [SV673: $i] :
( ( ! [SY3522: $i,SY3523: $i,SY3524: $i] :
( ~ ( class_Orderings_Opreorder @ SV673 )
| ( c_HOL_Oord__class_Oless @ SY3522 @ SY3523 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SY3524 @ SY3523 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SY3522 @ SY3524 @ SV673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3155,plain,
! [SV674: $i] :
( ( ! [SY3525: $i,SY3526: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV674 @ SY3525 @ tc_nat ) @ SY3526 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV674 @ SY3526 @ tc_nat ) @ SY3525 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3156,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(3157,plain,
! [SV675: $i] :
( ( ! [SY3527: $i,SY3528: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV675 @ SY3527 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV675 @ SY3528 @ tc_nat ) )
| ( SY3527 = SY3528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(3158,plain,
! [SV676: $i] :
( ( ( c_Suc @ SV676 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(3159,plain,
! [SV677: $i] :
( ( ! [SY3529: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV677 @ SY3529 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV677
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(3160,plain,
! [SV678: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV678 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV678 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3161,plain,
! [SV679: $i] :
( ( ! [SY3530: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV679 @ SY3530 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY3530 @ SV679 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3530 = SV679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3162,plain,
! [SV680: $i] :
( ( ! [SY3531: $i,SY3532: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SY3531 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SY3532 @ tc_nat ) )
| ( SY3531 = SY3532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3163,plain,
! [SV681: $i] :
( ( ! [SY3533: $i,SY3534: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV681 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3533 @ SY3533 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SY3534 @ SY3534 @ SV681 ) @ SV681 )
!= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
| ( SY3533
= ( c_HOL_Ozero__class_Ozero @ SV681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(3164,plain,
! [SV682: $i] :
( ( ! [SY3535: $i,SY3536: $i,SY3537: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV682 )
| ~ ( class_Int_Onumber__ring @ SV682 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3535 @ SY3536 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SY3535 @ SY3537 @ SV682 ) )
| ( SY3536 = SY3537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3165,plain,
! [SV683: $i] :
( ( ! [SY3538: $i,SY3539: $i,SY3540: $i,SY3541: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SY3538 @ SY3539 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY3540 @ ( c_HOL_Otimes__class_Otimes @ SY3538 @ SY3541 @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ SV683 @ SY3538 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SY3540 @ SY3538 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3166,plain,
! [SV684: $i] :
( ( ! [SY3542: $i,SY3543: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 )
| ( ( c_HOL_Oabs__class_Oabs @ SY3542 @ SV684 )
!= ( c_HOL_Oabs__class_Oabs @ SY3543 @ SV684 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3542 @ SY3543 @ SV684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3167,plain,
! [SV685: $i] :
( ( ! [SY3544: $i,SY3545: $i,SY3546: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3544 @ SY3545 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SY3544 @ SY3546 @ SV685 ) )
| ( SY3545 = SY3546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3168,plain,
! [SV686: $i] :
( ( ! [SY3547: $i,SY3548: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3547 @ SY3548 @ SV686 )
!= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SY3548 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SY3547 @ SV686 )
| ( SY3547
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3169,plain,
! [SV687: $i] :
( ( ! [SY3549: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV687 @ SY3549 @ tc_nat ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV687
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(3170,plain,
! [SV688: $i] :
( ( ! [SY3550: $i,SY3551: $i,SY3552: $i,SY3553: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3550 @ SY3551 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SY3552 @ SY3553 @ SV688 ) )
| ( c_lessequals @ SY3551 @ SY3550 @ SV688 )
| ~ ( c_lessequals @ SY3553 @ SY3552 @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3171,plain,
! [SV689: $i] :
( ( ! [SY3554: $i,SY3555: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3554 @ SY3555 @ SV689 )
!= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SY3555
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SY3554
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3172,plain,
! [SV690: $i] :
( ( ! [SY3556: $i,SY3557: $i,SY3558: $i,SY3559: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3556 @ SY3557 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SY3558 @ SY3559 @ SV690 ) )
| ( c_lessequals @ SY3559 @ SY3558 @ SV690 )
| ~ ( c_lessequals @ SY3557 @ SY3556 @ SV690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3173,plain,
! [SV691: $i] :
( ( ! [SY3560: $i,SY3561: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV691 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3560 @ SY3561 @ SV691 )
!= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
| ( SY3560 = SY3561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3174,plain,
! [SV692: $i] :
( ( SV692
!= ( c_Suc @ SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3175,plain,
! [SV693: $i] :
( ( ! [SY3562: $i,SY3563: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3562 @ SY3563 @ SV693 )
!= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SY3562
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SY3563
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(3176,plain,
! [SV694: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV694 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(3177,plain,
! [SV695: $i] :
( ( ! [SY3564: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV695 @ SY3564 @ tc_nat ) )
| ( SY3564
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY3564
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3178,plain,
! [SV696: $i] :
( ( ! [SY3565: $i,SY3566: $i,SY3567: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV696 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3565 @ SY3566 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SY3567 @ SY3567 @ SV696 ) )
| ( SY3565 = SY3566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3179,plain,
! [SV697: $i] :
( ( ! [SY3568: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV697 @ SY3568 @ tc_nat ) )
| ( SY3568
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV697
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3180,plain,
! [SV698: $i] :
( ( ! [SY3569: $i,SY3570: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV698 )
| ~ ( class_Int_Onumber__ring @ SV698 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3569 @ SY3570 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SY3569 = SY3570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3181,plain,
! [SV699: $i] :
( ( ! [SY3571: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV699 @ SY3571 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV699 @ SY3571 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3182,plain,
! [SV700: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3183,plain,
! [SV701: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV701 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Parity_Oeven__odd__class_Oeven @ SV701 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3184,plain,
! [SV702: $i] :
( ( ! [SY3572: $i,SY3573: $i,SY3574: $i,SY3575: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV702 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3572 @ ( c_HOL_Oplus__class_Oplus @ SY3573 @ SY3574 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SY3573 @ SY3575 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SY3572 @ SY3574 @ SV702 )
= SY3575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3185,plain,
! [SV703: $i] :
( ( ! [SY3576: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV703 @ SY3576 @ tc_nat ) )
| ( SV703
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3576
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3186,plain,
! [SV704: $i] :
( ( ! [SY3577: $i,SY3578: $i] :
( ~ ( class_Divides_Osemiring__div @ SV704 )
| ( ( c_Divides_Odiv__class_Omod @ SY3577 @ SY3578 @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3578 @ SY3577 @ SV704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3187,plain,
! [SV705: $i] :
( ( ! [SY3579: $i,SY3580: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3579 @ SY3580 @ SV705 )
!= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SY3580 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SY3579 @ SV705 )
| ( SY3580
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3188,plain,
! [SV706: $i] :
( ( ! [SY3581: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV706 @ SY3581 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3581
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV706
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3189,plain,
! [SV707: $i] :
( ( ( c_Suc @ SV707 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3190,plain,
! [SV708: $i] :
( ( ! [SY3582: $i,SY3583: $i,SY3584: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV708 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3582 @ SY3582 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SY3583 @ SY3584 @ SV708 ) )
| ( SY3583 = SY3584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3191,plain,
! [SV709: $i] :
( ( ! [SY3585: $i,SY3586: $i,SY3587: $i,SY3588: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV709 )
| ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3585 @ SY3586 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SY3587 @ SY3588 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3585 @ SY3588 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SY3587 @ SY3586 @ SV709 ) @ SV709 ) )
| ( SY3586 = SY3588 )
| ( SY3585 = SY3587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3192,plain,
! [SV710: $i] :
( ( ! [SY3589: $i,SY3590: $i,SY3591: $i,SY3592: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3589 @ SY3590 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SY3591 @ SY3592 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SY3589 @ SY3590 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SY3591 @ SY3592 @ SV710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3193,plain,
! [SV711: $i] :
( ( ! [SY3593: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV711 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3593 @ SY3593 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SY3593
= ( c_HOL_Ozero__class_Ozero @ SV711 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(3194,plain,
! [SV712: $i] :
( ( ! [SY3594: $i,SY3595: $i,SY3596: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SY3594 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY3595 @ SY3596 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3595 @ SY3594 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV712 @ SY3596 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3195,plain,
! [SV713: $i] :
( ( ! [SY3597: $i,SY3598: $i,SY3599: $i,SY3600: $i,SY3601: $i] :
( ~ ( class_Divides_Oring__div @ SV713 )
| ( ( c_Divides_Odiv__class_Omod @ SY3597 @ SY3598 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY3599 @ SY3598 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3600 @ SY3598 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY3601 @ SY3598 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3600 @ SY3597 @ SV713 ) @ SY3598 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3601 @ SY3599 @ SV713 ) @ SY3598 @ SV713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3196,plain,
! [SV714: $i] :
( ( ! [SY3602: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SY3602 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY3602
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV714
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3197,plain,
! [SV715: $i] :
( ( ! [SY3603: $i,SY3604: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV715 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY3603 @ SV715 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY3604 @ SV715 ) )
| ( SY3603 = SY3604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3198,plain,
! [SV716: $i] :
( ( ! [SY3605: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV716 @ SY3605 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV716
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3199,plain,
! [SV717: $i] :
( ( ! [SY3606: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV717 @ SY3606 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3606
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3200,plain,
! [SV718: $i] :
( ( ! [SY3607: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV718 @ SY3607 @ tc_nat ) )
!= SY3607 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV718 ) @ SY3607 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3201,plain,
! [SV719: $i] :
( ( ! [SY3608: $i] :
( ( ( c_Suc @ SV719 )
!= ( c_Suc @ SY3608 ) )
| ( SV719 = SY3608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3202,plain,
! [SV720: $i] :
( ( ! [SY3609: $i,SY3610: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV720 @ SY3609 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SY3610 @ SY3609 @ tc_nat ) )
| ( SY3609
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV720 = SY3610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3203,plain,
! [SV721: $i] :
( ( ! [SY3611: $i,SY3612: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV721 @ SY3611 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV721 @ SY3612 @ tc_nat ) )
| ( SY3611 = SY3612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3204,plain,
! [SV722: $i] :
( ( ! [SY3613: $i,SY3614: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV722 )
| ~ ( class_Int_Onumber__ring @ SV722 )
| ( SY3613
!= ( c_HOL_Oplus__class_Oplus @ SY3613 @ SY3614 @ SV722 ) )
| ( SY3614
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3205,plain,
! [SV723: $i] :
( ( ! [SY3615: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV723 @ SY3615 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY3615
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY3615
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3206,plain,
! [SV724: $i] :
( ( ! [SY3616: $i,SY3617: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
| ( ( c_HOL_Otimes__class_Otimes @ SY3616 @ SY3617 @ SV724 )
!= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SY3617
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SY3616
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3207,plain,
! [SV725: $i] :
( ( ! [SY3618: $i,SY3619: $i,SY3620: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3618 @ SY3619 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SY3620 @ SY3619 @ SV725 ) )
| ( SY3618 = SY3620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3208,plain,
! [SV726: $i] :
( ( ! [SY3621: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV726 @ SY3621 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY3621
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3209,plain,
! [SV727: $i] :
( ( ! [SY3622: $i,SY3623: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV727 @ SY3622 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV727 @ SY3623 @ tc_nat ) )
| ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3622 = SY3623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3210,plain,
! [SV728: $i] :
( ( ! [SY3624: $i,SY3625: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV728 @ SY3624 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY3625 @ SY3624 @ tc_nat ) )
| ( SV728 = SY3625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3211,plain,
! [SV729: $i] :
( ( ! [SY3626: $i,SY3627: $i,SY3628: $i,SY3629: $i,SY3630: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV729 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3626 @ SY3627 @ SV729 ) @ SY3628 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3629 @ SY3627 @ SV729 ) @ SY3630 @ SV729 ) )
| ( SY3628
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3629 @ SY3626 @ SV729 ) @ SY3627 @ SV729 ) @ SY3630 @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3212,plain,
! [SV730: $i] :
( ( ! [SY3631: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV730 )
| ( ( c_HOL_Oabs__class_Oabs @ SY3631 @ SV730 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ( SY3631
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3213,plain,
! [SV731: $i] :
( ( ! [SY3632: $i] :
( ( SV731
!= ( c_HOL_Oplus__class_Oplus @ SV731 @ SY3632 @ tc_nat ) )
| ( SY3632
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3214,plain,
! [SV732: $i] :
( ( ! [SY3633: $i,SY3634: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV732 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3633 @ SY3634 @ SV732 )
!= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
| ( SY3633 = SY3634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3215,plain,
! [SV733: $i] :
( ( ! [SY3635: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV733 @ SY3635 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV733
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3635
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3216,plain,
! [SV734: $i] :
( ( ! [SY3636: $i,SY3637: $i] :
( ~ ( class_Orderings_Olinorder @ SV734 )
| ( ( c_Orderings_Oord__class_Omin @ SY3636 @ SY3637 @ SV734 )
!= SY3636 )
| ( c_lessequals @ SY3636 @ SY3637 @ SV734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(3217,plain,
! [SV735: $i] :
( ( ! [SY3638: $i,SY3639: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SY3638 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY3639 @ SY3638 @ tc_nat ) )
| ~ ( c_lessequals @ SY3638 @ SY3639 @ tc_nat )
| ~ ( c_lessequals @ SY3638 @ SV735 @ tc_nat )
| ( SV735 = SY3639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3218,plain,
! [SV736: $i] :
( ( ! [SY3640: $i] :
( ( ( c_Suc @ SV736 )
!= ( c_Suc @ SY3640 ) )
| ( SV736 = SY3640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3219,plain,
! [SV737: $i] :
( ( ! [SY3641: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV737 @ SY3641 @ tc_nat )
!= SV737 )
| ( SY3641
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3220,plain,
! [SV738: $i] :
( ( ! [SY3642: $i,SY3643: $i,SY3644: $i,SY3645: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SY3642 @ tc_nat ) @ SY3643 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3644 @ SY3642 @ tc_nat ) @ SY3645 @ tc_nat ) )
| ~ ( c_lessequals @ SV738 @ SY3644 @ tc_nat )
| ( SY3643
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3644 @ SV738 @ tc_nat ) @ SY3642 @ tc_nat ) @ SY3645 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3221,plain,
! [SV739: $i] :
( ( ! [SY3646: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SY3646 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV739
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3222,plain,
! [SV740: $i] :
( ( ( c_Suc @ SV740 )
!= SV740 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3223,plain,
! [SV741: $i] :
( ( ! [SY3647: $i,SY3648: $i,SY3649: $i,SY3650: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3647 @ SY3648 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SY3649 @ SY3650 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SY3649 @ SY3650 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SY3647 @ SY3648 @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3224,plain,
! [SV742: $i] :
( ( ! [SY3651: $i,SY3652: $i,SY3653: $i,SY3654: $i,SY3655: $i] :
( ~ ( class_Divides_Osemiring__div @ SV742 )
| ( ( c_Divides_Odiv__class_Omod @ SY3651 @ SY3652 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY3653 @ SY3652 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3654 @ SY3652 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY3655 @ SY3652 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3654 @ SY3651 @ SV742 ) @ SY3652 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3655 @ SY3653 @ SV742 ) @ SY3652 @ SV742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3225,plain,
! [SV743: $i] :
( ( ! [SY3656: $i,SY3657: $i,SY3658: $i,SY3659: $i,SY3660: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV743 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3656 @ SY3657 @ SV743 ) @ SY3658 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3659 @ SY3657 @ SV743 ) @ SY3660 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3656 @ SY3659 @ SV743 ) @ SY3657 @ SV743 ) @ SY3658 @ SV743 )
= SY3660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3226,plain,
! [SV744: $i] :
( ( ! [SY3661: $i,SY3662: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV744 @ SY3661 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV744 @ SY3662 @ tc_nat ) )
| ( SY3661 = SY3662 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(3227,plain,
! [SV745: $i] :
( ( ! [SY3663: $i,SY3664: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SY3663 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV745 @ SY3664 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat )
| ( SY3663 = SY3664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3228,plain,
! [SV746: $i] :
( ( ! [SY3665: $i,SY3666: $i,SY3667: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SY3665 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3666 @ SY3667 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SY3667 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3666 @ SY3665 @ tc_nat ) @ tc_nat ) )
| ( SY3665 = SY3667 )
| ( SV746 = SY3666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3229,plain,
! [SV747: $i] :
( ( ! [SY3668: $i,SY3669: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3668 @ SY3668 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SY3669 @ SY3669 @ SV747 ) @ SV747 )
!= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
| ( SY3669
= ( c_HOL_Ozero__class_Ozero @ SV747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3230,plain,
! [SV748: $i] :
( ( ! [SY3670: $i,SY3671: $i,SY3672: $i,SY3673: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV748 )
| ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3670 @ SY3671 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SY3672 @ SY3673 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3670 @ SY3673 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SY3672 @ SY3671 @ SV748 ) @ SV748 ) )
| ( SY3671 = SY3673 )
| ( SY3670 = SY3672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3231,plain,
! [SV749: $i] :
( ( ! [SY3674: $i,SY3675: $i,SY3676: $i,SY3677: $i,SY3678: $i] :
( ~ ( class_Divides_Osemiring__div @ SV749 )
| ( ( c_Divides_Odiv__class_Omod @ SY3674 @ SY3675 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY3676 @ SY3675 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3677 @ SY3675 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY3678 @ SY3675 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY3677 @ SY3674 @ SV749 ) @ SY3675 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY3678 @ SY3676 @ SV749 ) @ SY3675 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3232,plain,
! [SV750: $i] :
( ( ! [SY3679: $i,SY3680: $i,SY3681: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SY3679 @ SY3680 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SY3679 @ SY3681 @ tc_nat ) @ tc_nat ) )
| ( SY3680 = SY3681 )
| ( SY3679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3233,plain,
! [SV751: $i] :
( ( ! [SY3682: $i,SY3683: $i,SY3684: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3682 @ SY3683 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SY3682 @ SY3684 @ SV751 ) )
| ( SY3683 = SY3684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3234,plain,
! [SV752: $i] :
( ( ! [SY3685: $i,SY3686: $i,SY3687: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SY3685 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3686 @ SY3687 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SY3687 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3686 @ SY3685 @ tc_nat ) @ tc_nat ) )
| ( SY3685 = SY3687 )
| ( SV752 = SY3686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3235,plain,
! [SV753: $i] :
( ( ! [SY3688: $i,SY3689: $i,SY3690: $i,SY3691: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SY3688 @ tc_nat ) @ SY3689 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3690 @ SY3688 @ tc_nat ) @ SY3691 @ tc_nat ) )
| ~ ( c_lessequals @ SY3690 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SY3690 @ tc_nat ) @ SY3688 @ tc_nat ) @ SY3689 @ tc_nat )
= SY3691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3236,plain,
! [SV754: $i] :
( ( ! [SY3692: $i,SY3693: $i,SY3694: $i,SY3695: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV754 )
| ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SY3692 @ ( c_HOL_Otimes__class_Otimes @ SY3693 @ SY3694 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SY3692 @ ( c_HOL_Otimes__class_Otimes @ SY3693 @ SY3695 @ SV754 ) @ SV754 ) )
| ( SY3694 = SY3695 )
| ( SY3693
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3237,plain,
! [SV755: $i,SV1: $i] :
( ( ! [SY3696: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SY3696 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SY3696 @ SV755 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3238,plain,
! [SV756: $i,SV2: $i] :
( ( ! [SY3697: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SY3697 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SY3697 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3239,plain,
! [SV757: $i,SV3: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV3 ) @ SV757 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV757 @ ( c_HOL_Otimes__class_Otimes @ SV3 @ SV757 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3240,plain,
! [SV758: $i,SV4: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV4 @ ( c_Suc @ SV758 ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV4 @ ( c_HOL_Otimes__class_Otimes @ SV4 @ SV758 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3241,plain,
! [SV759: $i,SV5: $i] :
( ( ! [SY3698: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV5 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV759 @ SV759 @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SY3698 @ SY3698 @ SV5 ) @ SV5 ) @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3242,plain,
! [SV760: $i,SV6: $i] :
( ( ! [SY3699: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SY3699 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_lessequals @ SY3699 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3243,plain,
! [SV761: $i,SV7: $i] :
( ( ! [SY3700: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SY3700 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SY3700 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3244,plain,
! [SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV8 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(3245,plain,
! [SV762: $i,SV9: $i] :
( ( ! [SY3701: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV9 @ SV762 @ tc_nat ) @ SY3701 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV9 @ SY3701 @ tc_nat ) @ SV762 @ tc_nat ) )
| ~ ( c_lessequals @ SY3701 @ SV9 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3246,plain,
! [SV763: $i,SV10: $i] :
( ( ! [SY3702: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV10 @ SV763 @ tc_nat ) @ SY3702 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV10 @ ( c_HOL_Ominus__class_Ominus @ SV763 @ SY3702 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SY3702 @ SV763 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3247,plain,
! [SV764: $i,SV11: $i] :
( ( ! [SY3703: $i,SY3704: $i,SY3705: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SY3703 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SY3704 @ SY3705 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SY3704 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SY3703 @ SY3705 @ SV11 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3248,plain,
! [SV765: $i,SV12: $i] :
( ( ! [SY3706: $i,SY3707: $i,SY3708: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV765 @ SY3706 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SY3707 @ SY3708 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SV765 @ ( c_HOL_Otimes__class_Otimes @ SY3706 @ ( c_HOL_Otimes__class_Otimes @ SY3707 @ SY3708 @ SV12 ) @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3249,plain,
! [SV766: $i,SV13: $i] :
( ( ! [SY3709: $i,SY3710: $i,SY3711: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SY3709 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SY3710 @ SY3711 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SY3710 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SY3709 @ SV13 ) @ SY3711 @ SV13 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3250,plain,
! [SV767: $i,SV14: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV14 )
| ( SV767
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV767 @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3251,plain,
! [SV768: $i,SV15: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV15 )
| ( ( c_Orderings_Oord__class_Omin @ SV768 @ SV768 @ SV15 )
= SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3252,plain,
! [SV769: $i,SV16: $i] :
( ( ! [SY3712: $i,SY3713: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
| ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SY3712 @ ( c_HOL_Oabs__class_Oabs @ SY3713 @ SV16 ) @ SV16 ) @ SV16 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SY3713 @ SV16 ) @ SY3712 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3253,plain,
! [SV17: $i] :
( ( ( SV17
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV17 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(3254,plain,
! [SV770: $i,SV18: $i] :
( ( ! [SY3714: $i] :
( ~ ( class_Orderings_Oorder @ SV18 )
| ( SV770 = SY3714 )
| ~ ( c_lessequals @ SY3714 @ SV770 @ SV18 )
| ~ ( c_lessequals @ SV770 @ SY3714 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3255,plain,
! [SV771: $i,SV19: $i] :
( ( ! [SY3715: $i] :
( ~ ( class_Orderings_Oorder @ SV19 )
| ( SV771 = SY3715 )
| ~ ( c_lessequals @ SY3715 @ SV771 @ SV19 )
| ~ ( c_lessequals @ SV771 @ SY3715 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3256,plain,
! [SV772: $i,SV20: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV772 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV772 @ SV20 @ tc_nat )
| ( SV772 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3257,plain,
! [SV773: $i,SV21: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SV773 @ tc_nat )
| ( SV773 = SV21 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV773 @ SV21 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3258,plain,
! [SV774: $i,SV22: $i] :
( ( ( SV22 = SV774 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV22 @ SV774 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV774 @ SV22 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3259,plain,
! [SV775: $i,SV23: $i] :
( ( ( SV23 = SV775 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV775 @ SV23 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV23 @ SV775 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3260,plain,
! [SV776: $i,SV24: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV24 @ SV776 @ tc_nat )
| ( SV776 = SV24 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV776 @ SV24 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3261,plain,
! [SV777: $i,SV25: $i] :
( ( ( SV25 = SV777 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV777 @ SV25 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV25 @ SV777 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3262,plain,
! [SV778: $i,SV26: $i] :
( ( ( SV26 = SV778 )
| ~ ( c_lessequals @ SV778 @ SV26 @ tc_nat )
| ~ ( c_lessequals @ SV26 @ SV778 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3263,plain,
! [SV779: $i,SV27: $i] :
( ( ( SV27 = SV779 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV779 @ SV27 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV27 @ SV779 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3264,plain,
! [SV780: $i,SV28: $i] :
( ( ! [SY3716: $i] :
( ~ ( class_Orderings_Oorder @ SV28 )
| ( SV780 = SY3716 )
| ~ ( c_lessequals @ SV780 @ SY3716 @ SV28 )
| ~ ( c_lessequals @ SY3716 @ SV780 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3265,plain,
! [SV781: $i,SV29: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV29 )
| ( ( c_HOL_Oabs__class_Oabs @ SV781 @ SV29 )
= SV781 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV781 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3266,plain,
! [SV782: $i,SV30: $i] :
( ( ! [SY3717: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV782 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3717 @ SV782 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SY3717 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3267,plain,
! [SV783: $i,SV31: $i] :
( ( ! [SY3718: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SY3718 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3718 @ SV783 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3718 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SY3718 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(3268,plain,
! [SV784: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV32 @ SV784 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV784 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3269,plain,
! [SV785: $i,SV34: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV34 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV785 @ SV785 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3270,plain,
! [SV786: $i,SV35: $i] :
( ( ! [SY3719: $i,SY3720: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SY3719 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3720 @ SY3719 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SY3720 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(3271,plain,
! [SV787: $i,SV36: $i] :
( ( ! [SY3721: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV36 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV787 @ SY3721 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SY3721 @ tc_nat ) @ ( c_Suc @ SV787 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY3721 @ SV787 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3272,plain,
! [SV788: $i,SV37: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV37 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV788 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3273,plain,
! [SV789: $i,SV38: $i] :
( ( ! [SY3722: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV38 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV789 @ SV38 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SY3722 @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3274,plain,
! [SV790: $i,SV39: $i] :
( ( ! [SY3723: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV39 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV790 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ ( c_HOL_Otimes__class_Otimes @ SY3723 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3275,plain,
! [SV791: $i,SV40: $i] :
( ( ! [SY3724: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV791 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SY3724 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV791 @ SY3724 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3276,plain,
! [SV792: $i,SV41: $i] :
( ( ! [SY3725: $i] :
( ( c_lessequals @ SV41 @ SV792 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3725 @ SV41 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3725 @ SV792 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3277,plain,
! [SV793: $i,SV42: $i] :
( ( ! [SY3726: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV42 @ SV793 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3726 @ SV793 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV42 @ SY3726 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3278,plain,
! [SV794: $i,SV43: $i] :
( ( ! [SY3727: $i,SY3728: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SY3727 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SY3728 @ SV43 ) @ SV43 )
| ~ ( c_lessequals @ SY3727 @ SY3728 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3279,plain,
! [SV795: $i,SV44: $i] :
( ( ! [SY3729: $i,SY3730: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SY3729 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SY3730 @ SY3729 @ SV44 ) @ SV44 )
| ~ ( c_lessequals @ SV795 @ SY3730 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3280,plain,
! [SV796: $i,SV45: $i] :
( ( ! [SY3731: $i,SY3732: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
| ( c_lessequals @ SV796 @ SY3731 @ SV45 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3732 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SY3732 @ SY3731 @ SV45 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3281,plain,
! [SV797: $i,SV46: $i] :
( ( ! [SY3733: $i,SY3734: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SY3733 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SY3734 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ SY3733 @ SY3734 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3282,plain,
! [SV798: $i,SV47: $i] :
( ( ! [SY3735: $i,SY3736: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
| ( c_lessequals @ SV798 @ SY3735 @ SV47 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SY3736 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SY3735 @ SY3736 @ SV47 ) @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3283,plain,
! [SV799: $i,SV48: $i] :
( ( ! [SY3737: $i,SY3738: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SY3737 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SY3738 @ SY3737 @ SV48 ) @ SV48 )
| ~ ( c_lessequals @ SV799 @ SY3738 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3284,plain,
! [SV800: $i,SV49: $i] :
( ( ! [SY3739: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV49 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SY3739 @ SV49 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV800 @ SV49 ) @ ( c_HOL_Oabs__class_Oabs @ SY3739 @ SV49 ) @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3285,plain,
! [SV801: $i,SV50: $i] :
( ( ! [SY3740: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SY3740 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SY3740 @ SV50 ) @ SV50 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY3740 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3286,plain,
! [SV802: $i,SV51: $i] :
( ( ! [SY3741: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SY3741 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SY3741 @ SV51 ) @ SV51 ) )
| ~ ( c_lessequals @ SY3741 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3287,plain,
! [SV803: $i,SV52: $i] :
( ( ! [SY3742: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SY3742 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SY3742 @ SV52 ) @ SV52 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SY3742 @ SV52 )
| ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3288,plain,
! [SV804: $i,SV53: $i] :
( ( ! [SY3743: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SY3743 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SY3743 @ SV53 ) @ SV53 ) )
| ~ ( c_lessequals @ SY3743 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
| ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3289,plain,
! [SV805: $i,SV54: $i] :
( ( ! [SY3744: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ SV805 @ ( c_HOL_Otimes__class_Otimes @ SV805 @ SY3744 @ SV54 ) @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV805 @ SY3744 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3290,plain,
! [SV55: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV55 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV55 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(3291,plain,
! [SV806: $i,SV56: $i] :
( ( ! [SY3745: $i] :
( ~ ( class_Divides_Osemiring__div @ SV56 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SY3745 @ SV56 ) @ SV806 @ SV56 )
= ( c_Divides_Odiv__class_Omod @ SY3745 @ SV806 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3292,plain,
! [SV807: $i,SV57: $i] :
( ( ! [SY3746: $i] :
( ~ ( class_Divides_Osemiring__div @ SV57 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SY3746 @ SV57 ) @ SY3746 @ SV57 )
= ( c_Divides_Odiv__class_Omod @ SV807 @ SY3746 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3293,plain,
! [SV808: $i,SV58: $i] :
( ( ! [SY3747: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
| ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SY3747 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3294,plain,
! [SV809: $i,SV59: $i] :
( ( ! [SY3748: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SY3748 @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3748 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3295,plain,
! [SV810: $i,SV60: $i] :
( ( ! [SY3749: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
| ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ( c_lessequals @ SY3749 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SY3749 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3296,plain,
! [SV811: $i,SV61: $i] :
( ( ! [SY3750: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
| ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3750 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3297,plain,
! [SV812: $i,SV62: $i] :
( ( ! [SY3751: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SY3751 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SY3751 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3298,plain,
! [SV813: $i,SV63: $i] :
( ( ! [SY3752: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SY3752 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY3752 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3299,plain,
! [SV814: $i,SV64: $i] :
( ( ! [SY3753: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SY3753 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SY3753 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3300,plain,
! [SV815: $i,SV65: $i] :
( ( ! [SY3754: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SY3754 @ SV65 ) @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SY3754 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3301,plain,
! [SV816: $i,SV66: $i] :
( ( ! [SY3755: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SY3755 @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SY3755 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3302,plain,
! [SV817: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV67 @ SV817 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV817 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV67 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3303,plain,
! [SV818: $i,SV68: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV68 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV818 @ SV818 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ SV818 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3304,plain,
! [SV819: $i,SV69: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV819 @ SV819 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3305,plain,
! [SV820: $i,SV70: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV70 )
| ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV820 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3306,plain,
! [SV821: $i,SV71: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV71 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV821 @ SV71 ) @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3307,plain,
! [SV822: $i,SV73: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV73 @ SV822 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV73 @ SV822 @ tc_nat ) @ SV822 @ tc_nat ) )
| ~ ( c_lessequals @ SV822 @ SV73 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3308,plain,
! [SV823: $i,SV76: $i] :
( ( ! [SY3756: $i,SY3757: $i] :
( ~ ( c_lessequals @ SV76 @ SV823 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SY3756 @ tc_nat ) @ SY3757 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV76 @ SY3756 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV823 @ SV76 @ tc_nat ) @ SY3756 @ tc_nat ) @ SY3757 @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3309,plain,
! [SV824: $i,SV77: $i] :
( ( ! [SY3758: $i,SY3759: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
| ( c_HOL_Oord__class_Oless @ SV824 @ SY3758 @ SV77 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SY3759 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SY3759 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SY3758 @ SY3759 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3310,plain,
! [SV825: $i,SV78: $i] :
( ( ! [SY3760: $i,SY3761: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
| ( c_HOL_Oord__class_Oless @ SV825 @ SY3760 @ SV78 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SY3761 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3761 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SY3761 @ SY3760 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3311,plain,
! [SV826: $i,SV79: $i] :
( ( ! [SY3762: $i,SY3763: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV79 )
| ( c_HOL_Oord__class_Oless @ SV826 @ SY3762 @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SY3763 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SY3763 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SY3762 @ SY3763 @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3312,plain,
! [SV827: $i,SV80: $i] :
( ( ! [SY3764: $i,SY3765: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV80 )
| ( c_HOL_Oord__class_Oless @ SV827 @ SY3764 @ SV80 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SY3765 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3765 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SY3765 @ SY3764 @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3313,plain,
! [SV828: $i,SV81: $i] :
( ( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV81 @ SV828 @ tc_nat ) @ SV828 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV828 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3314,plain,
! [SV829: $i,SV82: $i] :
( ( ! [SY3766: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV82 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV829 @ SV82 ) @ ( c_HOL_Otimes__class_Otimes @ SY3766 @ SY3766 @ SV82 ) @ SV82 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3315,plain,
! [SV830: $i,SV83: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV83 ) @ SV830 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV83 @ SV830 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV830 @ SV83 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3316,plain,
! [SV831: $i,SV84: $i] :
( ( ! [SY3767: $i,SY3768: $i] :
( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SY3767 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SY3768 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SY3767 @ SY3768 @ SV84 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3317,plain,
! [SV832: $i,SV85: $i] :
( ( ! [SY3769: $i,SY3770: $i] :
( ~ ( class_Divides_Osemiring__div @ SV85 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SY3769 @ SY3770 @ SV85 ) @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SY3769 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SY3770 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3318,plain,
! [SV833: $i,SV86: $i] :
( ( ! [SY3771: $i,SY3772: $i] :
( ~ ( class_Divides_Osemiring__div @ SV86 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SY3771 @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SY3771 @ SY3772 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SY3772 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3319,plain,
! [SV834: $i,SV87: $i] :
( ( ! [SY3773: $i,SY3774: $i] :
( ~ ( class_Divides_Osemiring__div @ SV87 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SY3773 @ SY3774 @ SV87 ) @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SY3774 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SY3773 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3320,plain,
! [SV835: $i,SV88: $i] :
( ( ! [SY3775: $i,SY3776: $i,SY3777: $i,SY3778: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SY3775 @ SV88 ) @ SY3776 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3777 @ SY3775 @ SV88 ) @ SY3778 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SY3776 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3777 @ SV835 @ SV88 ) @ SY3775 @ SV88 ) @ SY3778 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3321,plain,
! [SV836: $i,SV89: $i] :
( ( ! [SY3779: $i,SY3780: $i,SY3781: $i,SY3782: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 )
| ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3779 @ SY3780 @ SV89 ) @ SY3781 @ SV89 ) @ SY3782 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3780 @ SY3781 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3779 @ SY3781 @ SV89 ) @ SY3782 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3322,plain,
! [SV837: $i,SV90: $i] :
( ( ! [SY3783: $i,SY3784: $i,SY3785: $i,SY3786: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SY3783 @ SV90 ) @ SY3784 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3785 @ SY3783 @ SV90 ) @ SY3786 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SY3785 @ SV90 ) @ SY3783 @ SV90 ) @ SY3784 @ SV90 ) @ SY3786 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3323,plain,
! [SV838: $i,SV91: $i] :
( ( ! [SY3787: $i,SY3788: $i,SY3789: $i,SY3790: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SY3787 @ SV91 ) @ SY3788 @ SV91 ) @ SY3789 @ SV91 ) @ SY3790 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SY3788 @ SV91 ) @ SY3789 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3787 @ SY3788 @ SV91 ) @ SY3790 @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3324,plain,
! [SV839: $i,SV92: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV92 ) @ SV839 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV92 @ SV839 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3325,plain,
! [SV840: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV93 @ SV840 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV93 ) @ SV840 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3326,plain,
! [SV841: $i,SV94: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV94 ) @ SV841 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV841 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3327,plain,
! [SV842: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ SV842 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV95 ) @ SV842 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3328,plain,
! [SV843: $i,SV96: $i] :
( ( ! [SY3791: $i,SY3792: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SY3791 @ SY3792 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SY3791 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SY3792 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3329,plain,
! [SV844: $i,SV97: $i] :
( ( ! [SY3793: $i,SY3794: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
| ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SY3793 @ SY3794 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SY3794 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SY3793 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3330,plain,
! [SV845: $i,SV98: $i] :
( ( ! [SY3795: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SV845 @ tc_nat ) @ SY3795 @ tc_nat )
| ~ ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SY3795 @ SV845 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV845 @ SY3795 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3331,plain,
! [SV846: $i,SV99: $i] :
( ( ! [SY3796: $i] :
( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SV846 @ SY3796 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SY3796 @ tc_nat ) @ SV846 @ tc_nat )
| ~ ( c_lessequals @ SY3796 @ SV846 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3332,plain,
! [SV847: $i,SV100: $i] :
( ( c_HOL_Oord__class_Oless @ SV100 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV100 @ SV847 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3333,plain,
! [SV848: $i,SV101: $i] :
( ( c_HOL_Oord__class_Oless @ SV101 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV848 @ SV101 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3334,plain,
! [SV849: $i,SV102: $i] :
( ( c_HOL_Oord__class_Oless @ SV102 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV102 @ SV849 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3335,plain,
! [SV850: $i,SV103: $i] :
( ( ! [SY3797: $i,SY3798: $i,SY3799: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SY3797 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3798 @ SV850 @ tc_nat ) @ SY3799 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3797 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3798 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SY3799 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV103 @ SY3798 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3336,plain,
! [SV851: $i,SV104: $i] :
( ( ! [SY3800: $i,SY3801: $i,SY3802: $i] :
( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SY3800 @ tc_nat ) @ SY3801 @ tc_nat ) @ SY3802 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3800 @ SY3801 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SY3801 @ tc_nat ) @ SY3802 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3800 @ SV851 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3337,plain,
! [SV852: $i,SV105: $i] :
( ( ! [SY3803: $i,SY3804: $i,SY3805: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SY3803 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3804 @ SV852 @ tc_nat ) @ SY3805 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SY3804 @ tc_nat ) @ SV852 @ tc_nat ) @ SY3803 @ tc_nat ) @ SY3805 @ tc_nat )
| ~ ( c_lessequals @ SY3804 @ SV105 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3338,plain,
! [SV853: $i,SV106: $i] :
( ( ! [SY3806: $i,SY3807: $i,SY3808: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SY3806 @ tc_nat ) @ SY3807 @ tc_nat ) @ SY3808 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SY3806 @ tc_nat ) @ SY3807 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SY3806 @ tc_nat ) @ SY3808 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3339,plain,
! [SV854: $i,SV107: $i] :
( ( ! [SY3809: $i,SY3810: $i,SY3811: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV107 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SY3809 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY3810 @ SV854 @ SV107 ) @ SY3809 @ SV107 ) @ SY3811 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY3810 @ SY3809 @ SV107 ) @ SY3811 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3340,plain,
! [SV855: $i,SV108: $i] :
( ( ! [SY3812: $i] :
( ~ ( class_Ring__and__Field_Olordered__ring @ SV108 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV855 @ SY3812 @ SV108 ) @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV855 @ SV108 ) @ ( c_HOL_Oabs__class_Oabs @ SY3812 @ SV108 ) @ SV108 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3341,plain,
! [SV856: $i,SV109: $i] :
( ( ! [SY3813: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 )
| ( c_lessequals @ SV856 @ SY3813 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV856 @ SV109 ) @ SY3813 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3342,plain,
! [SV857: $i,SV110: $i] :
( ( ! [SY3814: $i,SY3815: $i,SY3816: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SY3814 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SY3815 @ SY3816 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SY3814 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SY3815 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SY3814 @ SY3816 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SY3815 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3343,plain,
! [SV858: $i,SV111: $i] :
( ( ! [SY3817: $i,SY3818: $i] :
( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV858 @ SY3817 @ SV111 ) @ SY3818 @ SV111 ) @ SY3817 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV858 @ SY3818 @ SV111 ) @ SY3817 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3344,plain,
! [SV859: $i,SV112: $i] :
( ( ! [SY3819: $i,SY3820: $i] :
( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SY3819 @ SY3820 @ SV112 ) @ SV112 )
| ~ ( c_lessequals @ SV859 @ SY3820 @ SV112 )
| ~ ( c_lessequals @ SV859 @ SY3819 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3345,plain,
! [SV860: $i,SV113: $i] :
( ( ! [SY3821: $i,SY3822: $i] :
( ~ ( class_Orderings_Olinorder @ SV113 )
| ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SY3821 @ SY3822 @ SV113 ) @ SV113 )
| ~ ( c_lessequals @ SV860 @ SY3822 @ SV113 )
| ~ ( c_lessequals @ SV860 @ SY3821 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3346,plain,
! [SV861: $i,SV114: $i] :
( ( ! [SY3823: $i,SY3824: $i] :
( ~ ( class_Orderings_Olinorder @ SV114 )
| ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SY3823 @ SY3824 @ SV114 ) @ SV114 )
| ~ ( c_lessequals @ SV861 @ SY3824 @ SV114 )
| ~ ( c_lessequals @ SV861 @ SY3823 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3347,plain,
! [SV862: $i,SV115: $i] :
( ( ! [SY3825: $i] :
( ~ ( class_Orderings_Olinorder @ SV115 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV862 @ SY3825 @ SV115 ) @ SY3825 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3348,plain,
! [SV863: $i,SV116: $i] :
( ( ! [SY3826: $i] :
( ~ ( class_Orderings_Olinorder @ SV116 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV863 @ SY3826 @ SV116 ) @ SV863 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3349,plain,
! [SV864: $i,SV117: $i] :
( ( ! [SY3827: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV864 @ tc_nat ) ) @ SY3827 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV117 ) @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SY3827 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV864 @ SV117 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3350,plain,
! [SV865: $i,SV118: $i] :
( ( ! [SY3828: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV865 @ ( c_HOL_Otimes__class_Otimes @ SY3828 @ SV865 @ SV118 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3351,plain,
! [SV866: $i,SV119: $i] :
( ( ! [SY3829: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV119 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV866 @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SY3829 @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3352,plain,
! [SV867: $i,SV120: $i] :
( ( ! [SY3830: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV120 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV867 @ ( c_HOL_Otimes__class_Otimes @ SV867 @ SY3830 @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3353,plain,
! [SV868: $i,SV121: $i] :
( ( ! [SY3831: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV121 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV868 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3831 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ SV868 @ SY3831 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3354,plain,
! [SV869: $i,SV122: $i] :
( ( ! [SY3832: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV122 )
| ( c_lessequals @ SV869 @ SY3832 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV869 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3832 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3355,plain,
! [SV870: $i,SV123: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV123 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV870 @ SV123 )
= ( c_HOL_Ozero__class_Ozero @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3356,plain,
! [SV871: $i,SV124: $i] :
( ( ! [SY3833: $i,SY3834: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV124 )
| ~ ( class_Int_Onumber__ring @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SY3833 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SY3834 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SY3834 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SY3833 @ SV124 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3357,plain,
! [SV872: $i,SV125: $i] :
( ( ! [SY3835: $i,SY3836: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV125 )
| ~ ( class_Int_Onumber__ring @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SY3835 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SY3836 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SY3836 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SY3835 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3358,plain,
! [SV873: $i,SV126: $i] :
( ( ! [SY3837: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SV873 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SY3837 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SY3837 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SV873 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3359,plain,
! [SV874: $i,SV127: $i] :
( ( ! [SY3838: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SV874 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SY3838 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SY3838 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SV874 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3360,plain,
! [SV128: $i] :
( ( ( SV128
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV128 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(3361,plain,
! [SV875: $i,SV129: $i] :
( ( ! [SY3839: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV129 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV875 @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ SY3839 @ SV129 ) @ SV129 ) @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV875 @ SY3839 @ SV129 ) @ SV129 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3362,plain,
! [SV876: $i,SV130: $i] :
( ( ! [SY3840: $i] :
( ~ ( class_Orderings_Olinorder @ SV130 )
| ( ( c_Orderings_Oord__class_Omin @ SV876 @ ( c_Orderings_Oord__class_Omin @ SV876 @ SY3840 @ SV130 ) @ SV130 )
= ( c_Orderings_Oord__class_Omin @ SV876 @ SY3840 @ SV130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3363,plain,
! [SV877: $i,SV131: $i] :
( ( ! [SY3841: $i,SY3842: $i,SY3843: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV131 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SY3841 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SY3842 @ SY3843 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SY3841 @ SV131 ) @ SY3843 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SY3842 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3364,plain,
! [SV878: $i,SV132: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV132 ) @ SV878 @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV132 @ SV878 @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV132 @ SV878 @ tc_nat ) )
= SV878 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3365,plain,
! [SV879: $i,SV133: $i] :
( ( ! [SY3844: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SV879 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SY3844 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV133 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3366,plain,
! [SV880: $i,SV134: $i] :
( ( ! [SY3845: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV134 @ SV880 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3845 @ SV880 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV880 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3367,plain,
! [SV135: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(3368,plain,
! [SV881: $i,SV136: $i] :
( ( ! [SY3846: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Otimes__class_Otimes @ SV881 @ SY3846 @ SV136 )
= ( c_HOL_Otimes__class_Otimes @ SY3846 @ SV881 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3369,plain,
! [SV137: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV137 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV137 ) @ ( c_HOL_Ozero__class_Ozero @ SV137 ) @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(3370,plain,
! [SV882: $i,SV138: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV138 @ SV882 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV882 @ SV138 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3371,plain,
! [SV883: $i,SV139: $i] :
( ( ! [SY3847: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV139 )
| ( ( c_HOL_Otimes__class_Otimes @ SV883 @ SY3847 @ SV139 )
= ( c_HOL_Otimes__class_Otimes @ SY3847 @ SV883 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3372,plain,
! [SV884: $i,SV140: $i] :
( ( ! [SY3848: $i,SY3849: $i] :
( ~ ( class_Divides_Osemiring__div @ SV140 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV884 @ SY3848 @ SV140 ) @ SY3849 @ SV140 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV884 @ SY3849 @ SV140 ) @ ( c_Divides_Odiv__class_Omod @ SY3848 @ SY3849 @ SV140 ) @ SV140 ) @ SY3849 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3373,plain,
! [SV141: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV141 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(3374,plain,
! [SV885: $i,SV142: $i] :
( ( ! [SY3850: $i,SY3851: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV142 )
| ( ( c_HOL_Oplus__class_Oplus @ SV885 @ ( c_HOL_Oplus__class_Oplus @ SY3850 @ SY3851 @ SV142 ) @ SV142 )
= ( c_HOL_Oplus__class_Oplus @ SY3850 @ ( c_HOL_Oplus__class_Oplus @ SV885 @ SY3851 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3375,plain,
! [SV886: $i,SV143: $i] :
( ( ! [SY3852: $i,SY3853: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV143 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV886 @ SY3852 @ SV143 ) @ SY3853 @ SV143 )
= ( c_HOL_Oplus__class_Oplus @ SV886 @ ( c_HOL_Oplus__class_Oplus @ SY3852 @ SY3853 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3376,plain,
! [SV887: $i,SV144: $i] :
( ( ! [SY3854: $i,SY3855: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SY3854 @ SY3855 @ SV144 ) @ SV144 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SY3855 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3377,plain,
! [SV888: $i,SV145: $i] :
( ( ! [SY3856: $i,SY3857: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SY3856 @ SY3857 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SY3856 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3378,plain,
! [SV889: $i,SV146: $i] :
( ( ! [SY3858: $i,SY3859: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SY3858 @ SV146 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SY3859 @ SV146 ) @ SY3858 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3379,plain,
! [SV890: $i,SV147: $i] :
( ( ! [SY3860: $i,SY3861: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SY3860 @ SV147 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY3861 @ SV890 @ SV147 ) @ SY3860 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3380,plain,
! [SV891: $i,SV148: $i] :
( ( ! [SY3862: $i,SY3863: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 )
| ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SY3862 @ SY3863 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SY3863 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SY3862 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3381,plain,
! [SV892: $i,SV149: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV149 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV892 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3382,plain,
! [SV893: $i,SV150: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV150 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV893 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3383,plain,
! [SV894: $i,SV151: $i] :
( ( ! [SY3864: $i,SY3865: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SY3864 @ tc_nat ) @ tc_nat ) @ SY3865 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SY3864 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3865 @ SV151 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3864 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3384,plain,
! [SV895: $i,SV152: $i] :
( ( ! [SY3866: $i,SY3867: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ SV152 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY3866 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY3867 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
| ~ ( c_lessequals @ SY3866 @ SY3867 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3385,plain,
! [SV896: $i,SV153: $i] :
( ( ! [SY3868: $i,SY3869: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV153 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SY3868 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SY3869 @ SV153 ) @ SV153 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
| ~ ( c_lessequals @ SY3868 @ SY3869 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3386,plain,
! [SV897: $i,SV154: $i] :
( ( ! [SY3870: $i,SY3871: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV154 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SY3870 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SY3871 @ SY3870 @ SV154 ) @ SV154 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SY3870 @ SV154 )
| ~ ( c_lessequals @ SV897 @ SY3871 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3387,plain,
! [SV898: $i,SV155: $i] :
( ( ! [SY3872: $i,SY3873: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV155 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SY3872 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SY3873 @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SY3873 @ SY3872 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3388,plain,
! [SV899: $i,SV156: $i] :
( ( ! [SY3874: $i,SY3875: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV156 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SY3874 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SY3875 @ SY3874 @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SY3874 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SY3875 @ SV899 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3389,plain,
! [SV900: $i,SV157: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV157 )
| ( ( c_HOL_Otimes__class_Otimes @ SV900 @ SV900 @ SV157 )
= SV900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3390,plain,
! [SV901: $i,SV158: $i] :
( ( ! [SY3876: $i,SY3877: $i,SY3878: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SY3876 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SY3877 @ SY3878 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SY3876 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SY3876 @ SY3878 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SY3877 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3391,plain,
! [SV902: $i,SV159: $i] :
( ( ! [SY3879: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV159 @ SV902 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3879 @ SV902 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV159 @ SY3879 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3392,plain,
! [SV903: $i,SV160: $i] :
( ( ! [SY3880: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV903 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SY3880 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV903 @ SY3880 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3393,plain,
! [SV904: $i,SV161: $i] :
( ( ! [SY3881: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV904 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SY3881 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV904 @ SY3881 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3394,plain,
! [SV905: $i,SV162: $i] :
( ( ! [SY3882: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV162 @ SV905 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3882 @ SV905 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV162 @ SY3882 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3395,plain,
! [SV906: $i,SV163: $i] :
( ( ! [SY3883: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV163 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV906 @ SY3883 @ tc_nat ) @ SV163 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV906 @ SV163 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3883 @ SV163 ) @ SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3396,plain,
! [SV907: $i,SV164: $i] :
( ( ! [SY3884: $i,SY3885: $i] :
( ~ ( class_Divides_Osemiring__div @ SV164 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ ( c_Divides_Odiv__class_Omod @ SY3884 @ SY3885 @ SV164 ) @ SV164 ) @ SY3885 @ SV164 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ SY3884 @ SV164 ) @ SY3885 @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3397,plain,
! [SV908: $i,SV165: $i] :
( ( ! [SY3886: $i,SY3887: $i] :
( ~ ( class_Divides_Osemiring__div @ SV165 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV908 @ SY3886 @ SV165 ) @ SY3887 @ SV165 ) @ SY3886 @ SV165 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV908 @ SY3887 @ SV165 ) @ SY3886 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3398,plain,
! [SV909: $i,SV166: $i] :
( ( ! [SY3888: $i,SY3889: $i,SY3890: $i,SY3891: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV166 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY3888 @ ( c_HOL_Otimes__class_Otimes @ SY3889 @ SY3890 @ SV166 ) @ SV166 ) @ SY3891 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SY3888 @ SY3891 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SY3890 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3399,plain,
! [SV910: $i,SV167: $i] :
( ( ! [SY3892: $i,SY3893: $i,SY3894: $i,SY3895: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV167 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SY3892 @ SY3893 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY3892 @ ( c_HOL_Otimes__class_Otimes @ SY3894 @ SY3895 @ SV167 ) @ SV167 ) @ SY3893 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SY3895 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3400,plain,
! [SV911: $i,SV168: $i] :
( ( ! [SY3896: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV168 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SY3896 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SY3896 @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3401,plain,
! [SV912: $i,SV169: $i] :
( ( ! [SY3897: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV169 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SY3897 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SY3897 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3402,plain,
! [SV913: $i,SV170: $i] :
( ( ! [SY3898: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV170 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SY3898 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SY3898 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3403,plain,
! [SV914: $i,SV171: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV171 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV171 ) @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV914 @ SV171 ) @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3404,plain,
! [SV915: $i,SV172: $i] :
( ( ! [SY3899: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SY3899 @ SV172 ) @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SY3899 @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3405,plain,
! [SV916: $i,SV173: $i] :
( ( ! [SY3900: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SY3900 @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SY3900 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3406,plain,
! [SV917: $i,SV174: $i] :
( ( ! [SY3901: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SY3901 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SY3901 @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3407,plain,
! [SV918: $i,SV175: $i] :
( ( ! [SY3902: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV175 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV918 @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ SY3902 @ SV175 ) @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SY3902 @ SV175 ) @ SV175 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3408,plain,
! [SV919: $i,SV176: $i] :
( ( ! [SY3903: $i,SY3904: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV176 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV919 @ SY3903 @ SV176 ) @ SY3904 @ SV176 )
= ( c_HOL_Otimes__class_Otimes @ SV919 @ ( c_HOL_Otimes__class_Otimes @ SY3903 @ SY3904 @ SV176 ) @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3409,plain,
! [SV920: $i,SV177: $i] :
( ( ! [SY3905: $i,SY3906: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV177 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SY3905 @ SV177 ) @ SY3906 @ SV177 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SY3906 @ SV177 ) @ SY3905 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3410,plain,
! [SV921: $i,SV178: $i] :
( ( ! [SY3907: $i,SY3908: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV178 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SY3907 @ SV178 ) @ SY3908 @ SV178 )
= ( c_HOL_Otimes__class_Otimes @ SV921 @ ( c_HOL_Otimes__class_Otimes @ SY3907 @ SY3908 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3411,plain,
! [SV922: $i,SV179: $i] :
( ( ! [SY3909: $i,SY3910: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV179 )
| ( ( c_HOL_Otimes__class_Otimes @ SV922 @ ( c_HOL_Otimes__class_Otimes @ SY3909 @ SY3910 @ SV179 ) @ SV179 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV922 @ SY3909 @ SV179 ) @ SY3910 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3412,plain,
! [SV923: $i,SV180: $i] :
( ( ! [SY3911: $i,SY3912: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV180 )
| ( ( c_HOL_Otimes__class_Otimes @ SV923 @ ( c_HOL_Otimes__class_Otimes @ SY3911 @ SY3912 @ SV180 ) @ SV180 )
= ( c_HOL_Otimes__class_Otimes @ SY3911 @ ( c_HOL_Otimes__class_Otimes @ SV923 @ SY3912 @ SV180 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3413,plain,
! [SV924: $i,SV181: $i] :
( ( ! [SY3913: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV181 @ SV924 @ tc_nat ) @ SY3913 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV181 @ ( c_HOL_Otimes__class_Otimes @ SV924 @ SY3913 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3414,plain,
! [SV925: $i,SV182: $i] :
( ( ! [SY3914: $i,SY3915: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV182 )
| ( ( c_HOL_Otimes__class_Otimes @ SV925 @ ( c_HOL_Otimes__class_Otimes @ SY3914 @ SY3915 @ SV182 ) @ SV182 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV925 @ SY3914 @ SV182 ) @ SY3915 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3415,plain,
! [SV926: $i,SV183: $i] :
( ( ! [SY3916: $i,SY3917: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV926 @ SY3916 @ SV183 ) @ SY3917 @ SV183 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV926 @ SY3917 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SY3916 @ SY3917 @ SV183 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3416,plain,
! [SV927: $i,SV184: $i] :
( ( ! [SY3918: $i,SY3919: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV184 )
| ( ( c_HOL_Otimes__class_Otimes @ SV927 @ ( c_HOL_Oplus__class_Oplus @ SY3918 @ SY3919 @ SV184 ) @ SV184 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SY3918 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SY3919 @ SV184 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3417,plain,
! [SV928: $i,SV185: $i] :
( ( ! [SY3920: $i,SY3921: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV185 )
| ( ( c_HOL_Otimes__class_Otimes @ SV928 @ ( c_HOL_Oplus__class_Oplus @ SY3920 @ SY3921 @ SV185 ) @ SV185 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SY3920 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SY3921 @ SV185 ) @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3418,plain,
! [SV929: $i,SV186: $i] :
( ( ! [SY3922: $i,SY3923: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV929 @ SY3922 @ SV186 ) @ SY3923 @ SV186 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SY3923 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SY3922 @ SY3923 @ SV186 ) @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3419,plain,
! [SV930: $i,SV187: $i] :
( ( ! [SY3924: $i,SY3925: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV187 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV930 @ SY3924 @ SV187 ) @ SY3925 @ SV187 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV930 @ SY3925 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SY3924 @ SY3925 @ SV187 ) @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3420,plain,
! [SV931: $i,SV188: $i] :
( ( ! [SY3926: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV188 @ ( c_HOL_Oplus__class_Oplus @ SV931 @ SY3926 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV188 @ SV931 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV188 @ SY3926 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3421,plain,
! [SV932: $i,SV189: $i] :
( ( ! [SY3927: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV189 @ SV932 @ tc_nat ) @ SY3927 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV189 @ SY3927 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV932 @ SY3927 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3422,plain,
! [SV933: $i,SV190: $i] :
( ( ! [SY3928: $i,SY3929: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV190 )
| ( ( c_HOL_Otimes__class_Otimes @ SV933 @ ( c_HOL_Oplus__class_Oplus @ SY3928 @ SY3929 @ SV190 ) @ SV190 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SY3928 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SY3929 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3423,plain,
! [SV934: $i,SV191: $i] :
( ( ! [SY3930: $i,SY3931: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV934 @ SY3930 @ SV191 ) @ SY3931 @ SV191 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SY3931 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SY3930 @ SY3931 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3424,plain,
! [SV935: $i,SV192: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV192 @ SV935 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV935 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3425,plain,
! [SV936: $i,SV193: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV193 @ SV936 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV193 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3426,plain,
! [SV937: $i,SV194: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV194 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV937 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV937 @ SV194 ) @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3427,plain,
! [SV938: $i,SV195: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV195 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV938 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV938 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3428,plain,
! [SV939: $i,SV196: $i] :
( ( ! [SY3932: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
| ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SY3932 @ SV196 ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3429,plain,
! [SV940: $i,SV197: $i] :
( ( ! [SY3933: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
| ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY3933 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SY3933 @ SV940 @ SV197 ) @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3430,plain,
! [SV941: $i,SV198: $i] :
( ( ! [SY3934: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
| ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SY3934 @ SV198 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SY3934 @ SV198 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3431,plain,
! [SV942: $i,SV199: $i] :
( ( ! [SY3935: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
| ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SY3935 @ SV942 @ SV199 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3432,plain,
! [SV200: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV200 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ SV200 ) @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(3433,plain,
! [SV943: $i,SV201: $i] :
( ( ! [SY3936: $i,SY3937: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV943 @ SY3936 @ SV201 ) @ ( c_HOL_Otimes__class_Otimes @ SY3937 @ SY3936 @ SV201 ) @ SV201 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV943 @ SY3937 @ SV201 ) @ SY3936 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3434,plain,
! [SV944: $i,SV202: $i] :
( ( ! [SY3938: $i,SY3939: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3938 @ SY3939 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV944 @ SY3939 @ tc_nat )
| ~ ( c_lessequals @ SV202 @ SY3938 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3435,plain,
! [SV945: $i,SV204: $i] :
( ( ! [SY3940: $i,SY3941: $i,SY3942: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV204 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SY3940 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SY3941 @ SY3942 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY3940 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY3941 @ SV204 )
| ~ ( c_lessequals @ SY3940 @ SY3942 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SY3941 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3436,plain,
! [SV946: $i,SV205: $i] :
( ( ! [SY3943: $i,SY3944: $i,SY3945: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV205 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SY3943 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SY3944 @ SY3945 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SY3943 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SY3943 @ SY3945 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SY3944 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3437,plain,
! [SV947: $i,SV206: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV206 @ SV947 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV947 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV206 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3438,plain,
! [SV948: $i,SV207: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV207 @ SV948 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV948 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV207 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3439,plain,
! [SV949: $i,SV208: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV208 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV949 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV208 @ SV949 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3440,plain,
! [SV950: $i,SV209: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV209 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV950 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV950 @ SV209 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3441,plain,
! [SV951: $i,SV210: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SV951 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV951 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV210 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3442,plain,
! [SV952: $i,SV211: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV211 @ SV952 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV952 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV211 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3443,plain,
! [SV953: $i,SV212: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV212 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV953 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV212 @ SV953 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3444,plain,
! [SV954: $i,SV213: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV213 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV954 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV954 @ SV213 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3445,plain,
! [SV955: $i,SV214: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV214 @ SV955 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV955 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV214 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3446,plain,
! [SV956: $i,SV215: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV215 @ SV956 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV956 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV215 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3447,plain,
! [SV957: $i,SV216: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV216 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV957 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV216 @ SV957 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3448,plain,
! [SV958: $i,SV217: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV217 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV958 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV217 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3449,plain,
! [SV959: $i,SV218: $i] :
( ( ( SV218
= ( c_Suc @ SV959 ) )
| ( c_lessequals @ SV218 @ SV959 @ tc_nat )
| ~ ( c_lessequals @ SV218 @ ( c_Suc @ SV959 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3450,plain,
! [SV960: $i,SV219: $i] :
( ( ! [SY3946: $i,SY3947: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SY3946 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SY3947 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3451,plain,
! [SV961: $i,SV220: $i] :
( ( ! [SY3948: $i,SY3949: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY3948 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SY3949 @ SV961 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3452,plain,
! [SV962: $i,SV221: $i] :
( ( ! [SY3950: $i,SY3951: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SY3950 @ SY3951 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SY3951 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SY3950 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3453,plain,
! [SV222: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV222 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV222 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(3454,plain,
! [SV963: $i,SV223: $i] :
( ( ! [SY3952: $i,SY3953: $i,SY3954: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SY3952 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SY3953 @ SY3954 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SY3953 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SY3952 @ SY3954 @ SV223 ) @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3455,plain,
! [SV964: $i,SV224: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV224 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV964 @ SV224 ) @ SV224 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV964 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3456,plain,
! [SV965: $i,SV225: $i] :
( ( ! [SY3955: $i,SY3956: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ SV965 @ SY3955 @ SV225 ) @ SY3956 @ SV225 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ SV965 @ SY3956 @ SV225 ) @ ( c_HOL_Oplus__class_Oplus @ SY3955 @ SY3956 @ SV225 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3457,plain,
! [SV966: $i,SV226: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV966 @ SV966 @ SV226 ) @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3458,plain,
! [SV967: $i,SV227: $i] :
( ( ! [SY3957: $i,SY3958: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ SV967 @ ( c_HOL_Oplus__class_Oplus @ SY3957 @ SY3958 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SY3957 @ SV227 ) @ SY3958 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3459,plain,
! [SV968: $i,SV228: $i] :
( ( ! [SY3959: $i,SY3960: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ SV968 @ ( c_HOL_Oplus__class_Oplus @ SY3959 @ SY3960 @ SV228 ) @ SV228 )
= ( c_HOL_Oplus__class_Oplus @ SY3959 @ ( c_HOL_Oplus__class_Oplus @ SV968 @ SY3960 @ SV228 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3460,plain,
! [SV969: $i,SV229: $i] :
( ( ! [SY3961: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV229 @ SV969 @ tc_nat ) @ SY3961 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV229 @ ( c_HOL_Oplus__class_Oplus @ SV969 @ SY3961 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3461,plain,
! [SV970: $i,SV230: $i] :
( ( ! [SY3962: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV230 @ ( c_HOL_Oplus__class_Oplus @ SV970 @ SY3962 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV970 @ ( c_HOL_Oplus__class_Oplus @ SV230 @ SY3962 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3462,plain,
! [SV971: $i,SV231: $i] :
( ( ! [SY3963: $i,SY3964: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV971 @ SY3963 @ SV231 ) @ SY3964 @ SV231 )
= ( c_HOL_Oplus__class_Oplus @ SV971 @ ( c_HOL_Oplus__class_Oplus @ SY3963 @ SY3964 @ SV231 ) @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3463,plain,
! [SV972: $i,SV232: $i] :
( ( ! [SY3965: $i,SY3966: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ SV972 @ ( c_HOL_Oplus__class_Oplus @ SY3965 @ SY3966 @ SV232 ) @ SV232 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV972 @ SY3965 @ SV232 ) @ SY3966 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3464,plain,
! [SV973: $i,SV233: $i] :
( ( ! [SY3967: $i,SY3968: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SY3967 @ SV233 ) @ SY3968 @ SV233 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SY3968 @ SV233 ) @ SY3967 @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3465,plain,
! [SV974: $i,SV234: $i] :
( ( ! [SY3969: $i,SY3970: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ SV974 @ ( c_HOL_Oplus__class_Oplus @ SY3969 @ SY3970 @ SV234 ) @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SY3969 @ ( c_HOL_Oplus__class_Oplus @ SV974 @ SY3970 @ SV234 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3466,plain,
! [SV975: $i,SV235: $i] :
( ( ! [SY3971: $i,SY3972: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SY3971 @ SV235 ) @ SY3972 @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV975 @ ( c_HOL_Oplus__class_Oplus @ SY3971 @ SY3972 @ SV235 ) @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3467,plain,
! [SV976: $i,SV236: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV236 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV976 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV976 @ SV236 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3468,plain,
! [SV977: $i,SV238: $i] :
( ( ! [SY3973: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV238 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ SV977 @ SY3973 @ SV238 ) @ SV238 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV977 @ SV238 ) @ ( c_HOL_Oabs__class_Oabs @ SY3973 @ SV238 ) @ SV238 ) @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3469,plain,
! [SV978: $i,SV239: $i] :
( ( ! [SY3974: $i] :
( ( c_lessequals @ SV239 @ ( c_HOL_Oplus__class_Oplus @ SV978 @ SY3974 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV239 @ SV978 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3470,plain,
! [SV979: $i,SV240: $i] :
( ( ! [SY3975: $i] :
( ( c_lessequals @ SV240 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SY3975 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV240 @ SY3975 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3471,plain,
! [SV980: $i,SV241: $i] :
( ( ! [SY3976: $i] :
( ( c_lessequals @ SV241 @ SV980 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SY3976 @ tc_nat ) @ SV980 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3472,plain,
! [SV981: $i,SV242: $i] :
( ( ! [SY3977: $i] :
( ( c_lessequals @ SV242 @ SV981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3977 @ SV242 @ tc_nat ) @ SV981 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3473,plain,
! [SV982: $i,SV243: $i] :
( ( ! [SY3978: $i] :
( ( c_lessequals @ SV243 @ ( c_HOL_Oplus__class_Oplus @ SV982 @ SY3978 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV243 @ SV982 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3474,plain,
! [SV983: $i,SV244: $i] :
( ( ! [SY3979: $i] :
( ( c_lessequals @ SV244 @ ( c_HOL_Oplus__class_Oplus @ SV983 @ SY3979 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV244 @ SY3979 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3475,plain,
! [SV245: $i] :
( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SV245 @ tc_nat ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(3476,plain,
! [SV984: $i,SV246: $i] :
( ( ! [SY3980: $i,SY3981: $i] :
( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ SY3980 @ SV246 ) @ SY3981 @ SV246 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ ( c_Divides_Odiv__class_Omod @ SY3980 @ SY3981 @ SV246 ) @ SV246 ) @ SY3981 @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3477,plain,
! [SV985: $i,SV247: $i] :
( ( ! [SY3982: $i,SY3983: $i] :
( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV985 @ SY3982 @ SV247 ) @ SY3983 @ SV247 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV985 @ SY3983 @ SV247 ) @ SY3982 @ SV247 ) @ SY3983 @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3478,plain,
! [SV986: $i,SV248: $i] :
( ( ! [SY3984: $i,SY3985: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SY3984 @ SY3985 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SY3985 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SY3984 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3479,plain,
! [SV987: $i,SV249: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV249 @ ( c_HOL_Oplus__class_Oplus @ SV249 @ SV987 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3480,plain,
! [SV988: $i,SV250: $i] :
( ( ! [SY3986: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV250 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV988 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SY3986 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3481,plain,
! [SV989: $i,SV251: $i] :
( ( ! [SY3987: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV251 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV989 @ SV251 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY3987 @ SV251 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3482,plain,
! [SV990: $i,SV252: $i] :
( ( ! [SY3988: $i,SY3989: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
| ( c_lessequals @ SV990 @ SY3988 @ SV252 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SY3989 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SY3989 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SY3988 @ SY3989 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3483,plain,
! [SV991: $i,SV253: $i] :
( ( ! [SY3990: $i,SY3991: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
| ( c_lessequals @ SV991 @ SY3990 @ SV253 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SY3991 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3991 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SY3991 @ SY3990 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3484,plain,
! [SV992: $i,SV254: $i] :
( ( ! [SY3992: $i,SY3993: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SY3992 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SY3993 @ SV254 ) @ SV254 )
| ~ ( c_lessequals @ SY3992 @ SY3993 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3485,plain,
! [SV993: $i,SV255: $i] :
( ( ! [SY3994: $i,SY3995: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
| ( c_lessequals @ SV993 @ SY3994 @ SV255 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3995 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SY3995 @ SY3994 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SY3995 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3486,plain,
! [SV994: $i,SV256: $i] :
( ( ! [SY3996: $i,SY3997: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SY3996 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SY3997 @ SV256 ) @ SV256 )
| ~ ( c_lessequals @ SY3997 @ SY3996 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3487,plain,
! [SV995: $i,SV257: $i] :
( ( ! [SY3998: $i,SY3999: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
| ( c_lessequals @ SV995 @ SY3998 @ SV257 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY3999 @ SY3998 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SY3999 @ SV995 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY3999 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3488,plain,
! [SV996: $i,SV258: $i] :
( ( ! [SY4000: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV996 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SY4000 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV996 @ SY4000 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3489,plain,
! [SV997: $i,SV259: $i] :
( ( ! [SY4001: $i] :
( ( c_lessequals @ SV259 @ SV997 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4001 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4001 @ SV997 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4001 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3490,plain,
! [SV998: $i,SV260: $i] :
( ( ! [SY4002: $i] :
( ( c_lessequals @ SV260 @ SV998 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4002 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4002 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4002 @ SV998 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3491,plain,
! [SV999: $i,SV261: $i] :
( ( ! [SY4003: $i] :
( ( c_lessequals @ SV261 @ SV999 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4003 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SY4003 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV999 @ SY4003 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3492,plain,
! [SV262: $i] :
( ( ( SV262
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV262
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV262 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(3493,plain,
! [SV1000: $i,SV263: $i] :
( ( ! [SY4004: $i,SY4005: $i,SY4006: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV263 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SY4004 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SY4005 @ SY4006 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SY4005 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SY4004 @ SY4006 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SY4005 @ SV263 ) @ SY4006 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SY4005 @ ( c_HOL_Ominus__class_Ominus @ SY4004 @ SY4006 @ SV263 ) @ SV263 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3494,plain,
! [SV1001: $i,SV266: $i] :
( ( ! [SY4007: $i] :
( ~ ( class_Orderings_Olinorder @ SV266 )
| ( ( c_Orderings_Oord__class_Omin @ SV1001 @ SY4007 @ SV266 )
= ( c_Orderings_Oord__class_Omin @ SY4007 @ SV1001 @ SV266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3495,plain,
! [SV1002: $i,SV267: $i] :
( ( ! [SY4008: $i,SY4009: $i,SY4010: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV267 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SY4008 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4009 @ SY4008 @ SV267 ) @ SY4010 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV1002 @ SY4009 @ SV267 ) @ SY4008 @ SV267 ) @ SY4010 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3496,plain,
! [SV1003: $i,SV268: $i] :
( ( ! [SY4011: $i,SY4012: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1003 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4011 @ SV1003 @ tc_nat ) @ SY4012 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV268 @ SY4011 @ tc_nat ) @ SV1003 @ tc_nat ) @ SY4012 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3497,plain,
! [SV1004: $i,SV269: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV269 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV269 @ SV1004 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3498,plain,
! [SV1005: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV270 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV270 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3499,plain,
! [SV1006: $i,SV271: $i] :
( ( ! [SY4013: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SY4013 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SY4013 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3500,plain,
! [SV1007: $i,SV272: $i] :
( ( ! [SY4014: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV272 )
| ( SV1007
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4014 @ SY4014 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SV1007 @ SV1007 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3501,plain,
! [SV1008: $i,SV273: $i] :
( ( ! [SY4015: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV273 )
| ( SV1008
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1008 @ SV1008 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SY4015 @ SY4015 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3502,plain,
! [SV1009: $i,SV275: $i] :
( ( ! [SY4016: $i] :
( ( c_HOL_Oord__class_Oless @ SV275 @ SV1009 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY4016 ) @ SV275 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY4016 ) @ SV1009 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3503,plain,
! [SV1010: $i,SV276: $i] :
( ( ! [SY4017: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1010 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SY4017 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SY4017 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3504,plain,
! [SV1011: $i,SV277: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV277 ) @ SV1011 @ tc_nat )
| ( c_lessequals @ SV1011 @ SV277 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3505,plain,
! [SV1012: $i,SV278: $i] :
( ( ~ ( c_lessequals @ SV278 @ SV1012 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV1012 ) @ SV278 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3506,plain,
! [SV279: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV279 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV279 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(3507,plain,
! [SV1013: $i,SV280: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV280 @ SV1013 @ tc_nat ) @ SV280 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3508,plain,
! [SV1014: $i,SV281: $i] :
( ( ! [SY4018: $i] :
( ( c_lessequals @ SV281 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1014 @ SV281 @ tc_nat ) @ SY4018 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4018 @ SV1014 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3509,plain,
! [SV1015: $i,SV282: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV282 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1015 @ SV282 )
= SV1015 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV1015 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3510,plain,
! [SV1016: $i,SV283: $i] :
( ( ! [SY4019: $i,SY4020: $i] :
( ~ ( class_Divides_Osemiring__div @ SV283 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ SY4019 @ SV283 ) @ SY4020 @ SV283 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ ( c_Divides_Odiv__class_Omod @ SY4019 @ SY4020 @ SV283 ) @ SV283 ) @ SY4020 @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3511,plain,
! [SV1017: $i,SV284: $i] :
( ( ! [SY4021: $i,SY4022: $i] :
( ~ ( class_Divides_Osemiring__div @ SV284 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1017 @ SY4021 @ SV284 ) @ SY4022 @ SV284 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1017 @ SY4022 @ SV284 ) @ SY4021 @ SV284 ) @ SY4022 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3512,plain,
! [SV1018: $i,SV285: $i] :
( ( ! [SY4023: $i] :
( ( c_lessequals @ SV285 @ SV1018 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY4023 ) @ SV285 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SY4023 ) @ SV1018 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3513,plain,
! [SV1019: $i,SV286: $i] :
( ( ! [SY4024: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1019 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SY4024 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1019 @ SY4024 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3514,plain,
! [SV1020: $i,SV287: $i] :
( ( ! [SY4025: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV287 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV287 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1020 @ SV1020 @ SV287 ) @ ( c_HOL_Otimes__class_Otimes @ SY4025 @ SY4025 @ SV287 ) @ SV287 ) @ SV287 )
| ( SY4025
= ( c_HOL_Ozero__class_Ozero @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3515,plain,
! [SV1021: $i,SV288: $i] :
( ( ! [SY4026: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV288 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV288 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1021 @ SV1021 @ SV288 ) @ ( c_HOL_Otimes__class_Otimes @ SY4026 @ SY4026 @ SV288 ) @ SV288 ) @ SV288 )
| ( SV1021
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3516,plain,
! [SV1022: $i,SV289: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV289 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1022 @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV289 ) @ SV289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3517,plain,
! [SV291: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV291 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ SV291 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(3518,plain,
! [SV292: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ SV292 ) @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV292 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(3519,plain,
! [SV293: $i] :
( ( ( SV293
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV293 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3520,plain,
! [SV1023: $i,SV295: $i] :
( ( ( c_Orderings_Oord__class_Omin @ ( c_Suc @ SV295 ) @ ( c_Suc @ SV1023 ) @ tc_nat )
= ( c_Suc @ ( c_Orderings_Oord__class_Omin @ SV295 @ SV1023 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3521,plain,
! [SV1024: $i,SV296: $i] :
( ( ! [SY4027: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV296 @ SV1024 @ tc_nat ) @ SY4027 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV296 @ SY4027 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1024 @ SY4027 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3522,plain,
! [SV1025: $i,SV297: $i] :
( ( ! [SY4028: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV297 @ ( c_Divides_Odiv__class_Omod @ SV1025 @ SY4028 @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV297 @ SV1025 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV297 @ SY4028 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3523,plain,
! [SV1026: $i,SV298: $i] :
( ( ! [SY4029: $i,SY4030: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SY4029 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SY4030 @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SY4029 @ SY4030 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3524,plain,
! [SV1027: $i,SV299: $i] :
( ( ! [SY4031: $i,SY4032: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SY4031 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SY4032 @ SY4031 @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SY4032 @ SV1027 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SY4031 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3525,plain,
! [SV1028: $i,SV300: $i] :
( ( ! [SY4033: $i,SY4034: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SY4033 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SY4034 @ SY4033 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SY4034 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SY4033 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3526,plain,
! [SV1029: $i,SV301: $i] :
( ( ! [SY4035: $i,SY4036: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SY4035 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SY4036 @ SY4035 @ SV301 ) @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SY4035 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SY4036 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3527,plain,
! [SV1030: $i,SV302: $i] :
( ( ! [SY4037: $i,SY4038: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SY4037 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SY4038 @ SY4037 @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SY4037 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SY4038 @ SV1030 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3528,plain,
! [SV1031: $i,SV303: $i] :
( ( ! [SY4039: $i,SY4040: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SY4039 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SY4040 @ SV303 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SY4040 @ SY4039 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3529,plain,
! [SV1032: $i,SV304: $i] :
( ( ! [SY4041: $i,SY4042: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SY4041 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SY4042 @ SV304 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SY4041 @ SY4042 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3530,plain,
! [SV1033: $i,SV305: $i] :
( ( ! [SY4043: $i,SY4044: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SY4043 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SY4044 @ SV305 ) @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SY4043 @ SY4044 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3531,plain,
! [SV1034: $i,SV306: $i] :
( ( ! [SY4045: $i,SY4046: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SY4045 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SY4046 @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SY4046 @ SY4045 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3532,plain,
! [SV1035: $i,SV307: $i] :
( ( ! [SY4047: $i,SY4048: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SY4047 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SY4048 @ SV307 ) @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SY4047 @ SY4048 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3533,plain,
! [SV1036: $i,SV308: $i] :
( ( ! [SY4049: $i,SY4050: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
| ( c_HOL_Oord__class_Oless @ SV1036 @ SY4049 @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4050 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SY4050 @ SY4049 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SY4050 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3534,plain,
! [SV1037: $i,SV309: $i] :
( ( ! [SY4051: $i,SY4052: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SY4051 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SY4052 @ SV309 ) @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SY4052 @ SY4051 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3535,plain,
! [SV1038: $i,SV310: $i] :
( ( ! [SY4053: $i,SY4054: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1038 @ SY4053 @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4054 @ SY4053 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SY4054 @ SV1038 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SY4054 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3536,plain,
! [SV1039: $i,SV311: $i] :
( ( ! [SY4055: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1039 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SY4055 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SY4055 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3537,plain,
! [SV1040: $i,SV312: $i] :
( ( ! [SY4056: $i] :
( ( c_HOL_Oord__class_Oless @ SV312 @ SV1040 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4056 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4056 @ SV1040 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4056 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3538,plain,
! [SV1041: $i,SV313: $i] :
( ( ! [SY4057: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SV1041 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4057 @ SV1041 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1041 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SY4057 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3539,plain,
! [SV1042: $i,SV314: $i] :
( ( ! [SY4058: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1042 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SY4058 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SY4058 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3540,plain,
! [SV1043: $i,SV315: $i] :
( ( ! [SY4059: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1043 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SY4059 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1043 @ SY4059 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3541,plain,
! [SV1044: $i,SV316: $i] :
( ( ! [SY4060: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SV1044 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4060 @ SV1044 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV316 @ SY4060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1044 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3542,plain,
! [SV1045: $i,SV317: $i] :
( ( ! [SY4061: $i,SY4062: $i] :
( ~ ( class_Divides_Osemiring__div @ SV317 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1045 @ ( c_HOL_Otimes__class_Otimes @ SY4061 @ SY4062 @ SV317 ) @ SV317 ) @ SY4061 @ SV317 )
= ( c_Divides_Odiv__class_Omod @ SV1045 @ SY4061 @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3543,plain,
! [SV1046: $i,SV318: $i] :
( ( ! [SY4063: $i,SY4064: $i] :
( ~ ( class_Divides_Osemiring__div @ SV318 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1046 @ ( c_HOL_Otimes__class_Otimes @ SY4063 @ SY4064 @ SV318 ) @ SV318 ) @ SY4064 @ SV318 )
= ( c_Divides_Odiv__class_Omod @ SV1046 @ SY4064 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3544,plain,
! [SV1047: $i,SV319: $i] :
( ( ! [SY4065: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV319 @ SV1047 @ tc_nat ) @ SY4065 @ tc_nat ) @ SV1047 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SY4065 @ SV1047 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3545,plain,
! [SV1048: $i,SV320: $i] :
( ( ! [SY4066: $i,SY4067: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV320 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SY4066 @ SV320 )
| ( SY4067
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SY4067 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SY4066 @ SY4067 @ SV320 ) @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3546,plain,
! [SV1049: $i,SV321: $i] :
( ( ! [SY4068: $i,SY4069: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV321 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SY4068 @ SV321 )
| ( SY4069
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY4069 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SY4069 @ SY4068 @ SV321 ) @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3547,plain,
! [SV1050: $i,SV322: $i] :
( ( ! [SY4070: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV322 @ SV1050 @ tc_nat )
| ( SY4070
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY4070 @ SV322 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4070 @ SV1050 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3548,plain,
! [SV1051: $i,SV323: $i] :
( ( ! [SY4071: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SY4071 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ SY4071 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3549,plain,
! [SV1052: $i,SV324: $i] :
( ( ! [SY4072: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SY4072 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SY4072 @ SV324 )
| ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3550,plain,
! [SV1053: $i,SV325: $i] :
( ( ! [SY4073: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SY4073 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ SY4073 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3551,plain,
! [SV1054: $i,SV326: $i] :
( ( ! [SY4074: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SY4074 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SY4074 @ SV326 )
| ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3552,plain,
! [SV1055: $i,SV327: $i] :
( ( ! [SY4075: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SY4075 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ SY4075 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3553,plain,
! [SV1056: $i,SV328: $i] :
( ( ! [SY4076: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SY4076 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SY4076 @ SV328 )
| ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3554,plain,
! [SV1057: $i,SV329: $i] :
( ( ! [SY4077: $i] :
( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SY4077 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SY4077 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3555,plain,
! [SV330: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV330 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV330 ) @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(3556,plain,
! [SV1058: $i,SV331: $i] :
( ( ! [SY4078: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SY4078 @ SV331 ) @ SV331 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SY4078 @ SV331 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3557,plain,
! [SV1059: $i,SV332: $i] :
( ( ! [SY4079: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SY4079 @ SV332 ) @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SY4079 @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3558,plain,
! [SV1060: $i,SV333: $i] :
( ( ! [SY4080: $i] :
( ~ ( class_Divides_Osemiring__div @ SV333 )
| ( ( c_Divides_Odiv__class_Omod @ SV1060 @ SY4080 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4080 @ SV1060 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3559,plain,
! [SV1061: $i,SV334: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 )
| ( SV1061
= ( c_HOL_Ozero__class_Ozero @ SV334 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV334 ) @ SV1061 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3560,plain,
! [SV335: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV335 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV335 )
= ( c_HOL_Ozero__class_Ozero @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(3561,plain,
! [SV1062: $i,SV336: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV1062 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV336 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1062 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3562,plain,
! [SV1063: $i,SV337: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV337 ) @ SV1063 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV337 @ ( c_Suc @ SV1063 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3563,plain,
! [SV1064: $i,SV338: $i] :
( ( ! [SY4081: $i,SY4082: $i] :
( ~ ( class_Orderings_Olinorder @ SV338 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1064 @ SY4081 @ SV338 ) @ SY4082 @ SV338 )
= ( c_Orderings_Oord__class_Omin @ SV1064 @ ( c_Orderings_Oord__class_Omin @ SY4081 @ SY4082 @ SV338 ) @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3564,plain,
! [SV1065: $i,SV339: $i] :
( ( ! [SY4083: $i,SY4084: $i] :
( ~ ( class_Orderings_Olinorder @ SV339 )
| ( ( c_Orderings_Oord__class_Omin @ SV1065 @ ( c_Orderings_Oord__class_Omin @ SY4083 @ SY4084 @ SV339 ) @ SV339 )
= ( c_Orderings_Oord__class_Omin @ SY4083 @ ( c_Orderings_Oord__class_Omin @ SV1065 @ SY4084 @ SV339 ) @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3565,plain,
! [SV1066: $i,SV340: $i] :
( ( ! [SY4085: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SY4085 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4085 @ SV340 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY4085 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SY4085 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3566,plain,
! [SV1067: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV341 @ SV1067 @ tc_nat ) @ SV1067 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1067 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3567,plain,
! [SV1068: $i,SV342: $i] :
( ( ! [SY4086: $i] :
( ~ ( class_Orderings_Olinorder @ SV342 )
| ( ( c_Orderings_Oord__class_Omin @ SV1068 @ SY4086 @ SV342 )
= SV1068 )
| ~ ( c_lessequals @ SV1068 @ SY4086 @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3568,plain,
! [SV1069: $i,SV343: $i] :
( ( ! [SY4087: $i] :
( ~ ( class_Orderings_Olinorder @ SV343 )
| ( ( c_Orderings_Oord__class_Omin @ SV1069 @ SY4087 @ SV343 )
= SY4087 )
| ~ ( c_lessequals @ SY4087 @ SV1069 @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3569,plain,
! [SV1070: $i,SV344: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV344 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1070 @ SV344 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3570,plain,
! [SV1071: $i,SV345: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV345 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV1071 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3571,plain,
! [SV1072: $i,SV346: $i] :
( ( ! [SY4088: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SY4088 @ SV346 ) @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SY4088 @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3572,plain,
! [SV1073: $i,SV347: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV347 @ ( c_Suc @ SV1073 ) @ tc_nat )
| ~ ( c_lessequals @ SV347 @ SV1073 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3573,plain,
! [SV1074: $i,SV348: $i] :
( ( ( c_lessequals @ SV348 @ SV1074 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV348 @ ( c_Suc @ SV1074 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3574,plain,
! [SV349: $i] :
( ( ( ~ ( c_lessequals @ SV349 @ SV349 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Suc @ SV349 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(3575,plain,
! [SV1075: $i,SV350: $i] :
( ( ! [SY4089: $i,SY4090: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY4089 @ SY4090 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1075 @ SY4090 @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SY4089 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3576,plain,
! [SV1076: $i,SV351: $i] :
( ( ! [SY4091: $i,SY4092: $i,SY4093: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SY4091 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SY4092 @ SY4093 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SY4091 @ SY4093 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SY4092 @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3577,plain,
! [SV1077: $i,SV352: $i] :
( ( ! [SY4094: $i,SY4095: $i,SY4096: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SV1077 @ tc_nat ) @ SY4094 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4095 @ SV1077 @ tc_nat ) @ SY4096 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SY4095 @ tc_nat ) @ SV1077 @ tc_nat ) @ SY4094 @ tc_nat ) @ SY4096 @ tc_nat ) )
| ~ ( c_lessequals @ SY4095 @ SV352 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3578,plain,
! [SV1078: $i,SV353: $i] :
( ( ! [SY4097: $i,SY4098: $i,SY4099: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV1078 @ tc_nat ) @ SY4097 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4098 @ SV1078 @ tc_nat ) @ SY4099 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY4097 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4098 @ SV353 @ tc_nat ) @ SV1078 @ tc_nat ) @ SY4099 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV353 @ SY4098 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2833]) ).
thf(3579,plain,
! [SV1079: $i,SV354: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV354 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV1079 @ SV354 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ ( c_HOL_Oplus__class_Oplus @ SV1079 @ SV1079 @ SV354 ) @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3580,plain,
! [SV1080: $i,SV355: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV355 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ ( c_HOL_Oplus__class_Oplus @ SV1080 @ SV1080 @ SV355 ) @ SV355 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ SV1080 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3581,plain,
! [SV1081: $i,SV356: $i] :
( ( ! [SY4100: $i] :
( ~ ( class_Divides_Osemiring__div @ SV356 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1081 @ SY4100 @ SV356 ) @ SY4100 @ SV356 )
= ( c_Divides_Odiv__class_Omod @ SV1081 @ SY4100 @ SV356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3582,plain,
! [SV1082: $i,SV357: $i] :
( ( ! [SY4101: $i,SY4102: $i,SY4103: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1082 @ SY4101 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SY4102 @ SY4103 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1082 @ SY4102 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY4101 @ SY4103 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3583,plain,
! [SV1083: $i,SV358: $i] :
( ( ! [SY4104: $i,SY4105: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SY4104 @ SY4105 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SY4105 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SY4104 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3584,plain,
! [SV1084: $i,SV359: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SV1084 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV359 @ SV1084 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3585,plain,
! [SV1085: $i,SV360: $i] :
( ( ! [SY4106: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
| ~ ( c_lessequals @ SV1085 @ SY4106 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SY4106 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SY4106 @ SV1085 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3586,plain,
! [SV1086: $i,SV361: $i] :
( ( ! [SY4107: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
| ~ ( c_lessequals @ SY4107 @ SV1086 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SY4107 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SY4107 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3587,plain,
! [SV1087: $i,SV362: $i] :
( ( ! [SY4108: $i,SY4109: $i,SY4110: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV362 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SY4108 @ SV362 ) @ SY4109 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4110 @ SY4108 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SY4110 @ SV362 ) @ SY4108 @ SV362 ) @ SY4109 @ SV362 ) @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3588,plain,
! [SV1088: $i,SV363: $i] :
( ( ! [SY4111: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1088 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SY4111 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1088 @ SY4111 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3589,plain,
! [SV1089: $i,SV364: $i] :
( ( ! [SY4112: $i,SY4113: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV364 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SY4112 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SY4113 @ SV364 ) @ SV364 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4112 @ SY4113 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3590,plain,
! [SV1090: $i,SV365: $i] :
( ( ! [SY4114: $i,SY4115: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV365 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SY4114 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SY4115 @ SY4114 @ SV365 ) @ SV365 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SY4115 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3591,plain,
! [SV1091: $i,SV366: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV366 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV1091 @ SV366 ) @ SV366 )
= ( c_HOL_Oabs__class_Oabs @ SV1091 @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3592,plain,
! [SV1092: $i,SV367: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV367 ) @ SV1092 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV367 @ SV1092 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3593,plain,
! [SV1093: $i,SV368: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV368 @ ( c_Suc @ SV1093 ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV368 @ SV1093 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3594,plain,
! [SV1094: $i,SV369: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV369 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oabs__class_Oabs @ SV1094 @ SV369 ) @ SV369 )
| ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3595,plain,
! [SV1095: $i,SV370: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV370 @ SV1095 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV1095 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3596,plain,
! [SV1096: $i,SV371: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV371 @ SV1096 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV371 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3597,plain,
! [SV1097: $i,SV372: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV372 )
| ( ( c_Divides_Odiv__class_Omod @ SV1097 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 )
= SV1097 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3598,plain,
! [SV1098: $i,SV373: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV373 )
| ( ( c_Divides_Odiv__class_Omod @ SV1098 @ SV1098 @ SV373 )
= ( c_HOL_Ozero__class_Ozero @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3599,plain,
! [SV1099: $i,SV374: $i] :
( ( ! [SY4116: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1099 @ SY4116 @ SV374 )
= ( c_HOL_Oplus__class_Oplus @ SY4116 @ SV1099 @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3600,plain,
! [SV1100: $i,SV375: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV375 @ SV1100 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1100 @ SV375 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3601,plain,
! [SV1101: $i,SV376: $i] :
( ( ! [SY4117: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV376 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1101 @ SY4117 @ SV376 )
= ( c_HOL_Oplus__class_Oplus @ SY4117 @ SV1101 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3602,plain,
! [SV1102: $i,SV377: $i] :
( ( ! [SY4118: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1102 @ SY4118 @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ SY4118 @ SV1102 @ SV377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3603,plain,
! [SV1103: $i,SV378: $i] :
( ( ! [SY4119: $i,SY4120: $i] :
( ~ ( class_Divides_Osemiring__div @ SV378 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1103 @ SY4119 @ SV378 ) @ SY4120 @ SV378 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1103 @ SY4120 @ SV378 ) @ ( c_Divides_Odiv__class_Omod @ SY4119 @ SY4120 @ SV378 ) @ SV378 ) @ SY4120 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3604,plain,
! [SV1104: $i,SV379: $i] :
( ( ! [SY4121: $i,SY4122: $i] :
( ~ ( class_Orderings_Olinorder @ SV379 )
| ( c_lessequals @ SV1104 @ SY4121 @ SV379 )
| ~ ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SY4121 @ SY4122 @ SV379 ) @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3605,plain,
! [SV1105: $i,SV380: $i] :
( ( ! [SY4123: $i,SY4124: $i] :
( ~ ( class_Orderings_Olinorder @ SV380 )
| ( c_lessequals @ SV1105 @ SY4123 @ SV380 )
| ~ ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SY4124 @ SY4123 @ SV380 ) @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3606,plain,
! [SV1106: $i,SV381: $i] :
( ( ! [SY4125: $i,SY4126: $i] :
( ~ ( class_Orderings_Olinorder @ SV381 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SY4125 @ SV381 ) @ SY4126 @ SV381 )
| ~ ( c_lessequals @ SV1106 @ SY4126 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3607,plain,
! [SV1107: $i,SV382: $i] :
( ( ! [SY4127: $i,SY4128: $i] :
( ~ ( class_Orderings_Olinorder @ SV382 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SY4127 @ SV382 ) @ SY4128 @ SV382 )
| ~ ( c_lessequals @ SY4127 @ SY4128 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3608,plain,
! [SV1108: $i,SV383: $i] :
( ( ! [SY4129: $i,SY4130: $i] :
( ~ ( class_Orderings_Olinorder @ SV383 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SY4129 @ SV383 ) @ SY4130 @ SV383 )
| ~ ( c_lessequals @ SV1108 @ SY4130 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3609,plain,
! [SV1109: $i,SV384: $i] :
( ( ! [SY4131: $i,SY4132: $i] :
( ~ ( class_Orderings_Olinorder @ SV384 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SY4131 @ SV384 ) @ SY4132 @ SV384 )
| ~ ( c_lessequals @ SY4131 @ SY4132 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3610,plain,
! [SV1110: $i,SV385: $i] :
( ( ! [SY4133: $i,SY4134: $i] :
( ~ ( class_Orderings_Olinorder @ SV385 )
| ( c_lessequals @ SV1110 @ SY4133 @ SV385 )
| ~ ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SY4133 @ SY4134 @ SV385 ) @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3611,plain,
! [SV1111: $i,SV386: $i] :
( ( ! [SY4135: $i,SY4136: $i] :
( ~ ( class_Orderings_Olinorder @ SV386 )
| ( c_lessequals @ SV1111 @ SY4135 @ SV386 )
| ~ ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SY4136 @ SY4135 @ SV386 ) @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3612,plain,
! [SV1112: $i,SV387: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV387 )
| ( c_lessequals @ SV1112 @ ( c_HOL_Oabs__class_Oabs @ SV1112 @ SV387 ) @ SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3613,plain,
! [SV1113: $i,SV388: $i] :
( ( ! [SY4137: $i,SY4138: $i] :
( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_lessequals @ SV1113 @ SY4137 @ SV388 )
| ( c_lessequals @ SY4138 @ SY4137 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY4138 @ SV1113 @ SV388 ) @ SY4137 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3614,plain,
! [SV1114: $i,SV389: $i] :
( ( ! [SY4139: $i,SY4140: $i] :
( ~ ( c_lessequals @ SV389 @ SV1114 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV389 @ SY4139 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1114 @ SV389 @ tc_nat ) @ SY4139 @ tc_nat ) @ SY4140 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1114 @ SY4139 @ tc_nat ) @ SY4140 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3615,plain,
! [SV1115: $i,SV390: $i] :
( ( ! [SY4141: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV390 @ SV1115 @ tc_nat ) @ SY4141 @ tc_nat )
| ~ ( c_lessequals @ SV390 @ ( c_HOL_Oplus__class_Oplus @ SY4141 @ SV1115 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3616,plain,
! [SV1116: $i,SV391: $i] :
( ( ! [SY4142: $i] :
( ( c_lessequals @ SV391 @ ( c_HOL_Oplus__class_Oplus @ SV1116 @ SY4142 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV391 @ SY4142 @ tc_nat ) @ SV1116 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3617,plain,
! [SV1117: $i,SV392: $i] :
( ( ! [SY4143: $i,SY4144: $i,SY4145: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SY4143 @ tc_nat ) @ SY4144 @ tc_nat ) @ SY4145 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SY4143 @ tc_nat ) @ SY4144 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SY4143 @ tc_nat ) @ SY4145 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3618,plain,
! [SV1118: $i,SV393: $i] :
( ( ! [SY4146: $i,SY4147: $i,SY4148: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SY4146 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4147 @ SV1118 @ tc_nat ) @ SY4148 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SY4147 @ tc_nat ) @ SV1118 @ tc_nat ) @ SY4146 @ tc_nat ) @ SY4148 @ tc_nat )
| ~ ( c_lessequals @ SY4147 @ SV393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3619,plain,
! [SV1119: $i,SV394: $i] :
( ( ! [SY4149: $i,SY4150: $i,SY4151: $i] :
( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SY4149 @ tc_nat ) @ SY4150 @ tc_nat ) @ SY4151 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4149 @ SY4150 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SY4150 @ tc_nat ) @ SY4151 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4149 @ SV1119 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3620,plain,
! [SV1120: $i,SV395: $i] :
( ( ! [SY4152: $i,SY4153: $i,SY4154: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SY4152 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4153 @ SV1120 @ tc_nat ) @ SY4154 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4152 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4153 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SY4154 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV395 @ SY4153 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3621,plain,
! [SV1121: $i,SV396: $i] :
( ( ! [SY4155: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV396 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SY4155 @ tc_nat ) @ SV396 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1121 @ SV396 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4155 @ SV396 ) @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3622,plain,
! [SV1122: $i,SV397: $i] :
( ( ! [SY4156: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV1122 @ tc_nat ) @ SY4156 @ tc_nat ) ) @ SV1122 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SY4156 ) @ SV1122 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3623,plain,
! [SV1123: $i,SV398: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV398 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1123 @ SV398 ) @ ( c_HOL_Oabs__class_Oabs @ SV1123 @ SV398 ) @ SV398 )
= ( c_HOL_Otimes__class_Otimes @ SV1123 @ SV1123 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3624,plain,
! [SV1124: $i,SV399: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV399 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV399 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1124 @ SV399 ) @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3625,plain,
! [SV1125: $i,SV400: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV400 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV400 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1125 @ SV400 ) @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3626,plain,
! [SV1126: $i,SV401: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV401 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1126 @ ( c_HOL_Ozero__class_Ozero @ SV401 ) @ SV401 )
= SV1126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3627,plain,
! [SV1127: $i,SV402: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV402 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV402 ) @ SV1127 @ SV402 )
= SV1127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3628,plain,
! [SV1128: $i,SV403: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV403 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1128 @ ( c_HOL_Ozero__class_Ozero @ SV403 ) @ SV403 )
= SV1128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3629,plain,
! [SV1129: $i,SV404: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV404 )
| ~ ( class_Int_Onumber__ring @ SV404 )
| ( SV1129
= ( c_HOL_Oplus__class_Oplus @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3630,plain,
! [SV1130: $i,SV405: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV405 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1130 @ SV405 )
= SV1130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3631,plain,
! [SV1131: $i,SV406: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV406 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1131 @ SV406 )
= SV1131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3632,plain,
! [SV1132: $i,SV410: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV410 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1132 @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV410 )
= SV1132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3633,plain,
! [SV1133: $i,SV411: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV411 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV411 ) @ SV1133 @ SV411 )
= SV1133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3634,plain,
! [SV1134: $i,SV412: $i] :
( ( ! [SY4157: $i,SY4158: $i,SY4159: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SY4157 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SY4158 @ SY4159 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SY4157 @ SY4159 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SY4158 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3635,plain,
! [SV1135: $i,SV413: $i] :
( ( ! [SY4160: $i,SY4161: $i,SY4162: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SY4160 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SY4161 @ SY4162 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SY4160 @ SY4162 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SY4161 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3636,plain,
! [SV1136: $i,SV414: $i] :
( ( ! [SY4163: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SY4163 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4163 @ SV414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SY4163 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3637,plain,
! [SV1137: $i,SV415: $i] :
( ( ! [SY4164: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4164 @ SV415 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY4164 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SY4164 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3638,plain,
! [SV1138: $i,SV416: $i] :
( ( ! [SY4165: $i,SY4166: $i] :
( ~ ( class_Orderings_Oorder @ SV416 )
| ( c_HOL_Oord__class_Oless @ SV1138 @ SY4165 @ SV416 )
| ~ ( c_lessequals @ SV1138 @ SY4166 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SY4166 @ SY4165 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3639,plain,
! [SV1139: $i,SV417: $i] :
( ( ! [SY4167: $i,SY4168: $i] :
( ~ ( class_Orderings_Oorder @ SV417 )
| ( c_HOL_Oord__class_Oless @ SV1139 @ SY4167 @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SY4168 @ SV417 )
| ~ ( c_lessequals @ SY4168 @ SY4167 @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3640,plain,
! [SV1140: $i,SV418: $i] :
( ( ! [SY4169: $i,SY4170: $i] :
( ~ ( class_Orderings_Opreorder @ SV418 )
| ( c_HOL_Oord__class_Oless @ SV1140 @ SY4169 @ SV418 )
| ~ ( c_lessequals @ SY4170 @ SY4169 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SY4170 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3641,plain,
! [SV1141: $i,SV419: $i] :
( ( ! [SY4171: $i,SY4172: $i] :
( ~ ( class_Orderings_Opreorder @ SV419 )
| ( c_HOL_Oord__class_Oless @ SV1141 @ SY4171 @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SY4172 @ SY4171 @ SV419 )
| ~ ( c_lessequals @ SV1141 @ SY4172 @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3642,plain,
! [SV1142: $i,SV420: $i] :
( ( ! [SY4173: $i,SY4174: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SY4173 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SY4174 @ SY4173 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SV1142 @ SY4174 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3643,plain,
! [SV1143: $i,SV421: $i] :
( ( ! [SY4175: $i,SY4176: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SY4175 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SY4176 @ SY4175 @ SV421 ) @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SV1143 @ SY4176 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3644,plain,
! [SV1144: $i,SV422: $i] :
( ( ! [SY4177: $i,SY4178: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_HOL_Oord__class_Oless @ SV1144 @ SY4177 @ SV422 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SY4178 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SY4177 @ SY4178 @ SV422 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3645,plain,
! [SV1145: $i,SV423: $i] :
( ( ! [SY4179: $i,SY4180: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SY4179 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SY4180 @ SV423 ) @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SY4179 @ SY4180 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3646,plain,
! [SV1146: $i,SV424: $i] :
( ( ! [SY4181: $i,SY4182: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SY4181 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SY4182 @ SV424 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ SY4181 @ SY4182 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3647,plain,
! [SV1147: $i,SV425: $i] :
( ( ! [SY4183: $i,SY4184: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
| ( c_HOL_Oord__class_Oless @ SV1147 @ SY4183 @ SV425 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY4184 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SY4184 @ SY4183 @ SV425 ) @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3648,plain,
! [SV1148: $i,SV426: $i] :
( ( ! [SY4185: $i] :
( ~ ( class_Orderings_Opreorder @ SV426 )
| ( c_lessequals @ SV1148 @ SY4185 @ SV426 )
| ~ ( c_HOL_Oord__class_Oless @ SV1148 @ SY4185 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3649,plain,
! [SV1149: $i,SV427: $i] :
( ( ! [SY4186: $i] :
( ~ ( class_Orderings_Oorder @ SV427 )
| ( c_lessequals @ SV1149 @ SY4186 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1149 @ SY4186 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3650,plain,
! [SV1150: $i,SV428: $i] :
( ( ! [SY4187: $i,SY4188: $i,SY4189: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SY4187 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SY4188 @ SY4189 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SY4187 @ SY4189 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SY4188 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3651,plain,
! [SV1151: $i,SV429: $i] :
( ( ! [SY4190: $i] :
( ~ ( class_Orderings_Opreorder @ SV429 )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SY4190 @ SV429 )
| ( c_lessequals @ SY4190 @ SV1151 @ SV429 )
| ~ ( c_lessequals @ SV1151 @ SY4190 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3652,plain,
! [SV1152: $i,SV430: $i] :
( ( ! [SY4191: $i,SY4192: $i] :
( ~ ( class_Orderings_Olinorder @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1152 @ SY4191 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SY4192 @ SY4191 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY4192 @ SV1152 @ SV430 ) @ SY4191 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3653,plain,
! [SV1153: $i,SV431: $i] :
( ( ! [SY4193: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV431 )
| ( c_HOL_Oord__class_Oless @ SV1153 @ SY4193 @ SV431 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1153 @ SV431 ) @ SY4193 @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3654,plain,
! [SV1154: $i,SV432: $i] :
( ( ! [SY4194: $i,SY4195: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1154 @ SY4194 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SY4194 @ SV1154 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4194 @ SY4195 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SY4195 @ SV432 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3655,plain,
! [SV1155: $i,SV433: $i] :
( ( ! [SY4196: $i,SY4197: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1155 @ SY4196 @ SV433 )
| ( c_HOL_Oord__class_Oless @ SY4196 @ SV1155 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4197 @ SY4196 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SY4197 @ SV1155 @ SV433 ) @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3656,plain,
! [SV1156: $i,SV434: $i] :
( ( ! [SY4198: $i] :
( ~ ( class_Orderings_Oorder @ SV434 )
| ( c_HOL_Oord__class_Oless @ SV1156 @ SY4198 @ SV434 )
| ( SY4198 = SV1156 )
| ~ ( c_lessequals @ SV1156 @ SY4198 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3657,plain,
! [SV1157: $i,SV435: $i] :
( ( ! [SY4199: $i] :
( ~ ( class_Orderings_Oorder @ SV435 )
| ( c_HOL_Oord__class_Oless @ SV1157 @ SY4199 @ SV435 )
| ~ ( c_lessequals @ SV1157 @ SY4199 @ SV435 )
| ( SY4199 = SV1157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3658,plain,
! [SV1158: $i,SV436: $i] :
( ( ! [SY4200: $i] :
( ~ ( class_Orderings_Olinorder @ SV436 )
| ( SV1158 = SY4200 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SY4200 @ SV436 )
| ~ ( c_lessequals @ SV1158 @ SY4200 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3659,plain,
! [SV1159: $i,SV437: $i] :
( ( ! [SY4201: $i] :
( ~ ( class_Orderings_Olinorder @ SV437 )
| ( SV1159 = SY4201 )
| ~ ( c_lessequals @ SV1159 @ SY4201 @ SV437 )
| ( c_HOL_Oord__class_Oless @ SV1159 @ SY4201 @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3660,plain,
! [SV1160: $i,SV438: $i] :
( ( ! [SY4202: $i] :
( ~ ( class_Orderings_Oorder @ SV438 )
| ( c_HOL_Oord__class_Oless @ SV1160 @ SY4202 @ SV438 )
| ~ ( c_lessequals @ SV1160 @ SY4202 @ SV438 )
| ( SV1160 = SY4202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3661,plain,
! [SV1161: $i,SV439: $i] :
( ( ! [SY4203: $i] :
( ~ ( class_Orderings_Oorder @ SV439 )
| ( c_HOL_Oord__class_Oless @ SV1161 @ SY4203 @ SV439 )
| ( SV1161 = SY4203 )
| ~ ( c_lessequals @ SV1161 @ SY4203 @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3662,plain,
! [SV1162: $i,SV440: $i] :
( ( ! [SY4204: $i] :
( ~ ( class_Orderings_Oorder @ SV440 )
| ( SV1162 = SY4204 )
| ( c_HOL_Oord__class_Oless @ SV1162 @ SY4204 @ SV440 )
| ~ ( c_lessequals @ SV1162 @ SY4204 @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3663,plain,
! [SV1163: $i,SV441: $i] :
( ( ! [SY4205: $i] :
( ~ ( class_Orderings_Oorder @ SV441 )
| ( c_HOL_Oord__class_Oless @ SV1163 @ SY4205 @ SV441 )
| ( SV1163 = SY4205 )
| ~ ( c_lessequals @ SV1163 @ SY4205 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3664,plain,
! [SV1164: $i,SV442: $i] :
( ( ! [SY4206: $i,SY4207: $i] :
( ~ ( class_Orderings_Olinorder @ SV442 )
| ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SY4206 @ SY4207 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SY4207 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SY4206 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3665,plain,
! [SV1165: $i,SV443: $i] :
( ( ! [SY4208: $i] :
( ~ ( class_Orderings_Opreorder @ SV443 )
| ~ ( c_lessequals @ SV1165 @ SY4208 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ SY4208 @ SV1165 @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3666,plain,
! [SV1166: $i,SV444: $i] :
( ( ! [SY4209: $i] :
( ~ ( class_Orderings_Olinorder @ SV444 )
| ( c_HOL_Oord__class_Oless @ SV1166 @ SY4209 @ SV444 )
| ( c_lessequals @ SY4209 @ SV1166 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3667,plain,
! [SV1167: $i,SV445: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV445 )
| ~ ( c_lessequals @ SV1167 @ SV1167 @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1167 @ SV1167 @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3668,plain,
! [SV1168: $i,SV446: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV446 )
| ( c_HOL_Oord__class_Oless @ SV1168 @ SV1168 @ SV446 )
| ( c_lessequals @ SV1168 @ SV1168 @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3669,plain,
! [SV1169: $i,SV447: $i] :
( ( ! [SY4210: $i] :
( ~ ( class_Orderings_Olinorder @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1169 @ SY4210 @ SV447 )
| ~ ( c_lessequals @ SY4210 @ SV1169 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3670,plain,
! [SV1170: $i,SV448: $i] :
( ( ! [SY4211: $i] :
( ~ ( class_Orderings_Olinorder @ SV448 )
| ( c_lessequals @ SV1170 @ SY4211 @ SV448 )
| ( c_HOL_Oord__class_Oless @ SY4211 @ SV1170 @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3671,plain,
! [SV1171: $i,SV449: $i] :
( ( ! [SY4212: $i] :
( ~ ( class_Orderings_Olinorder @ SV449 )
| ( c_HOL_Oord__class_Oless @ SV1171 @ SY4212 @ SV449 )
| ( c_lessequals @ SY4212 @ SV1171 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3672,plain,
! [SV1172: $i,SV450: $i] :
( ( ! [SY4213: $i] :
( ~ ( class_Orderings_Olinorder @ SV450 )
| ~ ( c_lessequals @ SV1172 @ SY4213 @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ SY4213 @ SV1172 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3673,plain,
! [SV1173: $i,SV451: $i] :
( ( ! [SY4214: $i,SY4215: $i] :
( ~ ( class_Orderings_Olinorder @ SV451 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SY4214 @ SV451 ) @ SY4215 @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ SY4214 @ SY4215 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3674,plain,
! [SV1174: $i,SV452: $i] :
( ( ! [SY4216: $i,SY4217: $i] :
( ~ ( class_Orderings_Olinorder @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SY4216 @ SV452 ) @ SY4217 @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SY4217 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3675,plain,
! [SV1175: $i,SV453: $i] :
( ( ! [SY4218: $i,SY4219: $i] :
( ~ ( class_Orderings_Olinorder @ SV453 )
| ( c_HOL_Oord__class_Oless @ SV1175 @ SY4218 @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SY4219 @ SY4218 @ SV453 ) @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3676,plain,
! [SV1176: $i,SV454: $i] :
( ( ! [SY4220: $i,SY4221: $i] :
( ~ ( class_Orderings_Olinorder @ SV454 )
| ( c_HOL_Oord__class_Oless @ SV1176 @ SY4220 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SY4220 @ SY4221 @ SV454 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3677,plain,
! [SV1177: $i,SV455: $i] :
( ( ! [SY4222: $i,SY4223: $i] :
( ~ ( class_Orderings_Olinorder @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SY4222 @ SV455 ) @ SY4223 @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SY4222 @ SY4223 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3678,plain,
! [SV1178: $i,SV456: $i] :
( ( ! [SY4224: $i,SY4225: $i] :
( ~ ( class_Orderings_Olinorder @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SY4224 @ SV456 ) @ SY4225 @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SY4225 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3679,plain,
! [SV1179: $i,SV457: $i] :
( ( ! [SY4226: $i,SY4227: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV457 )
| ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SY4226 @ SY4227 @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SY4226 @ SV457 ) @ SV457 ) @ SY4227 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3680,plain,
! [SV1180: $i,SV458: $i] :
( ( ! [SY4228: $i,SY4229: $i,SY4230: $i,SY4231: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SY4228 @ SV458 ) @ SY4229 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4230 @ SY4228 @ SV458 ) @ SY4231 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SY4229 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4230 @ SV1180 @ SV458 ) @ SY4228 @ SV458 ) @ SY4231 @ SV458 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3681,plain,
! [SV1181: $i,SV459: $i] :
( ( ! [SY4232: $i,SY4233: $i,SY4234: $i,SY4235: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4232 @ SY4233 @ SV459 ) @ SY4234 @ SV459 ) @ SY4235 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4233 @ SY4234 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4232 @ SY4234 @ SV459 ) @ SY4235 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3682,plain,
! [SV1182: $i,SV460: $i] :
( ( ! [SY4236: $i,SY4237: $i,SY4238: $i,SY4239: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SY4236 @ SV460 ) @ SY4237 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4238 @ SY4236 @ SV460 ) @ SY4239 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SY4238 @ SV460 ) @ SY4236 @ SV460 ) @ SY4237 @ SV460 ) @ SY4239 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3683,plain,
! [SV1183: $i,SV461: $i] :
( ( ! [SY4240: $i,SY4241: $i,SY4242: $i,SY4243: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SY4240 @ SV461 ) @ SY4241 @ SV461 ) @ SY4242 @ SV461 ) @ SY4243 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SY4241 @ SV461 ) @ SY4242 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4240 @ SY4241 @ SV461 ) @ SY4243 @ SV461 ) @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3684,plain,
! [SV1184: $i,SV462: $i] :
( ( ! [SY4244: $i,SY4245: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV462 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SY4244 @ SV462 ) @ SV462 ) @ SY4245 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SY4244 @ SY4245 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY4244 @ SY4245 @ SV462 ) @ SV1184 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3685,plain,
! [SV1185: $i,SV463: $i] :
( ( ! [SY4246: $i,SY4247: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV463 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV1185 @ SY4246 @ SV463 ) @ SY4247 @ SV463 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV1185 @ SY4247 @ SV463 ) @ ( c_HOL_Ominus__class_Ominus @ SY4246 @ SY4247 @ SV463 ) @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3686,plain,
! [SV1186: $i,SV464: $i] :
( ( ! [SY4248: $i,SY4249: $i] :
( ~ ( class_Divides_Oring__div @ SV464 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ SY4248 @ SV464 ) @ SY4249 @ SV464 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ ( c_Divides_Odiv__class_Omod @ SY4248 @ SY4249 @ SV464 ) @ SV464 ) @ SY4249 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3687,plain,
! [SV1187: $i,SV465: $i] :
( ( ! [SY4250: $i,SY4251: $i] :
( ~ ( class_Divides_Oring__div @ SV465 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1187 @ SY4250 @ SV465 ) @ SY4251 @ SV465 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1187 @ SY4251 @ SV465 ) @ SY4250 @ SV465 ) @ SY4251 @ SV465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3688,plain,
! [SV1188: $i,SV466: $i] :
( ( ! [SY4252: $i,SY4253: $i] :
( ~ ( class_Divides_Oring__div @ SV466 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1188 @ SY4252 @ SV466 ) @ SY4253 @ SV466 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1188 @ SY4253 @ SV466 ) @ ( c_Divides_Odiv__class_Omod @ SY4252 @ SY4253 @ SV466 ) @ SV466 ) @ SY4253 @ SV466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3689,plain,
! [SV1189: $i,SV467: $i] :
( ( ! [SY4254: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV467 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1189 @ SY4254 @ SV467 ) @ SV467 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY4254 @ SV1189 @ SV467 ) @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3690,plain,
! [SV1190: $i,SV468: $i] :
( ( ! [SY4255: $i,SY4256: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SY4255 @ SY4256 @ SV468 ) @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SY4256 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SY4255 @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3691,plain,
! [SV1191: $i,SV469: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV469 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3692,plain,
! [SV1192: $i,SV470: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV470 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1192 @ SV1192 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3693,plain,
! [SV1193: $i,SV471: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV471 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1193 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= SV1193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3694,plain,
! [SV1194: $i,SV472: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV472 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1194 @ SV1194 @ SV472 )
= ( c_HOL_Ozero__class_Ozero @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3695,plain,
! [SV1195: $i,SV473: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV473 )
| ~ ( class_Int_Onumber__ring @ SV473 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1195 @ SV1195 @ SV473 )
= ( c_HOL_Ozero__class_Ozero @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3696,plain,
! [SV1196: $i,SV474: $i] :
( ( ! [SY4257: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV474 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1196 @ SY4257 @ SV474 ) @ SY4257 @ SV474 )
= SV1196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3697,plain,
! [SV1197: $i,SV475: $i] :
( ( ! [SY4258: $i,SY4259: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV475 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1197 @ ( c_HOL_Ominus__class_Ominus @ SY4258 @ SY4259 @ SV475 ) @ SV475 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SY4258 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SY4259 @ SV475 ) @ SV475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3698,plain,
! [SV1198: $i,SV476: $i] :
( ( ! [SY4260: $i,SY4261: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV476 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1198 @ ( c_HOL_Ominus__class_Ominus @ SY4260 @ SY4261 @ SV476 ) @ SV476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SY4260 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SY4261 @ SV476 ) @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3699,plain,
! [SV1199: $i,SV477: $i] :
( ( ! [SY4262: $i,SY4263: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV477 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1199 @ SY4262 @ SV477 ) @ SY4263 @ SV477 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1199 @ SY4263 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SY4262 @ SY4263 @ SV477 ) @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3700,plain,
! [SV1200: $i,SV478: $i] :
( ( ! [SY4264: $i,SY4265: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV478 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1200 @ SY4264 @ SV478 ) @ SY4265 @ SV478 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1200 @ SY4265 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SY4264 @ SY4265 @ SV478 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3701,plain,
! [SV1201: $i,SV479: $i] :
( ( ! [SY4266: $i,SY4267: $i,SY4268: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV479 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1201 @ SY4266 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SY4267 @ SY4268 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ SY4267 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SY4266 @ SY4268 @ SV479 ) @ SV479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3702,plain,
! [SV1202: $i,SV480: $i] :
( ( ! [SY4269: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV480 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1202 @ SY4269 @ SV480 ) @ SY4269 @ SV480 )
= SV1202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3703,plain,
! [SV1203: $i,SV481: $i] :
( ( ! [SY4270: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1203 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SY4270 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1203 @ SY4270 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3704,plain,
! [SV1204: $i,SV482: $i] :
( ( ! [SY4271: $i] :
( ( c_HOL_Oord__class_Oless @ SV482 @ SV1204 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY4271 @ SV482 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY4271 @ SV1204 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3705,plain,
! [SV1205: $i,SV483: $i] :
( ( ! [SY4272: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV483 @ SV1205 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY4272 @ SV1205 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SY4272 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3706,plain,
! [SV1206: $i,SV484: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV484 @ SV1206 @ tc_nat ) @ SV484 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3707,plain,
! [SV1207: $i,SV485: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV485 @ SV1207 @ tc_nat ) @ SV1207 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3708,plain,
! [SV486: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV486 @ tc_nat )
= $true )
| ( ( SV486
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3709,plain,
! [SV1208: $i,SV487: $i] :
( ( ( c_lessequals @ SV487 @ SV1208 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV487 @ SV1208 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3710,plain,
! [SV1209: $i,SV488: $i] :
( ( ( c_lessequals @ SV488 @ SV1209 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV488 @ SV1209 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3711,plain,
! [SV1210: $i,SV489: $i] :
( ( ! [SY4273: $i,SY4274: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY4273 @ SY4274 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1210 @ SY4274 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SY4273 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3712,plain,
! [SV1211: $i,SV490: $i] :
( ( ( SV490 = SV1211 )
| ( c_HOL_Oord__class_Oless @ SV490 @ SV1211 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV490 @ ( c_Suc @ SV1211 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3713,plain,
! [SV1212: $i,SV491: $i] :
( ( ( SV491 = SV1212 )
| ~ ( c_HOL_Oord__class_Oless @ SV1212 @ ( c_Suc @ SV491 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1212 @ SV491 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3714,plain,
! [SV1213: $i,SV493: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV493 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1213 @ ( c_HOL_Ozero__class_Ozero @ SV493 ) @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3715,plain,
! [SV1214: $i,SV494: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV494 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV494 ) @ SV1214 @ SV494 )
= ( c_HOL_Ozero__class_Ozero @ SV494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3716,plain,
! [SV1215: $i,SV495: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV495 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1215 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= ( c_HOL_Ozero__class_Ozero @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3717,plain,
! [SV1216: $i,SV496: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV496 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV496 ) @ SV1216 @ SV496 )
= ( c_HOL_Ozero__class_Ozero @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3718,plain,
! [SV1217: $i,SV497: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV497 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV497 ) @ SV1217 @ SV497 )
= ( c_HOL_Ozero__class_Ozero @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3719,plain,
! [SV1218: $i,SV500: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV500 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ SV500 ) @ SV500 )
= ( c_HOL_Ozero__class_Ozero @ SV500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3720,plain,
! [SV1219: $i,SV501: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV501 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1219 @ ( c_HOL_Ozero__class_Ozero @ SV501 ) @ SV501 )
= ( c_HOL_Ozero__class_Ozero @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3721,plain,
! [SV1220: $i,SV502: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV502 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV502 ) @ SV1220 @ SV502 )
= ( c_HOL_Ozero__class_Ozero @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3722,plain,
! [SV1221: $i,SV503: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV503 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV503 ) @ SV1221 @ SV503 )
= ( c_HOL_Ozero__class_Ozero @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3723,plain,
! [SV1222: $i,SV504: $i] :
( ( ~ ( class_Ring__and__Field_Omult__zero @ SV504 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1222 @ ( c_HOL_Ozero__class_Ozero @ SV504 ) @ SV504 )
= ( c_HOL_Ozero__class_Ozero @ SV504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3724,plain,
! [SV1223: $i,SV505: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV505 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV1223 @ SV505 )
= ( c_HOL_Ozero__class_Ozero @ SV505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3725,plain,
! [SV1224: $i,SV506: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV506 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1224 @ ( c_HOL_Ozero__class_Ozero @ SV506 ) @ SV506 )
= ( c_HOL_Ozero__class_Ozero @ SV506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3726,plain,
! [SV1225: $i,SV507: $i] :
( ( ! [SY4275: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV507 @ ( c_HOL_Ominus__class_Ominus @ SV1225 @ SY4275 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV507 @ SY4275 @ tc_nat ) @ SV1225 @ tc_nat ) )
| ~ ( c_lessequals @ SY4275 @ SV1225 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3727,plain,
! [SV1226: $i,SV509: $i] :
( ( ! [SY4276: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV509 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1226 @ SV509 ) @ SY4276 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV1226 @ SY4276 @ SV509 ) @ SV509 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SY4276 @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3728,plain,
! [SV1227: $i,SV510: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ ( c_HOL_Oplus__class_Oplus @ SV1227 @ SV510 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ SV1227 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3729,plain,
! [SV1228: $i,SV511: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ SV1228 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ ( c_HOL_Oplus__class_Oplus @ SV1228 @ SV511 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3730,plain,
! [SV1229: $i,SV512: $i] :
( ( ! [SY4277: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV512 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1229 @ SY4277 @ SV512 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1229 @ SV512 ) @ SY4277 @ SV512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3731,plain,
! [SV1230: $i,SV513: $i] :
( ( ! [SY4278: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV513 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1230 @ SV513 ) @ SY4278 @ SV513 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1230 @ SY4278 @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3732,plain,
! [SV1231: $i,SV514: $i] :
( ( ! [SY4279: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV514 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ SY4279 @ SV514 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ ( c_HOL_Oabs__class_Oabs @ SY4279 @ SV514 ) @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3733,plain,
! [SV1232: $i,SV515: $i] :
( ( ! [SY4280: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV515 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ ( c_HOL_Oabs__class_Oabs @ SY4280 @ SV515 ) @ SV515 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ SY4280 @ SV515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3734,plain,
! [SV1233: $i,SV516: $i] :
( ( ~ ( c_lessequals @ SV516 @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV516 @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV516 @ tc_nat ) @ SV516 @ tc_nat )
= SV1233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3735,plain,
! [SV1234: $i,SV517: $i] :
( ( ! [SY4281: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SY4281 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SY4281 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3736,plain,
! [SV1235: $i,SV518: $i] :
( ( c_lessequals @ SV518 @ ( c_HOL_Oplus__class_Oplus @ SV518 @ SV1235 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3737,plain,
! [SV1236: $i,SV519: $i] :
( ( c_lessequals @ SV519 @ ( c_HOL_Oplus__class_Oplus @ SV519 @ SV1236 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3738,plain,
! [SV1237: $i,SV520: $i] :
( ( c_lessequals @ SV520 @ ( c_HOL_Oplus__class_Oplus @ SV1237 @ SV520 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3739,plain,
! [SV1238: $i,SV521: $i] :
( ( c_lessequals @ SV521 @ ( c_HOL_Oplus__class_Oplus @ SV521 @ SV1238 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3740,plain,
! [SV1239: $i,SV522: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SV1239 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV522 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1239 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3741,plain,
! [SV1240: $i,SV523: $i] :
( ( ! [SY4282: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV523 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1240 @ SY4282 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1240 @ SY4282 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3742,plain,
! [SV1241: $i,SV524: $i] :
( ( ! [SY4283: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV524 )
| ( c_lessequals @ SV1241 @ SY4283 @ SV524 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1241 @ SY4283 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3743,plain,
! [SV1242: $i,SV525: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1242 @ SV525 ) @ ( c_HOL_Ozero__class_Ozero @ SV525 ) @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3744,plain,
! [SV1243: $i,SV526: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV526 @ SV1243 @ tc_nat ) @ SV1243 @ tc_nat )
= SV526 )
| ~ ( c_lessequals @ SV1243 @ SV526 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3745,plain,
! [SV1244: $i,SV527: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV527 @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV527 @ tc_nat ) @ tc_nat )
= SV1244 )
| ~ ( c_lessequals @ SV527 @ SV1244 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3746,plain,
! [SV1245: $i,SV528: $i] :
( ( ~ ( c_lessequals @ SV528 @ SV1245 @ tc_nat )
| ( SV1245
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ SV528 @ tc_nat ) @ SV528 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3747,plain,
! [SV1246: $i,SV529: $i] :
( ( ! [SY4284: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SV1246 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4284 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY4284 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4284 @ SV1246 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3748,plain,
! [SV1247: $i,SV530: $i] :
( ( ! [SY4285: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SV1247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY4285 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4285 @ SV1247 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4285 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3749,plain,
! [SV1248: $i,SV531: $i] :
( ( ! [SY4286: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1248 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SY4286 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1248 @ SY4286 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3750,plain,
! [SV1249: $i,SV532: $i] :
( ( ! [SY4287: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV532 @ SV1249 @ tc_nat ) @ SY4287 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SY4287 @ tc_nat ) @ SV1249 @ tc_nat ) )
| ~ ( c_lessequals @ SV1249 @ SV532 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3751,plain,
! [SV1250: $i,SV533: $i] :
( ( ! [SY4288: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV533 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SY4288 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV1250 @ tc_nat ) @ SY4288 @ tc_nat ) )
| ~ ( c_lessequals @ SY4288 @ SV1250 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3752,plain,
! [SV1251: $i,SV534: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV534 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1251 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV534 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1251 @ SV534 ) @ SV534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3753,plain,
! [SV1252: $i,SV535: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV535 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1252 @ SV535 ) @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1252 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3754,plain,
! [SV1253: $i,SV536: $i] :
( ( ! [SY4289: $i,SY4290: $i,SY4291: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SY4289 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SY4290 @ SY4291 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SY4289 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SY4289 @ SY4291 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SY4290 @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3755,plain,
! [SV1254: $i,SV537: $i] :
( ( ! [SY4292: $i,SY4293: $i,SY4294: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SY4292 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SY4293 @ SY4294 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SY4292 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SY4292 @ SY4294 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SY4293 @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3756,plain,
! [SV1255: $i,SV538: $i] :
( ( ! [SY4295: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV538 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SY4295 @ SV538 ) @ SV538 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1255 @ SV538 ) @ ( c_HOL_Oabs__class_Oabs @ SY4295 @ SV538 ) @ SV538 ) @ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3757,plain,
! [SV1256: $i,SV539: $i] :
( ( ( c_lessequals @ SV539 @ ( c_Suc @ SV1256 ) @ tc_nat )
| ~ ( c_lessequals @ SV539 @ SV1256 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3758,plain,
! [SV1257: $i,SV540: $i] :
( ( ( c_lessequals @ SV540 @ SV1257 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV540 ) @ SV1257 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3759,plain,
! [SV1258: $i,SV541: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV541 @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1258 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1258 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV541 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3760,plain,
! [SV1259: $i,SV542: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV542 @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV542 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1259 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV542 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3761,plain,
! [SV543: $i] :
( ( c_lessequals @ ( c_Suc @ SV543 ) @ SV543 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3762,plain,
! [SV1260: $i,SV544: $i] :
( ( ! [SY4296: $i,SY4297: $i] :
( ~ ( class_Divides_Osemiring__div @ SV544 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SY4296 @ SV544 ) @ SY4297 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SY4297 @ SV544 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4297 @ SY4296 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3763,plain,
! [SV1261: $i,SV545: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV545 )
| ( c_lessequals @ SV1261 @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1261 @ SV1261 @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3764,plain,
! [SV1262: $i,SV546: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV546 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1262 @ SV1262 @ SV546 ) @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
| ~ ( c_lessequals @ SV1262 @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3765,plain,
! [SV1263: $i,SV547: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV547 )
| ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1263 @ SV547 )
= SV1263 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3766,plain,
! [SV1264: $i,SV548: $i] :
( ( ~ ( class_Ring__and__Field_Oabs__if @ SV548 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1264 @ SV548 )
= SV1264 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ ( c_HOL_Ozero__class_Ozero @ SV548 ) @ SV548 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3767,plain,
! [SV1265: $i,SV549: $i] :
( ( ! [SY4298: $i,SY4299: $i,SY4300: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SY4298 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SY4299 @ SY4300 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4298 @ SY4300 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SY4299 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3768,plain,
! [SV1266: $i,SV550: $i] :
( ( ! [SY4301: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV550 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SY4301 @ SV550 ) @ SV550 ) @ SV550 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SY4301 @ SV550 ) @ SV550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3769,plain,
! [SV1267: $i,SV551: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV551 ) @ SV1267 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV551 @ SV1267 @ tc_nat ) ) @ SV1267 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3770,plain,
! [SV552: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV552 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ SV552 ) @ SV552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3033]) ).
thf(3771,plain,
! [SV1268: $i,SV553: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV553 @ SV1268 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1268 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV553 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3772,plain,
! [SV1269: $i,SV554: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV554 )
| ( c_lessequals @ SV1269 @ SV1269 @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3773,plain,
! [SV1270: $i,SV555: $i] :
( ( ~ ( class_Orderings_Oorder @ SV555 )
| ( c_lessequals @ SV1270 @ SV1270 @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3774,plain,
! [SV1271: $i,SV557: $i] :
( ( ! [SY4302: $i] :
( ( c_lessequals @ SV557 @ SV1271 @ tc_nat )
| ~ ( c_lessequals @ SY4302 @ SV1271 @ tc_nat )
| ~ ( c_lessequals @ SV557 @ SY4302 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3775,plain,
! [SV1272: $i,SV559: $i] :
( ( ! [SY4303: $i,SY4304: $i,SY4305: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
| ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SY4303 @ SY4304 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SY4305 @ SY4304 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SY4303 @ SY4305 @ SV559 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3776,plain,
! [SV1273: $i,SV560: $i] :
( ( ! [SY4306: $i,SY4307: $i] :
( ~ ( class_Orderings_Opreorder @ SV560 )
| ( c_lessequals @ SV1273 @ SY4306 @ SV560 )
| ~ ( c_lessequals @ SY4307 @ SY4306 @ SV560 )
| ~ ( c_lessequals @ SV1273 @ SY4307 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3777,plain,
! [SV1274: $i,SV561: $i] :
( ( ! [SY4308: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SY4308 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SY4308 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3778,plain,
! [SV1275: $i,SV562: $i] :
( ( ! [SY4309: $i,SY4310: $i] :
( ~ ( class_Orderings_Oorder @ SV562 )
| ( c_lessequals @ SV1275 @ SY4309 @ SV562 )
| ~ ( c_lessequals @ SV1275 @ SY4310 @ SV562 )
| ~ ( c_lessequals @ SY4310 @ SY4309 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3779,plain,
! [SV1276: $i,SV563: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV563 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV1276 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV1276 @ SV563 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3780,plain,
! [SV1277: $i,SV564: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV564 @ SV1277 @ tc_nat ) @ SV564 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3781,plain,
! [SV1278: $i,SV565: $i] :
( ( ! [SY4311: $i] :
( ~ ( class_Divides_Osemiring__div @ SV565 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1278 @ SY4311 @ SV565 ) @ SV1278 @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3782,plain,
! [SV1279: $i,SV566: $i] :
( ( ! [SY4312: $i] :
( ~ ( class_Divides_Osemiring__div @ SV566 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1279 @ SY4312 @ SV566 ) @ SY4312 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3783,plain,
! [SV1280: $i,SV567: $i] :
( ( ( SV567 = SV1280 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ ( c_Suc @ SV1280 ) @ tc_nat )
| ~ ( c_lessequals @ SV1280 @ SV567 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3784,plain,
! [SV568: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV568 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ SV568 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ SV568 ) @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3785,plain,
! [SV1281: $i,SV569: $i] :
( ( ! [SY4313: $i,SY4314: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
| ( c_HOL_Oord__class_Oless @ SV1281 @ SY4313 @ SV569 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SY4314 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4314 @ SY4313 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SY4314 @ SV1281 @ SV569 ) @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3786,plain,
! [SV1282: $i,SV570: $i] :
( ( ! [SY4315: $i,SY4316: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
| ( c_HOL_Oord__class_Oless @ SY4315 @ SY4316 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SY4315 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SY4316 @ SV570 ) @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3787,plain,
! [SV1283: $i,SV571: $i] :
( ( ! [SY4317: $i,SY4318: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
| ( c_HOL_Oord__class_Oless @ SV1283 @ SY4317 @ SV571 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SY4318 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4317 @ SY4318 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SY4318 @ SV571 ) @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3788,plain,
! [SV1284: $i,SV572: $i] :
( ( ! [SY4319: $i,SY4320: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
| ( c_HOL_Oord__class_Oless @ SY4319 @ SY4320 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4319 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SY4320 @ SV1284 @ SV572 ) @ SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3789,plain,
! [SV1285: $i,SV573: $i] :
( ( ! [SY4321: $i,SY4322: $i] :
( ~ ( class_Divides_Osemiring__div @ SV573 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SY4321 @ SV573 ) @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SY4322 @ SV573 ) @ SV573 )
= ( c_HOL_Otimes__class_Otimes @ SV1285 @ ( c_Divides_Odiv__class_Omod @ SY4321 @ SY4322 @ SV573 ) @ SV573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3790,plain,
! [SV1286: $i,SV574: $i] :
( ( ! [SY4323: $i,SY4324: $i] :
( ~ ( class_Divides_Osemiring__div @ SV574 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SY4323 @ SV574 ) @ ( c_HOL_Otimes__class_Otimes @ SY4324 @ SY4323 @ SV574 ) @ SV574 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1286 @ SY4324 @ SV574 ) @ SY4323 @ SV574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3791,plain,
! [SV1287: $i,SV575: $i] :
( ( ( c_lessequals @ SV575 @ SV1287 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1287 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV575 @ SV1287 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3792,plain,
! [SV1288: $i,SV576: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV576 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ ( c_HOL_Oabs__class_Oabs @ SV1288 @ SV576 ) @ SV576 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3793,plain,
! [SV1289: $i,SV577: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV577 ) @ ( c_Suc @ SV1289 ) @ tc_nat )
| ~ ( c_lessequals @ SV577 @ SV1289 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3794,plain,
! [SV1290: $i,SV578: $i] :
( ( ( c_lessequals @ SV578 @ SV1290 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV578 ) @ ( c_Suc @ SV1290 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3795,plain,
! [SV1291: $i,SV579: $i] :
( ( ! [SY4325: $i] :
( ~ ( class_Orderings_Olinorder @ SV579 )
| ( c_lessequals @ SV1291 @ SY4325 @ SV579 )
| ( c_lessequals @ SY4325 @ SV1291 @ SV579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3796,plain,
! [SV1292: $i,SV580: $i] :
( ( ! [SY4326: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4326 @ SV1292 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY4326 @ SV580 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SY4326 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3797,plain,
! [SV1293: $i,SV581: $i] :
( ( ! [SY4327: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SY4327 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4327 @ SV1293 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SY4327 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3798,plain,
! [SV1294: $i,SV582: $i] :
( ( ( c_lessequals @ SV582 @ SV1294 @ tc_nat )
| ( c_lessequals @ SV1294 @ SV582 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3799,plain,
! [SV1295: $i,SV583: $i] :
( ( ( SV583 = SV1295 )
| ~ ( c_HOL_Oord__class_Oless @ SV583 @ ( c_Suc @ SV1295 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV583 @ SV1295 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3800,plain,
! [SV584: $i] :
( ( c_HOL_Oord__class_Oless @ SV584 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3801,plain,
! [SV585: $i] :
( ( c_HOL_Oord__class_Oless @ SV585 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3802,plain,
! [SV1296: $i,SV586: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV586 @ ( c_Suc @ SV1296 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1296 @ SV586 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3803,plain,
! [SV1297: $i,SV587: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV587 @ SV1297 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1297 @ ( c_Suc @ SV587 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3804,plain,
! [SV588: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV588 @ SV588 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV588 @ ( c_Suc @ SV588 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3805,plain,
! [SV1298: $i,SV589: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV589 @ SV1298 @ tc_nat )
| ( SV589 = SV1298 )
| ~ ( c_lessequals @ SV589 @ SV1298 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3806,plain,
! [SV1299: $i,SV590: $i] :
( ( ( SV590 = SV1299 )
| ( c_HOL_Oord__class_Oless @ SV590 @ SV1299 @ tc_nat )
| ~ ( c_lessequals @ SV590 @ SV1299 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3807,plain,
! [SV1300: $i,SV591: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV591 @ SV1300 @ tc_nat )
| ( SV591 = SV1300 )
| ~ ( c_lessequals @ SV591 @ SV1300 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3808,plain,
! [SV1301: $i,SV592: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV592 @ SV1301 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV592 ) @ SV1301 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3809,plain,
! [SV1302: $i,SV593: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV593 @ ( c_Suc @ SV1302 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV593 @ SV1302 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3810,plain,
! [SV1303: $i,SV594: $i] :
( ( ! [SY4328: $i] :
( ( c_HOL_Oord__class_Oless @ SV594 @ SV1303 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4328 @ SV594 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4328 @ SV1303 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3811,plain,
! [SV1304: $i,SV595: $i] :
( ( ! [SY4329: $i] :
( ( c_HOL_Oord__class_Oless @ SV595 @ SV1304 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV595 @ SY4329 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SY4329 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3812,plain,
! [SV1305: $i,SV598: $i] :
( ( ! [SY4330: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SV1305 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4330 @ SV1305 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV598 @ SY4330 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3813,plain,
! [SV1306: $i,SV599: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV599 @ SV1306 @ tc_nat )
= SV599 )
| ~ ( c_HOL_Oord__class_Oless @ SV599 @ SV1306 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3814,plain,
! [SV1307: $i,SV600: $i] :
( ( ! [SY4331: $i] :
( ( c_HOL_Oord__class_Oless @ SV600 @ ( c_HOL_Oplus__class_Oplus @ SV1307 @ SY4331 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV1307 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3815,plain,
! [SV1308: $i,SV601: $i] :
( ( ! [SY4332: $i] :
( ( c_HOL_Oord__class_Oless @ SV601 @ ( c_HOL_Oplus__class_Oplus @ SV1308 @ SY4332 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV601 @ SY4332 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3816,plain,
! [SV1309: $i,SV602: $i] :
( ( ! [SY4333: $i] :
( ( c_HOL_Oord__class_Oless @ SV602 @ SV1309 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV602 @ SY4333 @ tc_nat ) @ SV1309 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3817,plain,
! [SV1310: $i,SV603: $i] :
( ( ! [SY4334: $i] :
( ( c_HOL_Oord__class_Oless @ SV603 @ ( c_HOL_Oplus__class_Oplus @ SV1310 @ SY4334 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV603 @ SV1310 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3818,plain,
! [SV1311: $i,SV604: $i] :
( ( ! [SY4335: $i] :
( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Oplus__class_Oplus @ SV1311 @ SY4335 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ SY4335 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3819,plain,
! [SV1312: $i,SV605: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV605 ) @ SV1312 @ tc_nat )
| ( ( c_Suc @ SV605 )
= SV1312 )
| ~ ( c_HOL_Oord__class_Oless @ SV605 @ SV1312 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3820,plain,
! [SV1313: $i,SV606: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV606 ) @ ( c_Suc @ SV1313 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV606 @ SV1313 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3821,plain,
! [SV1314: $i,SV607: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV607 @ SV1314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV607 ) @ ( c_Suc @ SV1314 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3822,plain,
! [SV1315: $i,SV608: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV608 ) @ ( c_Suc @ SV1315 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV608 @ SV1315 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3823,plain,
! [SV1316: $i,SV609: $i] :
( ( ! [SY4336: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV609 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1316 @ SY4336 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1316 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4336 @ SV609 ) @ SV609 ) )
| ~ ( c_lessequals @ SY4336 @ SV1316 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3824,plain,
! [SV1317: $i,SV610: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV610 @ ( c_Suc @ SV1317 ) @ tc_nat ) @ SV610 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV610 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3825,plain,
! [SV611: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV611 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV611 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV611 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3826,plain,
! [SV1318: $i,SV612: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV612 ) @ ( c_Suc @ SV1318 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV612 @ SV1318 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3827,plain,
! [SV1319: $i,SV613: $i] :
( ( ! [SY4337: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV613 @ SV1319 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV613 @ SY4337 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1319 @ SY4337 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3828,plain,
! [SV1320: $i,SV614: $i] :
( ( ! [SY4338: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV614 @ SV1320 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY4338 @ SV1320 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV614 @ SY4338 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3829,plain,
! [SV1321: $i,SV615: $i] :
( ( ! [SY4339: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV615 ) @ SV1321 @ tc_nat ) @ ( c_Suc @ SY4339 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV615 @ SV1321 @ tc_nat ) @ SY4339 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3830,plain,
! [SV1322: $i,SV616: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_HOL_Ominus__class_Ominus @ SV616 @ SV1322 @ tc_nat ) @ tc_nat )
= SV1322 )
| ~ ( c_lessequals @ SV1322 @ SV616 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3831,plain,
! [SV1323: $i,SV617: $i] :
( ( ! [SY4340: $i] :
( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV617 @ SV1323 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4340 @ SV1323 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV617 @ SY4340 @ tc_nat ) @ SV1323 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3832,plain,
! [SV1324: $i,SV618: $i] :
( ( ! [SY4341: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SV1324 @ SY4341 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SY4341 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1324 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3833,plain,
! [SV1325: $i,SV621: $i] :
( ( ! [SY4342: $i] :
( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SY4342 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SY4342 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4342 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ SY4342 @ SV621 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3834,plain,
! [SV1326: $i,SV622: $i] :
( ( ! [SY4343: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4343 @ SV1326 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV622 @ SY4343 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SY4343 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3835,plain,
! [SV1327: $i,SV623: $i] :
( ( ! [SY4344: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV623 @ SV1327 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4344 @ SV1327 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV623 @ SY4344 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3836,plain,
! [SV1328: $i,SV624: $i] :
( ( ! [SY4345: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1328 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SY4345 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4345 @ SV1328 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3837,plain,
! [SV1329: $i,SV625: $i] :
( ( ! [SY4346: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV625 @ SV1329 @ tc_nat ) @ SY4346 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV625 @ ( c_HOL_Oplus__class_Oplus @ SV1329 @ SY4346 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3838,plain,
! [SV1330: $i,SV627: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV627 @ SV1330 @ tc_nat ) @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV1330 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV627 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3839,plain,
! [SV1331: $i,SV628: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV628 @ SV1331 @ tc_nat ) @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV1331 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV628 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3840,plain,
! [SV1332: $i,SV629: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV629 @ SV1332 @ tc_nat ) @ SV629 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3841,plain,
! [SV1333: $i,SV630: $i] :
( ( ! [SY4347: $i] :
( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV630 @ SV1333 @ tc_nat ) @ SY4347 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV630 @ SY4347 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1333 @ SY4347 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3842,plain,
! [SV1334: $i,SV631: $i] :
( ( ! [SY4348: $i] :
( ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Ominus__class_Ominus @ SV1334 @ SY4348 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV631 @ SV1334 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV631 @ SY4348 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3843,plain,
! [SV1335: $i,SV632: $i] :
( ( ! [SY4349: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1335 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4349 @ SV1335 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SY4349 @ tc_nat ) )
| ~ ( c_lessequals @ SV1335 @ SY4349 @ tc_nat )
| ~ ( c_lessequals @ SV1335 @ SV632 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3844,plain,
! [SV1336: $i,SV633: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV633 @ SV1336 @ tc_nat ) @ SV633 @ tc_nat )
= SV1336 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3845,plain,
! [SV1337: $i,SV634: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV634 @ SV1337 @ tc_nat ) @ SV1337 @ tc_nat )
= SV634 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3846,plain,
! [SV1338: $i,SV635: $i] :
( ( ! [SY4350: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV635 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ SY4350 @ SV635 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1338 @ SY4350 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3847,plain,
! [SV1339: $i,SV636: $i] :
( ( ! [SY4351: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV636 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1339 @ SY4351 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
| ~ ( c_HOL_Oord__class_Oless @ SV1339 @ SY4351 @ SV636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3848,plain,
! [SV1340: $i,SV637: $i] :
( ( ! [SY4352: $i,SY4353: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV637 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SY4352 @ SV637 ) @ SY4353 @ SV637 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY4353 @ SV1340 @ SV637 ) @ SV637 ) @ SY4352 @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3849,plain,
! [SV1341: $i,SV638: $i] :
( ( ! [SY4354: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV638 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1341 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4354 @ SV638 ) @ SV638 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SY4354 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3850,plain,
! [SV1342: $i,SV639: $i] :
( ( ! [SY4355: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( c_HOL_Oord__class_Oless @ SV1342 @ SY4355 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1342 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY4355 @ SV639 ) @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3851,plain,
! [SV1343: $i,SV640: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV640 @ ( c_HOL_Ominus__class_Ominus @ SV1343 @ SV640 @ tc_nat ) @ tc_nat )
= SV1343 )
| ( c_HOL_Oord__class_Oless @ SV1343 @ SV640 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3852,plain,
! [SV1344: $i,SV641: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV1344 @ tc_nat ) @ SV641 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV641 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1344 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3853,plain,
! [SV1345: $i,SV642: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV1345 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV642 @ SV1345 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SV1345 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3854,plain,
! [SV1346: $i,SV643: $i] :
( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV1346 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1346 @ SV643 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV1346 @ SV643 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3855,plain,
! [SV1347: $i,SV644: $i] :
( ( ! [SY4356: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV644 @ SV1347 @ tc_nat ) @ SY4356 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV644 @ ( c_HOL_Ominus__class_Ominus @ SY4356 @ SV1347 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3856,plain,
! [SV1348: $i,SV645: $i] :
( ( ! [SY4357: $i] :
( ( c_HOL_Oord__class_Oless @ SV645 @ ( c_HOL_Ominus__class_Ominus @ SV1348 @ SY4357 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV645 @ SY4357 @ tc_nat ) @ SV1348 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3857,plain,
! [SV1349: $i,SV646: $i] :
( ( ! [SY4358: $i] :
( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SY4358 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SY4358 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY4358 @ SV1349 @ tc_nat )
| ~ ( c_lessequals @ SY4358 @ SV646 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3858,plain,
! [SV1350: $i,SV647: $i] :
( ( ! [SY4359: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4359 @ SV1350 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV647 @ SY4359 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SY4359 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3859,plain,
! [SV1351: $i,SV648: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SV1351 @ tc_nat ) @ ( c_Suc @ SV648 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3860,plain,
! [SV1352: $i,SV649: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV649 @ SV1352 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1352 @ SV649 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3861,plain,
! [SV1353: $i,SV650: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV650 @ SV1353 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1353 @ SV650 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3862,plain,
! [SV1354: $i,SV651: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV651 @ SV1354 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV651 @ SV1354 @ tc_nat ) @ SV1354 @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ SV651 @ SV1354 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3863,plain,
! [SV1355: $i,SV652: $i] :
( ( ! [SY4360: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SV1355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY4360 @ SV1355 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1355 @ SV652 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV652 @ SY4360 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3864,plain,
! [SV1356: $i,SV653: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV653 @ SV1356 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV653 @ SV1356 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3865,plain,
! [SV1357: $i,SV654: $i] :
( ( ! [SY4361: $i] :
( ~ ( class_Orderings_Oorder @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SY4361 @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SY4361 @ SV1357 @ SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3866,plain,
! [SV1358: $i,SV655: $i] :
( ( ! [SY4362: $i] :
( ~ ( class_Orderings_Olinorder @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SV1358 @ SY4362 @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SY4362 @ SV1358 @ SV655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3867,plain,
! [SV1359: $i,SV656: $i] :
( ( ! [SY4363: $i] :
( ~ ( class_Orderings_Opreorder @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ SY4363 @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SY4363 @ SV1359 @ SV656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(3868,plain,
! [SV1360: $i,SV657: $i] :
( ( ! [SY4364: $i] :
( ~ ( class_Orderings_Opreorder @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SV1360 @ SY4364 @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SY4364 @ SV1360 @ SV657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3869,plain,
! [SV1361: $i,SV658: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV658 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV1361 @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3870,plain,
! [SV1362: $i,SV659: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV659 )
| ~ ( c_HOL_Oord__class_Oless @ SV1362 @ SV1362 @ SV659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3871,plain,
! [SV660: $i] :
( ( c_HOL_Oord__class_Oless @ SV660 @ SV660 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3872,plain,
! [SV661: $i] :
( ( c_HOL_Oord__class_Oless @ SV661 @ SV661 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3873,plain,
! [SV1363: $i,SV662: $i] :
( ( ~ ( class_Orderings_Oorder @ SV662 )
| ~ ( c_HOL_Oord__class_Oless @ SV1363 @ SV1363 @ SV662 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3874,plain,
! [SV1364: $i,SV663: $i] :
( ( ! [SY4365: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV663 @ SV1364 @ tc_nat ) @ SY4365 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV663 @ SY4365 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3875,plain,
! [SV1365: $i,SV664: $i] :
( ( ! [SY4366: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SY4366 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4366 @ SV664 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4366 @ SV1365 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3876,plain,
! [SV1366: $i,SV665: $i] :
( ( ! [SY4367: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV665 )
| ( c_HOL_Oord__class_Oless @ SV1366 @ SY4367 @ SV665 )
| ( c_HOL_Oord__class_Oless @ SY4367 @ SV1366 @ SV665 )
| ( SY4367 = SV1366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3877,plain,
! [SV1367: $i,SV666: $i] :
( ( ! [SY4368: $i] :
( ~ ( class_Orderings_Olinorder @ SV666 )
| ( SV1367 = SY4368 )
| ( c_HOL_Oord__class_Oless @ SY4368 @ SV1367 @ SV666 )
| ( c_HOL_Oord__class_Oless @ SV1367 @ SY4368 @ SV666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3878,plain,
! [SV1368: $i,SV667: $i] :
( ( ! [SY4369: $i] :
( ~ ( class_Orderings_Olinorder @ SV667 )
| ( SV1368 = SY4369 )
| ( c_HOL_Oord__class_Oless @ SV1368 @ SY4369 @ SV667 )
| ( c_HOL_Oord__class_Oless @ SY4369 @ SV1368 @ SV667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3879,plain,
! [SV1369: $i,SV668: $i] :
( ( ! [SY4370: $i] :
( ~ ( class_Orderings_Olinorder @ SV668 )
| ( c_HOL_Oord__class_Oless @ SV1369 @ SY4370 @ SV668 )
| ( SY4370 = SV1369 )
| ( c_HOL_Oord__class_Oless @ SY4370 @ SV1369 @ SV668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3880,plain,
! [SV1370: $i,SV669: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV669 @ SV1370 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1370 @ SV669 @ tc_nat )
| ( SV1370 = SV669 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3881,plain,
! [SV1371: $i,SV670: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV670 @ SV1371 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1371 @ SV670 @ tc_nat )
| ( SV1371 = SV670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3882,plain,
! [SV1372: $i,SV671: $i] :
( ( ! [SY4371: $i] :
( ~ ( class_Orderings_Olinorder @ SV671 )
| ( c_HOL_Oord__class_Oless @ SV1372 @ SY4371 @ SV671 )
| ( c_HOL_Oord__class_Oless @ SY4371 @ SV1372 @ SV671 )
| ( SY4371 = SV1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3883,plain,
! [SV1373: $i,SV672: $i] :
( ( ! [SY4372: $i,SY4373: $i] :
( ~ ( class_Orderings_Oorder @ SV672 )
| ( c_HOL_Oord__class_Oless @ SV1373 @ SY4372 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SY4373 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SY4373 @ SY4372 @ SV672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3884,plain,
! [SV1374: $i,SV673: $i] :
( ( ! [SY4374: $i,SY4375: $i] :
( ~ ( class_Orderings_Opreorder @ SV673 )
| ( c_HOL_Oord__class_Oless @ SV1374 @ SY4374 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SY4375 @ SY4374 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SY4375 @ SV673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3885,plain,
! [SV1375: $i,SV674: $i] :
( ( ! [SY4376: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV674 @ SV1375 @ tc_nat ) @ SY4376 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV674 @ SY4376 @ tc_nat ) @ SV1375 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3886,plain,
! [SV1376: $i,SV675: $i] :
( ( ! [SY4377: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1376 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV675 @ SY4377 @ tc_nat ) )
| ( SV1376 = SY4377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3887,plain,
! [SV676: $i] :
( ( ( c_Suc @ SV676 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3888,plain,
! [SV1377: $i,SV677: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV677 @ SV1377 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV677
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3889,plain,
! [SV678: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV678 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV678 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3160]) ).
thf(3890,plain,
! [SV1378: $i,SV679: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV679 @ SV1378 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1378 @ SV679 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1378 = SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3891,plain,
! [SV1379: $i,SV680: $i] :
( ( ! [SY4378: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1379 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SY4378 @ tc_nat ) )
| ( SV1379 = SY4378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(3892,plain,
! [SV1380: $i,SV681: $i] :
( ( ! [SY4379: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV681 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1380 @ SV1380 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SY4379 @ SY4379 @ SV681 ) @ SV681 )
!= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
| ( SV1380
= ( c_HOL_Ozero__class_Ozero @ SV681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3893,plain,
! [SV1381: $i,SV682: $i] :
( ( ! [SY4380: $i,SY4381: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV682 )
| ~ ( class_Int_Onumber__ring @ SV682 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SY4380 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SY4381 @ SV682 ) )
| ( SY4380 = SY4381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3894,plain,
! [SV1382: $i,SV683: $i] :
( ( ! [SY4382: $i,SY4383: $i,SY4384: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SY4382 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY4383 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SY4384 @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ SV683 @ SV1382 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SY4383 @ SV1382 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3895,plain,
! [SV1383: $i,SV684: $i] :
( ( ! [SY4385: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1383 @ SV684 )
!= ( c_HOL_Oabs__class_Oabs @ SY4385 @ SV684 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1383 @ SY4385 @ SV684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3896,plain,
! [SV1384: $i,SV685: $i] :
( ( ! [SY4386: $i,SY4387: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SY4386 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SY4387 @ SV685 ) )
| ( SY4386 = SY4387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3897,plain,
! [SV1385: $i,SV686: $i] :
( ( ! [SY4388: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SY4388 @ SV686 )
!= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SY4388 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3898,plain,
! [SV1386: $i,SV687: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV687 @ SV1386 @ tc_nat ) )
| ( SV687
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV687
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3899,plain,
! [SV1387: $i,SV688: $i] :
( ( ! [SY4389: $i,SY4390: $i,SY4391: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SY4389 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SY4390 @ SY4391 @ SV688 ) )
| ( c_lessequals @ SY4389 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SY4391 @ SY4390 @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3900,plain,
! [SV1388: $i,SV689: $i] :
( ( ! [SY4392: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SY4392 @ SV689 )
!= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SY4392
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3901,plain,
! [SV1389: $i,SV690: $i] :
( ( ! [SY4393: $i,SY4394: $i,SY4395: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SY4393 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SY4394 @ SY4395 @ SV690 ) )
| ( c_lessequals @ SY4395 @ SY4394 @ SV690 )
| ~ ( c_lessequals @ SY4393 @ SV1389 @ SV690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3902,plain,
! [SV1390: $i,SV691: $i] :
( ( ! [SY4396: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV691 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1390 @ SY4396 @ SV691 )
!= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
| ( SV1390 = SY4396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3903,plain,
! [SV692: $i] :
( ( SV692
= ( c_Suc @ SV692 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3174]) ).
thf(3904,plain,
! [SV1391: $i,SV693: $i] :
( ( ! [SY4397: $i] :
( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SY4397 @ SV693 )
!= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SY4397
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3905,plain,
! [SV694: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV694 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3906,plain,
! [SV1392: $i,SV695: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1392 @ tc_nat ) )
| ( SV1392
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1392
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3907,plain,
! [SV1393: $i,SV696: $i] :
( ( ! [SY4398: $i,SY4399: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV696 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SY4398 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SY4399 @ SY4399 @ SV696 ) )
| ( SV1393 = SY4398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3908,plain,
! [SV1394: $i,SV697: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1394 @ tc_nat ) )
| ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV697
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3909,plain,
! [SV1395: $i,SV698: $i] :
( ( ! [SY4400: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV698 )
| ~ ( class_Int_Onumber__ring @ SV698 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SY4400 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SV1395 = SY4400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3910,plain,
! [SV1396: $i,SV699: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV699 @ SV1396 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV699 @ SV1396 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3911,plain,
! [SV700: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV700 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3912,plain,
! [SV701: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV701 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV701 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3183]) ).
thf(3913,plain,
! [SV1397: $i,SV702: $i] :
( ( ! [SY4401: $i,SY4402: $i,SY4403: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV702 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SY4401 @ SY4402 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SY4401 @ SY4403 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SY4402 @ SV702 )
= SY4403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3914,plain,
! [SV1398: $i,SV703: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV703 @ SV1398 @ tc_nat ) )
| ( SV703
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1398
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3915,plain,
! [SV1399: $i,SV704: $i] :
( ( ! [SY4404: $i] :
( ~ ( class_Divides_Osemiring__div @ SV704 )
| ( ( c_Divides_Odiv__class_Omod @ SV1399 @ SY4404 @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY4404 @ SV1399 @ SV704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3916,plain,
! [SV1400: $i,SV705: $i] :
( ( ! [SY4405: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SY4405 @ SV705 )
!= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SY4405 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SY4405
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3917,plain,
! [SV1401: $i,SV706: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV706 @ SV1401 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1401
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV706
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3918,plain,
! [SV707: $i] :
( ( ( c_Suc @ SV707 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3189]) ).
thf(3919,plain,
! [SV1402: $i,SV708: $i] :
( ( ! [SY4406: $i,SY4407: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV708 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SY4406 @ SY4407 @ SV708 ) )
| ( SY4406 = SY4407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3920,plain,
! [SV1403: $i,SV709: $i] :
( ( ! [SY4408: $i,SY4409: $i,SY4410: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV709 )
| ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SY4408 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SY4409 @ SY4410 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SY4410 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SY4409 @ SY4408 @ SV709 ) @ SV709 ) )
| ( SY4408 = SY4410 )
| ( SV1403 = SY4409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3921,plain,
! [SV1404: $i,SV710: $i] :
( ( ! [SY4411: $i,SY4412: $i,SY4413: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SY4411 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SY4412 @ SY4413 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SV1404 @ SY4411 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SY4412 @ SY4413 @ SV710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3922,plain,
! [SV1405: $i,SV711: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV711 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1405 @ SV1405 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1405
= ( c_HOL_Ozero__class_Ozero @ SV711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3923,plain,
! [SV1406: $i,SV712: $i] :
( ( ! [SY4414: $i,SY4415: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY4414 @ SY4415 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4414 @ SV1406 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV712 @ SY4415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(3924,plain,
! [SV1407: $i,SV713: $i] :
( ( ! [SY4416: $i,SY4417: $i,SY4418: $i,SY4419: $i] :
( ~ ( class_Divides_Oring__div @ SV713 )
| ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SY4416 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY4417 @ SY4416 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4418 @ SY4416 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY4419 @ SY4416 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4418 @ SV1407 @ SV713 ) @ SY4416 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4419 @ SY4417 @ SV713 ) @ SY4416 @ SV713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3925,plain,
! [SV1408: $i,SV714: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1408 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1408
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV714
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3926,plain,
! [SV1409: $i,SV715: $i] :
( ( ! [SY4420: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV715 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1409 @ SV715 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY4420 @ SV715 ) )
| ( SV1409 = SY4420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3927,plain,
! [SV1410: $i,SV716: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV716 @ SV1410 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV716
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3928,plain,
! [SV1411: $i,SV717: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV717 @ SV1411 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1411
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3929,plain,
! [SV1412: $i,SV718: $i] :
( ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV718 @ SV1412 @ tc_nat ) )
!= SV1412 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV718 ) @ SV1412 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3930,plain,
! [SV1413: $i,SV719: $i] :
( ( ( ( c_Suc @ SV719 )
!= ( c_Suc @ SV1413 ) )
| ( SV719 = SV1413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3931,plain,
! [SV1414: $i,SV720: $i] :
( ( ! [SY4421: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV720 @ SV1414 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SY4421 @ SV1414 @ tc_nat ) )
| ( SV1414
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV720 = SY4421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3932,plain,
! [SV1415: $i,SV721: $i] :
( ( ! [SY4422: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1415 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV721 @ SY4422 @ tc_nat ) )
| ( SV1415 = SY4422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3933,plain,
! [SV1416: $i,SV722: $i] :
( ( ! [SY4423: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV722 )
| ~ ( class_Int_Onumber__ring @ SV722 )
| ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SY4423 @ SV722 ) )
| ( SY4423
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3934,plain,
! [SV1417: $i,SV723: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV723 @ SV1417 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1417
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1417
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3935,plain,
! [SV1418: $i,SV724: $i] :
( ( ! [SY4424: $i] :
( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SY4424 @ SV724 )
!= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SY4424
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3936,plain,
! [SV1419: $i,SV725: $i] :
( ( ! [SY4425: $i,SY4426: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SY4425 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SY4426 @ SY4425 @ SV725 ) )
| ( SV1419 = SY4426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3937,plain,
! [SV1420: $i,SV726: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1420 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1420
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3938,plain,
! [SV1421: $i,SV727: $i] :
( ( ! [SY4427: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1421 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV727 @ SY4427 @ tc_nat ) )
| ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1421 = SY4427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3939,plain,
! [SV1422: $i,SV728: $i] :
( ( ! [SY4428: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV728 @ SV1422 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY4428 @ SV1422 @ tc_nat ) )
| ( SV728 = SY4428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3940,plain,
! [SV1423: $i,SV729: $i] :
( ( ! [SY4429: $i,SY4430: $i,SY4431: $i,SY4432: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV729 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SY4429 @ SV729 ) @ SY4430 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4431 @ SY4429 @ SV729 ) @ SY4432 @ SV729 ) )
| ( SY4430
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4431 @ SV1423 @ SV729 ) @ SY4429 @ SV729 ) @ SY4432 @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3941,plain,
! [SV1424: $i,SV730: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV730 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1424 @ SV730 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ( SV1424
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3942,plain,
! [SV1425: $i,SV731: $i] :
( ( ( SV731
!= ( c_HOL_Oplus__class_Oplus @ SV731 @ SV1425 @ tc_nat ) )
| ( SV1425
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3943,plain,
! [SV1426: $i,SV732: $i] :
( ( ! [SY4433: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV732 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1426 @ SY4433 @ SV732 )
!= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
| ( SV1426 = SY4433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3944,plain,
! [SV1427: $i,SV733: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV733 @ SV1427 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV733
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1427
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3945,plain,
! [SV1428: $i,SV734: $i] :
( ( ! [SY4434: $i] :
( ~ ( class_Orderings_Olinorder @ SV734 )
| ( ( c_Orderings_Oord__class_Omin @ SV1428 @ SY4434 @ SV734 )
!= SV1428 )
| ( c_lessequals @ SV1428 @ SY4434 @ SV734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3946,plain,
! [SV1429: $i,SV735: $i] :
( ( ! [SY4435: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY4435 @ SV1429 @ tc_nat ) )
| ~ ( c_lessequals @ SV1429 @ SY4435 @ tc_nat )
| ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
| ( SV735 = SY4435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3947,plain,
! [SV1430: $i,SV736: $i] :
( ( ( ( c_Suc @ SV736 )
!= ( c_Suc @ SV1430 ) )
| ( SV736 = SV1430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3948,plain,
! [SV1431: $i,SV737: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV737 @ SV1431 @ tc_nat )
!= SV737 )
| ( SV1431
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3949,plain,
! [SV1432: $i,SV738: $i] :
( ( ! [SY4436: $i,SY4437: $i,SY4438: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SY4436 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4437 @ SV1432 @ tc_nat ) @ SY4438 @ tc_nat ) )
| ~ ( c_lessequals @ SV738 @ SY4437 @ tc_nat )
| ( SY4436
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4437 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SY4438 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3950,plain,
! [SV1433: $i,SV739: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1433 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV739
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3951,plain,
! [SV740: $i] :
( ( ( c_Suc @ SV740 )
= SV740 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3952,plain,
! [SV1434: $i,SV741: $i] :
( ( ! [SY4439: $i,SY4440: $i,SY4441: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SY4439 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SY4440 @ SY4441 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SY4440 @ SY4441 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SY4439 @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3953,plain,
! [SV1435: $i,SV742: $i] :
( ( ! [SY4442: $i,SY4443: $i,SY4444: $i,SY4445: $i] :
( ~ ( class_Divides_Osemiring__div @ SV742 )
| ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SY4442 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY4443 @ SY4442 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4444 @ SY4442 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY4445 @ SY4442 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4444 @ SV1435 @ SV742 ) @ SY4442 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4445 @ SY4443 @ SV742 ) @ SY4442 @ SV742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3954,plain,
! [SV1436: $i,SV743: $i] :
( ( ! [SY4446: $i,SY4447: $i,SY4448: $i,SY4449: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV743 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SY4446 @ SV743 ) @ SY4447 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4448 @ SY4446 @ SV743 ) @ SY4449 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SY4448 @ SV743 ) @ SY4446 @ SV743 ) @ SY4447 @ SV743 )
= SY4449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3955,plain,
! [SV1437: $i,SV744: $i] :
( ( ! [SY4450: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1437 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV744 @ SY4450 @ tc_nat ) )
| ( SV1437 = SY4450 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3956,plain,
! [SV1438: $i,SV745: $i] :
( ( ! [SY4451: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1438 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV745 @ SY4451 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat )
| ( SV1438 = SY4451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3957,plain,
! [SV1439: $i,SV746: $i] :
( ( ! [SY4452: $i,SY4453: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV1439 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4452 @ SY4453 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SY4453 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4452 @ SV1439 @ tc_nat ) @ tc_nat ) )
| ( SV1439 = SY4453 )
| ( SV746 = SY4452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3958,plain,
! [SV1440: $i,SV747: $i] :
( ( ! [SY4454: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1440 @ SV1440 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SY4454 @ SY4454 @ SV747 ) @ SV747 )
!= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
| ( SY4454
= ( c_HOL_Ozero__class_Ozero @ SV747 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3959,plain,
! [SV1441: $i,SV748: $i] :
( ( ! [SY4455: $i,SY4456: $i,SY4457: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV748 )
| ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SY4455 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SY4456 @ SY4457 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SY4457 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SY4456 @ SY4455 @ SV748 ) @ SV748 ) )
| ( SY4455 = SY4457 )
| ( SV1441 = SY4456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3960,plain,
! [SV1442: $i,SV749: $i] :
( ( ! [SY4458: $i,SY4459: $i,SY4460: $i,SY4461: $i] :
( ~ ( class_Divides_Osemiring__div @ SV749 )
| ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SY4458 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY4459 @ SY4458 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4460 @ SY4458 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY4461 @ SY4458 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4460 @ SV1442 @ SV749 ) @ SY4458 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4461 @ SY4459 @ SV749 ) @ SY4458 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3961,plain,
! [SV1443: $i,SV750: $i] :
( ( ! [SY4462: $i,SY4463: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SY4462 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SY4463 @ tc_nat ) @ tc_nat ) )
| ( SY4462 = SY4463 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3962,plain,
! [SV1444: $i,SV751: $i] :
( ( ! [SY4464: $i,SY4465: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SY4464 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SY4465 @ SV751 ) )
| ( SY4464 = SY4465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3963,plain,
! [SV1445: $i,SV752: $i] :
( ( ! [SY4466: $i,SY4467: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV1445 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4466 @ SY4467 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SY4467 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SY4466 @ SV1445 @ tc_nat ) @ tc_nat ) )
| ( SV1445 = SY4467 )
| ( SV752 = SY4466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3964,plain,
! [SV1446: $i,SV753: $i] :
( ( ! [SY4468: $i,SY4469: $i,SY4470: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SY4468 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4469 @ SV1446 @ tc_nat ) @ SY4470 @ tc_nat ) )
| ~ ( c_lessequals @ SY4469 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SY4469 @ tc_nat ) @ SV1446 @ tc_nat ) @ SY4468 @ tc_nat )
= SY4470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3965,plain,
! [SV1447: $i,SV754: $i] :
( ( ! [SY4471: $i,SY4472: $i,SY4473: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV754 )
| ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SY4471 @ SY4472 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SY4471 @ SY4473 @ SV754 ) @ SV754 ) )
| ( SY4472 = SY4473 )
| ( SY4471
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3966,plain,
! [SV1448: $i,SV755: $i,SV1: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3967,plain,
! [SV1449: $i,SV756: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3968,plain,
! [SV1450: $i,SV759: $i,SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV5 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV759 @ SV759 @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV1450 @ SV1450 @ SV5 ) @ SV5 ) @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3969,plain,
! [SV1451: $i,SV760: $i,SV6: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3970,plain,
! [SV1452: $i,SV761: $i,SV7: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3971,plain,
! [SV8: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV8 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 ) @ SV8 ) @ ( c_HOL_Ozero__class_Ozero @ SV8 ) @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3972,plain,
! [SV1453: $i,SV762: $i,SV9: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV9 @ SV762 @ tc_nat ) @ SV1453 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV9 @ SV1453 @ tc_nat ) @ SV762 @ tc_nat ) )
| ~ ( c_lessequals @ SV1453 @ SV9 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3973,plain,
! [SV1454: $i,SV763: $i,SV10: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV10 @ SV763 @ tc_nat ) @ SV1454 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV10 @ ( c_HOL_Ominus__class_Ominus @ SV763 @ SV1454 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV1454 @ SV763 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3974,plain,
! [SV1455: $i,SV764: $i,SV11: $i] :
( ( ! [SY4474: $i,SY4475: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1455 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SY4474 @ SY4475 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SY4474 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1455 @ SY4475 @ SV11 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3975,plain,
! [SV1456: $i,SV765: $i,SV12: $i] :
( ( ! [SY4476: $i,SY4477: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV765 @ SV1456 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SY4476 @ SY4477 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SV765 @ ( c_HOL_Otimes__class_Otimes @ SV1456 @ ( c_HOL_Otimes__class_Otimes @ SY4476 @ SY4477 @ SV12 ) @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3976,plain,
! [SV1457: $i,SV766: $i,SV13: $i] :
( ( ! [SY4478: $i,SY4479: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SY4478 @ SY4479 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SY4478 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ SY4479 @ SV13 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3977,plain,
! [SV767: $i,SV14: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV14 ) )
= $true )
| ( ( ( SV767
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV767 @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3250]) ).
thf(3978,plain,
! [SV768: $i,SV15: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV15 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV768 @ SV768 @ SV15 )
= SV768 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3979,plain,
! [SV1458: $i,SV769: $i,SV16: $i] :
( ( ! [SY4480: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
| ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SV1458 @ ( c_HOL_Oabs__class_Oabs @ SY4480 @ SV16 ) @ SV16 ) @ SV16 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SY4480 @ SV16 ) @ SV1458 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3980,plain,
! [SV17: $i] :
( ( ( c_lessequals @ SV17 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV17
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3981,plain,
! [SV1459: $i,SV770: $i,SV18: $i] :
( ( ~ ( class_Orderings_Oorder @ SV18 )
| ( SV770 = SV1459 )
| ~ ( c_lessequals @ SV1459 @ SV770 @ SV18 )
| ~ ( c_lessequals @ SV770 @ SV1459 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3982,plain,
! [SV1460: $i,SV771: $i,SV19: $i] :
( ( ~ ( class_Orderings_Oorder @ SV19 )
| ( SV771 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV771 @ SV19 )
| ~ ( c_lessequals @ SV771 @ SV1460 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3983,plain,
! [SV772: $i,SV20: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV772 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV772 @ SV20 @ tc_nat )
| ( SV772 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3984,plain,
! [SV773: $i,SV21: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SV773 @ tc_nat ) )
= $true )
| ( ( ( SV773 = SV21 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV773 @ SV21 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3985,plain,
! [SV774: $i,SV22: $i] :
( ( ( SV22 = SV774 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV22 @ SV774 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV774 @ SV22 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3986,plain,
! [SV775: $i,SV23: $i] :
( ( ( SV23 = SV775 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV775 @ SV23 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV23 @ SV775 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3987,plain,
! [SV776: $i,SV24: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV24 @ SV776 @ tc_nat ) )
= $true )
| ( ( ( SV776 = SV24 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV776 @ SV24 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3988,plain,
! [SV777: $i,SV25: $i] :
( ( ( SV25 = SV777 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV777 @ SV25 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV25 @ SV777 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3989,plain,
! [SV778: $i,SV26: $i] :
( ( ( SV26 = SV778 )
= $true )
| ( ( ~ ( c_lessequals @ SV778 @ SV26 @ tc_nat )
| ~ ( c_lessequals @ SV26 @ SV778 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3262]) ).
thf(3990,plain,
! [SV779: $i,SV27: $i] :
( ( ( SV27 = SV779 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV779 @ SV27 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV27 @ SV779 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3991,plain,
! [SV1461: $i,SV780: $i,SV28: $i] :
( ( ~ ( class_Orderings_Oorder @ SV28 )
| ( SV780 = SV1461 )
| ~ ( c_lessequals @ SV780 @ SV1461 @ SV28 )
| ~ ( c_lessequals @ SV1461 @ SV780 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3992,plain,
! [SV781: $i,SV29: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV29 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV781 @ SV29 )
= SV781 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV781 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3993,plain,
! [SV1462: $i,SV782: $i,SV30: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV782 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1462 @ SV782 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV1462 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3994,plain,
! [SV1463: $i,SV783: $i,SV31: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3995,plain,
! [SV784: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV32 @ SV784 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV784 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3996,plain,
! [SV785: $i,SV34: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV34 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV785 @ SV785 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3997,plain,
! [SV1464: $i,SV786: $i,SV35: $i] :
( ( ! [SY4481: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4481 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SY4481 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3998,plain,
! [SV1465: $i,SV787: $i,SV36: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV36 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV787 @ SV1465 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SV1465 @ tc_nat ) @ ( c_Suc @ SV787 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV1465 @ SV787 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3999,plain,
! [SV1466: $i,SV789: $i,SV38: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV38 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV789 @ SV38 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV1466 @ SV38 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(4000,plain,
! [SV1467: $i,SV790: $i,SV39: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV39 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV790 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ ( c_HOL_Otimes__class_Otimes @ SV1467 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(4001,plain,
! [SV1468: $i,SV791: $i,SV40: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV791 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV1468 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV791 @ SV1468 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(4002,plain,
! [SV1469: $i,SV792: $i,SV41: $i] :
( ( ( c_lessequals @ SV41 @ SV792 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1469 @ SV41 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1469 @ SV792 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(4003,plain,
! [SV1470: $i,SV793: $i,SV42: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV42 @ SV793 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1470 @ SV793 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV42 @ SV1470 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(4004,plain,
! [SV1471: $i,SV794: $i,SV43: $i] :
( ( ! [SY4482: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1471 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SY4482 @ SV43 ) @ SV43 )
| ~ ( c_lessequals @ SV1471 @ SY4482 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(4005,plain,
! [SV1472: $i,SV795: $i,SV44: $i] :
( ( ! [SY4483: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SV1472 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SY4483 @ SV1472 @ SV44 ) @ SV44 )
| ~ ( c_lessequals @ SV795 @ SY4483 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(4006,plain,
! [SV1473: $i,SV796: $i,SV45: $i] :
( ( ! [SY4484: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
| ( c_lessequals @ SV796 @ SV1473 @ SV45 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY4484 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SY4484 @ SV1473 @ SV45 ) @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(4007,plain,
! [SV1474: $i,SV797: $i,SV46: $i] :
( ( ! [SY4485: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1474 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SY4485 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ SV1474 @ SY4485 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(4008,plain,
! [SV1475: $i,SV798: $i,SV47: $i] :
( ( ! [SY4486: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
| ( c_lessequals @ SV798 @ SV1475 @ SV47 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SY4486 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SV1475 @ SY4486 @ SV47 ) @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(4009,plain,
! [SV1476: $i,SV799: $i,SV48: $i] :
( ( ! [SY4487: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SV1476 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SY4487 @ SV1476 @ SV48 ) @ SV48 )
| ~ ( c_lessequals @ SV799 @ SY4487 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(4010,plain,
! [SV1477: $i,SV800: $i,SV49: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV49 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV1477 @ SV49 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV800 @ SV49 ) @ ( c_HOL_Oabs__class_Oabs @ SV1477 @ SV49 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(4011,plain,
! [SV1478: $i,SV801: $i,SV50: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(4012,plain,
! [SV1479: $i,SV802: $i,SV51: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
| ~ ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(4013,plain,
! [SV1480: $i,SV803: $i,SV52: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 )
| ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(4014,plain,
! [SV1481: $i,SV804: $i,SV53: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
| ~ ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
| ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(4015,plain,
! [SV1482: $i,SV805: $i,SV54: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV54 )
| ( ( c_HOL_Otimes__class_Otimes @ SV805 @ ( c_HOL_Otimes__class_Otimes @ SV805 @ SV1482 @ SV54 ) @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV805 @ SV1482 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(4016,plain,
! [SV55: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV55 @ tc_nat )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV55 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(4017,plain,
! [SV1483: $i,SV806: $i,SV56: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV56 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1483 @ SV56 ) @ SV806 @ SV56 )
= ( c_Divides_Odiv__class_Omod @ SV1483 @ SV806 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3291]) ).
thf(4018,plain,
! [SV1484: $i,SV807: $i,SV57: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV57 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1484 @ SV57 ) @ SV1484 @ SV57 )
= ( c_Divides_Odiv__class_Omod @ SV807 @ SV1484 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3292]) ).
thf(4019,plain,
! [SV1485: $i,SV808: $i,SV58: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
| ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SV1485 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3293]) ).
thf(4020,plain,
! [SV1486: $i,SV809: $i,SV59: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV1486 @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(4021,plain,
! [SV1487: $i,SV810: $i,SV60: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
| ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ( c_lessequals @ SV1487 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV1487 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(4022,plain,
! [SV1488: $i,SV811: $i,SV61: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
| ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1488 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(4023,plain,
! [SV1489: $i,SV812: $i,SV62: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(4024,plain,
! [SV1490: $i,SV813: $i,SV63: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(4025,plain,
! [SV1491: $i,SV814: $i,SV64: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(4026,plain,
! [SV1492: $i,SV815: $i,SV65: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(4027,plain,
! [SV1493: $i,SV816: $i,SV66: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(4028,plain,
! [SV817: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV67 @ SV817 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV817 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV67 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(4029,plain,
! [SV818: $i,SV68: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV68 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV818 @ SV818 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ SV818 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(4030,plain,
! [SV819: $i,SV69: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV69 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV819 @ SV819 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(4031,plain,
! [SV820: $i,SV70: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV70 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV820 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(4032,plain,
! [SV821: $i,SV71: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV71 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV821 @ SV71 ) @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(4033,plain,
! [SV822: $i,SV73: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV73 @ SV822 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV73 @ SV822 @ tc_nat ) @ SV822 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV822 @ SV73 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(4034,plain,
! [SV1494: $i,SV823: $i,SV76: $i] :
( ( ! [SY4488: $i] :
( ~ ( c_lessequals @ SV76 @ SV823 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1494 @ tc_nat ) @ SY4488 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV76 @ SV1494 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV823 @ SV76 @ tc_nat ) @ SV1494 @ tc_nat ) @ SY4488 @ tc_nat ) @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(4035,plain,
! [SV1495: $i,SV824: $i,SV77: $i] :
( ( ! [SY4489: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
| ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SY4489 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SY4489 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SY4489 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(4036,plain,
! [SV1496: $i,SV825: $i,SV78: $i] :
( ( ! [SY4490: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
| ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SY4490 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4490 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SY4490 @ SV1496 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(4037,plain,
! [SV1497: $i,SV826: $i,SV79: $i] :
( ( ! [SY4491: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV79 )
| ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SY4491 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SY4491 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SY4491 @ SV79 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(4038,plain,
! [SV1498: $i,SV827: $i,SV80: $i] :
( ( ! [SY4492: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring @ SV80 )
| ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SY4492 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4492 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SY4492 @ SV1498 @ SV80 ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(4039,plain,
! [SV828: $i,SV81: $i] :
( ( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV81 @ SV828 @ tc_nat ) @ SV828 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV828 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(4040,plain,
! [SV1499: $i,SV829: $i,SV82: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV82 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV829 @ SV82 ) @ ( c_HOL_Otimes__class_Otimes @ SV1499 @ SV1499 @ SV82 ) @ SV82 ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(4041,plain,
! [SV830: $i,SV83: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV83 ) @ SV830 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV83 @ SV830 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV830 @ SV83 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3315]) ).
thf(4042,plain,
! [SV1500: $i,SV831: $i,SV84: $i] :
( ( ! [SY4493: $i] :
( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SY4493 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SY4493 @ SV84 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(4043,plain,
! [SV1501: $i,SV832: $i,SV85: $i] :
( ( ! [SY4494: $i] :
( ~ ( class_Divides_Osemiring__div @ SV85 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SY4494 @ SV85 ) @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SY4494 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(4044,plain,
! [SV1502: $i,SV833: $i,SV86: $i] :
( ( ! [SY4495: $i] :
( ~ ( class_Divides_Osemiring__div @ SV86 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SY4495 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SY4495 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(4045,plain,
! [SV1503: $i,SV834: $i,SV87: $i] :
( ( ! [SY4496: $i] :
( ~ ( class_Divides_Osemiring__div @ SV87 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SY4496 @ SV87 ) @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SY4496 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(4046,plain,
! [SV1504: $i,SV835: $i,SV88: $i] :
( ( ! [SY4497: $i,SY4498: $i,SY4499: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SY4497 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4498 @ SV1504 @ SV88 ) @ SY4499 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SY4497 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4498 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SY4499 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(4047,plain,
! [SV1505: $i,SV836: $i,SV89: $i] :
( ( ! [SY4500: $i,SY4501: $i,SY4502: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 )
| ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SY4500 @ SV89 ) @ SY4501 @ SV89 ) @ SY4502 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4500 @ SY4501 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SY4501 @ SV89 ) @ SY4502 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(4048,plain,
! [SV1506: $i,SV837: $i,SV90: $i] :
( ( ! [SY4503: $i,SY4504: $i,SY4505: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SY4503 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4504 @ SV1506 @ SV90 ) @ SY4505 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SY4504 @ SV90 ) @ SV1506 @ SV90 ) @ SY4503 @ SV90 ) @ SY4505 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(4049,plain,
! [SV1507: $i,SV838: $i,SV91: $i] :
( ( ! [SY4506: $i,SY4507: $i,SY4508: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SY4506 @ SV91 ) @ SY4507 @ SV91 ) @ SY4508 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SY4506 @ SV91 ) @ SY4507 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SY4506 @ SV91 ) @ SY4508 @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(4050,plain,
! [SV839: $i,SV92: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV92 ) @ SV839 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV92 @ SV839 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3324]) ).
thf(4051,plain,
! [SV840: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV93 @ SV840 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV93 ) @ SV840 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3325]) ).
thf(4052,plain,
! [SV841: $i,SV94: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV94 ) @ SV841 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV841 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(4053,plain,
! [SV842: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ SV842 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV95 ) @ SV842 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(4054,plain,
! [SV1508: $i,SV843: $i,SV96: $i] :
( ( ! [SY4509: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SY4509 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SY4509 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3328]) ).
thf(4055,plain,
! [SV1509: $i,SV844: $i,SV97: $i] :
( ( ! [SY4510: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
| ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SY4510 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SY4510 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(4056,plain,
! [SV1510: $i,SV845: $i,SV98: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SV845 @ tc_nat ) @ SV1510 @ tc_nat )
| ~ ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SV1510 @ SV845 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV845 @ SV1510 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(4057,plain,
! [SV1511: $i,SV846: $i,SV99: $i] :
( ( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1511 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SV1511 @ tc_nat ) @ SV846 @ tc_nat )
| ~ ( c_lessequals @ SV1511 @ SV846 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(4058,plain,
! [SV1512: $i,SV850: $i,SV103: $i] :
( ( ! [SY4511: $i,SY4512: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4511 @ SV850 @ tc_nat ) @ SY4512 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4511 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SY4512 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV103 @ SY4511 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(4059,plain,
! [SV1513: $i,SV851: $i,SV104: $i] :
( ( ! [SY4513: $i,SY4514: $i] :
( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SY4513 @ tc_nat ) @ SY4514 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SY4513 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SY4513 @ tc_nat ) @ SY4514 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1513 @ SV851 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(4060,plain,
! [SV1514: $i,SV852: $i,SV105: $i] :
( ( ! [SY4515: $i,SY4516: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4515 @ SV852 @ tc_nat ) @ SY4516 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SY4515 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SY4516 @ tc_nat )
| ~ ( c_lessequals @ SY4515 @ SV105 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(4061,plain,
! [SV1515: $i,SV853: $i,SV106: $i] :
( ( ! [SY4517: $i,SY4518: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SY4517 @ tc_nat ) @ SY4518 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SY4517 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SY4518 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(4062,plain,
! [SV1516: $i,SV854: $i,SV107: $i] :
( ( ! [SY4519: $i,SY4520: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV107 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV1516 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4519 @ SV854 @ SV107 ) @ SV1516 @ SV107 ) @ SY4520 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4519 @ SV1516 @ SV107 ) @ SY4520 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(4063,plain,
! [SV1517: $i,SV855: $i,SV108: $i] :
( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV108 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV855 @ SV1517 @ SV108 ) @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV855 @ SV108 ) @ ( c_HOL_Oabs__class_Oabs @ SV1517 @ SV108 ) @ SV108 ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(4064,plain,
! [SV1518: $i,SV856: $i,SV109: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 )
| ( c_lessequals @ SV856 @ SV1518 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV856 @ SV109 ) @ SV1518 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(4065,plain,
! [SV1519: $i,SV857: $i,SV110: $i] :
( ( ! [SY4521: $i,SY4522: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SY4521 @ SY4522 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SY4521 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SY4522 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SY4521 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(4066,plain,
! [SV1520: $i,SV858: $i,SV111: $i] :
( ( ! [SY4523: $i] :
( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV858 @ SV1520 @ SV111 ) @ SY4523 @ SV111 ) @ SV1520 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV858 @ SY4523 @ SV111 ) @ SV1520 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(4067,plain,
! [SV1521: $i,SV859: $i,SV112: $i] :
( ( ! [SY4524: $i] :
( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SY4524 @ SV112 ) @ SV112 )
| ~ ( c_lessequals @ SV859 @ SY4524 @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(4068,plain,
! [SV1522: $i,SV860: $i,SV113: $i] :
( ( ! [SY4525: $i] :
( ~ ( class_Orderings_Olinorder @ SV113 )
| ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SY4525 @ SV113 ) @ SV113 )
| ~ ( c_lessequals @ SV860 @ SY4525 @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(4069,plain,
! [SV1523: $i,SV861: $i,SV114: $i] :
( ( ! [SY4526: $i] :
( ~ ( class_Orderings_Olinorder @ SV114 )
| ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SY4526 @ SV114 ) @ SV114 )
| ~ ( c_lessequals @ SV861 @ SY4526 @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(4070,plain,
! [SV1524: $i,SV862: $i,SV115: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV115 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV862 @ SV1524 @ SV115 ) @ SV1524 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(4071,plain,
! [SV1525: $i,SV863: $i,SV116: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV116 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV863 @ SV1525 @ SV116 ) @ SV863 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(4072,plain,
! [SV1526: $i,SV864: $i,SV117: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV864 @ tc_nat ) ) @ SV1526 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV117 ) @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SV1526 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV864 @ SV117 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(4073,plain,
! [SV1527: $i,SV865: $i,SV118: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV865 @ ( c_HOL_Otimes__class_Otimes @ SV1527 @ SV865 @ SV118 ) @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(4074,plain,
! [SV1528: $i,SV866: $i,SV119: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV119 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV866 @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV1528 @ SV119 ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(4075,plain,
! [SV1529: $i,SV867: $i,SV120: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV120 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV867 @ ( c_HOL_Otimes__class_Otimes @ SV867 @ SV1529 @ SV120 ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(4076,plain,
! [SV1530: $i,SV868: $i,SV121: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV121 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV868 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1530 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ SV868 @ SV1530 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(4077,plain,
! [SV1531: $i,SV869: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV122 )
| ( c_lessequals @ SV869 @ SV1531 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV869 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1531 @ SV122 ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(4078,plain,
! [SV870: $i,SV123: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV123 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV870 @ SV123 )
= ( c_HOL_Ozero__class_Ozero @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(4079,plain,
! [SV1532: $i,SV871: $i,SV124: $i] :
( ( ! [SY4527: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV124 )
| ~ ( class_Int_Onumber__ring @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SY4527 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SY4527 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(4080,plain,
! [SV1533: $i,SV872: $i,SV125: $i] :
( ( ! [SY4528: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV125 )
| ~ ( class_Int_Onumber__ring @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SY4528 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SY4528 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(4081,plain,
! [SV1534: $i,SV873: $i,SV126: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SV873 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SV1534 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SV1534 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV126 @ SV873 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(4082,plain,
! [SV1535: $i,SV874: $i,SV127: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SV874 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SV1535 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SV1535 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV127 @ SV874 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(4083,plain,
! [SV128: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV128 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV128
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(4084,plain,
! [SV1536: $i,SV875: $i,SV129: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV129 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV875 @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ SV1536 @ SV129 ) @ SV129 ) @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV875 @ SV1536 @ SV129 ) @ SV129 ) @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(4085,plain,
! [SV1537: $i,SV876: $i,SV130: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV130 )
| ( ( c_Orderings_Oord__class_Omin @ SV876 @ ( c_Orderings_Oord__class_Omin @ SV876 @ SV1537 @ SV130 ) @ SV130 )
= ( c_Orderings_Oord__class_Omin @ SV876 @ SV1537 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(4086,plain,
! [SV1538: $i,SV877: $i,SV131: $i] :
( ( ! [SY4529: $i,SY4530: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV131 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SY4529 @ SY4530 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SY4530 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SY4529 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(4087,plain,
! [SV878: $i,SV132: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV132 ) @ SV878 @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV132 @ SV878 @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV132 @ SV878 @ tc_nat ) )
= SV878 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(4088,plain,
! [SV1539: $i,SV879: $i,SV133: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SV879 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SV1539 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV133 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(4089,plain,
! [SV1540: $i,SV880: $i,SV134: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV134 @ SV880 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1540 @ SV880 @ tc_nat ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV880 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(4090,plain,
! [SV135: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(4091,plain,
! [SV1541: $i,SV881: $i,SV136: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Otimes__class_Otimes @ SV881 @ SV1541 @ SV136 )
= ( c_HOL_Otimes__class_Otimes @ SV1541 @ SV881 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(4092,plain,
! [SV137: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV137 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV137 ) @ ( c_HOL_Ozero__class_Ozero @ SV137 ) @ SV137 )
= ( c_HOL_Ozero__class_Ozero @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(4093,plain,
! [SV1542: $i,SV883: $i,SV139: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV139 )
| ( ( c_HOL_Otimes__class_Otimes @ SV883 @ SV1542 @ SV139 )
= ( c_HOL_Otimes__class_Otimes @ SV1542 @ SV883 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(4094,plain,
! [SV1543: $i,SV884: $i,SV140: $i] :
( ( ! [SY4531: $i] :
( ~ ( class_Divides_Osemiring__div @ SV140 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV884 @ SV1543 @ SV140 ) @ SY4531 @ SV140 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV884 @ SY4531 @ SV140 ) @ ( c_Divides_Odiv__class_Omod @ SV1543 @ SY4531 @ SV140 ) @ SV140 ) @ SY4531 @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(4095,plain,
! [SV141: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV141 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV141 ) @ SV141 )
= ( c_HOL_Ozero__class_Ozero @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3373]) ).
thf(4096,plain,
! [SV1544: $i,SV885: $i,SV142: $i] :
( ( ! [SY4532: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV142 )
| ( ( c_HOL_Oplus__class_Oplus @ SV885 @ ( c_HOL_Oplus__class_Oplus @ SV1544 @ SY4532 @ SV142 ) @ SV142 )
= ( c_HOL_Oplus__class_Oplus @ SV1544 @ ( c_HOL_Oplus__class_Oplus @ SV885 @ SY4532 @ SV142 ) @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(4097,plain,
! [SV1545: $i,SV886: $i,SV143: $i] :
( ( ! [SY4533: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV143 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV886 @ SV1545 @ SV143 ) @ SY4533 @ SV143 )
= ( c_HOL_Oplus__class_Oplus @ SV886 @ ( c_HOL_Oplus__class_Oplus @ SV1545 @ SY4533 @ SV143 ) @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(4098,plain,
! [SV1546: $i,SV887: $i,SV144: $i] :
( ( ! [SY4534: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SV1546 @ SY4534 @ SV144 ) @ SV144 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SY4534 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(4099,plain,
! [SV1547: $i,SV888: $i,SV145: $i] :
( ( ! [SY4535: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SV1547 @ SY4535 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SV1547 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3377]) ).
thf(4100,plain,
! [SV1548: $i,SV889: $i,SV146: $i] :
( ( ! [SY4536: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SV1548 @ SV146 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SY4536 @ SV146 ) @ SV1548 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(4101,plain,
! [SV1549: $i,SV890: $i,SV147: $i] :
( ( ! [SY4537: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SV1549 @ SV147 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY4537 @ SV890 @ SV147 ) @ SV1549 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(4102,plain,
! [SV1550: $i,SV891: $i,SV148: $i] :
( ( ! [SY4538: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 )
| ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SY4538 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SY4538 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(4103,plain,
! [SV1551: $i,SV894: $i,SV151: $i] :
( ( ! [SY4539: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SV1551 @ tc_nat ) @ tc_nat ) @ SY4539 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SV1551 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4539 @ SV151 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1551 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(4104,plain,
! [SV1552: $i,SV895: $i,SV152: $i] :
( ( ! [SY4540: $i] :
( ~ ( class_Ring__and__Field_Omult__mono1 @ SV152 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SY4540 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
| ~ ( c_lessequals @ SV1552 @ SY4540 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(4105,plain,
! [SV1553: $i,SV896: $i,SV153: $i] :
( ( ! [SY4541: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV153 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SY4541 @ SV153 ) @ SV153 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
| ~ ( c_lessequals @ SV1553 @ SY4541 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(4106,plain,
! [SV1554: $i,SV897: $i,SV154: $i] :
( ( ! [SY4542: $i] :
( ~ ( class_Ring__and__Field_Omult__mono @ SV154 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SY4542 @ SV1554 @ SV154 ) @ SV154 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
| ~ ( c_lessequals @ SV897 @ SY4542 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(4107,plain,
! [SV1555: $i,SV898: $i,SV155: $i] :
( ( ! [SY4543: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV155 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SY4543 @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SY4543 @ SV1555 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(4108,plain,
! [SV1556: $i,SV899: $i,SV156: $i] :
( ( ! [SY4544: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV156 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SY4544 @ SV1556 @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SY4544 @ SV899 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(4109,plain,
! [SV900: $i,SV157: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV157 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV900 @ SV900 @ SV157 )
= SV900 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3389]) ).
thf(4110,plain,
! [SV1557: $i,SV901: $i,SV158: $i] :
( ( ! [SY4545: $i,SY4546: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SY4545 @ SY4546 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SY4546 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SY4545 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(4111,plain,
! [SV1558: $i,SV902: $i,SV159: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV159 @ SV902 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1558 @ SV902 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV159 @ SV1558 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(4112,plain,
! [SV1559: $i,SV903: $i,SV160: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV903 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV1559 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV903 @ SV1559 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(4113,plain,
! [SV1560: $i,SV904: $i,SV161: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV904 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV1560 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV904 @ SV1560 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(4114,plain,
! [SV1561: $i,SV905: $i,SV162: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV162 @ SV905 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1561 @ SV905 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV162 @ SV1561 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(4115,plain,
! [SV1562: $i,SV906: $i,SV163: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV163 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV906 @ SV1562 @ tc_nat ) @ SV163 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV906 @ SV163 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1562 @ SV163 ) @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(4116,plain,
! [SV1563: $i,SV907: $i,SV164: $i] :
( ( ! [SY4547: $i] :
( ~ ( class_Divides_Osemiring__div @ SV164 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ ( c_Divides_Odiv__class_Omod @ SV1563 @ SY4547 @ SV164 ) @ SV164 ) @ SY4547 @ SV164 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ SV1563 @ SV164 ) @ SY4547 @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(4117,plain,
! [SV1564: $i,SV908: $i,SV165: $i] :
( ( ! [SY4548: $i] :
( ~ ( class_Divides_Osemiring__div @ SV165 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV908 @ SV1564 @ SV165 ) @ SY4548 @ SV165 ) @ SV1564 @ SV165 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV908 @ SY4548 @ SV165 ) @ SV1564 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(4118,plain,
! [SV1565: $i,SV909: $i,SV166: $i] :
( ( ! [SY4549: $i,SY4550: $i,SY4551: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV166 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SY4549 @ SY4550 @ SV166 ) @ SV166 ) @ SY4551 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SY4551 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SY4550 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(4119,plain,
! [SV1566: $i,SV910: $i,SV167: $i] :
( ( ! [SY4552: $i,SY4553: $i,SY4554: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV167 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SY4552 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SY4553 @ SY4554 @ SV167 ) @ SV167 ) @ SY4552 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SY4554 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(4120,plain,
! [SV1567: $i,SV911: $i,SV168: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV168 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(4121,plain,
! [SV1568: $i,SV912: $i,SV169: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV169 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(4122,plain,
! [SV1569: $i,SV913: $i,SV170: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV170 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(4123,plain,
! [SV914: $i,SV171: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV171 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV171 ) @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV914 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(4124,plain,
! [SV1570: $i,SV915: $i,SV172: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(4125,plain,
! [SV1571: $i,SV916: $i,SV173: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4126,plain,
! [SV1572: $i,SV917: $i,SV174: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4127,plain,
! [SV1573: $i,SV918: $i,SV175: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV175 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV918 @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ SV1573 @ SV175 ) @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1573 @ SV175 ) @ SV175 ) @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4128,plain,
! [SV1574: $i,SV919: $i,SV176: $i] :
( ( ! [SY4555: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV176 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1574 @ SV176 ) @ SY4555 @ SV176 )
= ( c_HOL_Otimes__class_Otimes @ SV919 @ ( c_HOL_Otimes__class_Otimes @ SV1574 @ SY4555 @ SV176 ) @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(4129,plain,
! [SV1575: $i,SV920: $i,SV177: $i] :
( ( ! [SY4556: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV177 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1575 @ SV177 ) @ SY4556 @ SV177 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SY4556 @ SV177 ) @ SV1575 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4130,plain,
! [SV1576: $i,SV921: $i,SV178: $i] :
( ( ! [SY4557: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV178 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1576 @ SV178 ) @ SY4557 @ SV178 )
= ( c_HOL_Otimes__class_Otimes @ SV921 @ ( c_HOL_Otimes__class_Otimes @ SV1576 @ SY4557 @ SV178 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4131,plain,
! [SV1577: $i,SV922: $i,SV179: $i] :
( ( ! [SY4558: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV179 )
| ( ( c_HOL_Otimes__class_Otimes @ SV922 @ ( c_HOL_Otimes__class_Otimes @ SV1577 @ SY4558 @ SV179 ) @ SV179 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV922 @ SV1577 @ SV179 ) @ SY4558 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4132,plain,
! [SV1578: $i,SV923: $i,SV180: $i] :
( ( ! [SY4559: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV180 )
| ( ( c_HOL_Otimes__class_Otimes @ SV923 @ ( c_HOL_Otimes__class_Otimes @ SV1578 @ SY4559 @ SV180 ) @ SV180 )
= ( c_HOL_Otimes__class_Otimes @ SV1578 @ ( c_HOL_Otimes__class_Otimes @ SV923 @ SY4559 @ SV180 ) @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4133,plain,
! [SV1579: $i,SV924: $i,SV181: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV181 @ SV924 @ tc_nat ) @ SV1579 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV181 @ ( c_HOL_Otimes__class_Otimes @ SV924 @ SV1579 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(4134,plain,
! [SV1580: $i,SV925: $i,SV182: $i] :
( ( ! [SY4560: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV182 )
| ( ( c_HOL_Otimes__class_Otimes @ SV925 @ ( c_HOL_Otimes__class_Otimes @ SV1580 @ SY4560 @ SV182 ) @ SV182 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV925 @ SV1580 @ SV182 ) @ SY4560 @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(4135,plain,
! [SV1581: $i,SV926: $i,SV183: $i] :
( ( ! [SY4561: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV926 @ SV1581 @ SV183 ) @ SY4561 @ SV183 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV926 @ SY4561 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV1581 @ SY4561 @ SV183 ) @ SV183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(4136,plain,
! [SV1582: $i,SV927: $i,SV184: $i] :
( ( ! [SY4562: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV184 )
| ( ( c_HOL_Otimes__class_Otimes @ SV927 @ ( c_HOL_Oplus__class_Oplus @ SV1582 @ SY4562 @ SV184 ) @ SV184 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1582 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SY4562 @ SV184 ) @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(4137,plain,
! [SV1583: $i,SV928: $i,SV185: $i] :
( ( ! [SY4563: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV185 )
| ( ( c_HOL_Otimes__class_Otimes @ SV928 @ ( c_HOL_Oplus__class_Oplus @ SV1583 @ SY4563 @ SV185 ) @ SV185 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1583 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SY4563 @ SV185 ) @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(4138,plain,
! [SV1584: $i,SV929: $i,SV186: $i] :
( ( ! [SY4564: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV929 @ SV1584 @ SV186 ) @ SY4564 @ SV186 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SY4564 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV1584 @ SY4564 @ SV186 ) @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4139,plain,
! [SV1585: $i,SV930: $i,SV187: $i] :
( ( ! [SY4565: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV187 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV930 @ SV1585 @ SV187 ) @ SY4565 @ SV187 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV930 @ SY4565 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV1585 @ SY4565 @ SV187 ) @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4140,plain,
! [SV1586: $i,SV931: $i,SV188: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV188 @ ( c_HOL_Oplus__class_Oplus @ SV931 @ SV1586 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV188 @ SV931 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV188 @ SV1586 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4141,plain,
! [SV1587: $i,SV932: $i,SV189: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV189 @ SV932 @ tc_nat ) @ SV1587 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV189 @ SV1587 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV932 @ SV1587 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4142,plain,
! [SV1588: $i,SV933: $i,SV190: $i] :
( ( ! [SY4566: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV190 )
| ( ( c_HOL_Otimes__class_Otimes @ SV933 @ ( c_HOL_Oplus__class_Oplus @ SV1588 @ SY4566 @ SV190 ) @ SV190 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1588 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SY4566 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(4143,plain,
! [SV1589: $i,SV934: $i,SV191: $i] :
( ( ! [SY4567: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV934 @ SV1589 @ SV191 ) @ SY4567 @ SV191 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SY4567 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV1589 @ SY4567 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(4144,plain,
! [SV935: $i,SV192: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV192 @ SV935 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV935 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(4145,plain,
! [SV936: $i,SV193: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV193 @ SV936 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV193 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(4146,plain,
! [SV937: $i,SV194: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV194 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV937 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV937 @ SV194 ) @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(4147,plain,
! [SV938: $i,SV195: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV195 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV938 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV938 @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(4148,plain,
! [SV1590: $i,SV939: $i,SV196: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
| ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SV1590 @ SV196 ) @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4149,plain,
! [SV1591: $i,SV940: $i,SV197: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
| ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1591 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SV1591 @ SV940 @ SV197 ) @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(4150,plain,
! [SV1592: $i,SV941: $i,SV198: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
| ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1592 @ SV198 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SV1592 @ SV198 ) @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4151,plain,
! [SV1593: $i,SV942: $i,SV199: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
| ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SV1593 @ SV942 @ SV199 ) @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(4152,plain,
! [SV200: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV200 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ SV200 ) @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(4153,plain,
! [SV1594: $i,SV943: $i,SV201: $i] :
( ( ! [SY4568: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV943 @ SV1594 @ SV201 ) @ ( c_HOL_Otimes__class_Otimes @ SY4568 @ SV1594 @ SV201 ) @ SV201 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV943 @ SY4568 @ SV201 ) @ SV1594 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(4154,plain,
! [SV1595: $i,SV944: $i,SV202: $i] :
( ( ! [SY4569: $i] :
( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1595 @ SY4569 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV944 @ SY4569 @ tc_nat )
| ~ ( c_lessequals @ SV202 @ SV1595 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4155,plain,
! [SV1596: $i,SV945: $i,SV204: $i] :
( ( ! [SY4570: $i,SY4571: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV204 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SY4570 @ SY4571 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY4570 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SY4571 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SY4570 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4156,plain,
! [SV1597: $i,SV946: $i,SV205: $i] :
( ( ! [SY4572: $i,SY4573: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV205 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SY4572 @ SY4573 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SY4573 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SY4572 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4157,plain,
! [SV947: $i,SV206: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV206 @ SV947 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV947 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV206 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(4158,plain,
! [SV948: $i,SV207: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV207 @ SV948 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV948 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV207 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3438]) ).
thf(4159,plain,
! [SV949: $i,SV208: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV208 @ tc_nat ) )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV949 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV208 @ SV949 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3439]) ).
thf(4160,plain,
! [SV950: $i,SV209: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV209 @ tc_nat ) )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV950 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV950 @ SV209 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(4161,plain,
! [SV951: $i,SV210: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SV951 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV951 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV210 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(4162,plain,
! [SV952: $i,SV211: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV211 @ SV952 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV952 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV211 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(4163,plain,
! [SV953: $i,SV212: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV212 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV953 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV212 @ SV953 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3443]) ).
thf(4164,plain,
! [SV954: $i,SV213: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV213 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV954 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV954 @ SV213 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3444]) ).
thf(4165,plain,
! [SV955: $i,SV214: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV214 @ SV955 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV955 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV214 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(4166,plain,
! [SV956: $i,SV215: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV215 @ SV956 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV956 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV215 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3446]) ).
thf(4167,plain,
! [SV957: $i,SV216: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV216 @ tc_nat )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV957 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV216 @ SV957 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3447]) ).
thf(4168,plain,
! [SV958: $i,SV217: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV217 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV958 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV217 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3448]) ).
thf(4169,plain,
! [SV959: $i,SV218: $i] :
( ( ( SV218
= ( c_Suc @ SV959 ) )
= $true )
| ( ( ( c_lessequals @ SV218 @ SV959 @ tc_nat )
| ~ ( c_lessequals @ SV218 @ ( c_Suc @ SV959 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(4170,plain,
! [SV1598: $i,SV960: $i,SV219: $i] :
( ( ! [SY4574: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SY4574 @ SV219 ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(4171,plain,
! [SV1599: $i,SV961: $i,SV220: $i] :
( ( ! [SY4575: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SY4575 @ SV961 @ SV220 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4172,plain,
! [SV1600: $i,SV962: $i,SV221: $i] :
( ( ! [SY4576: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SY4576 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SY4576 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4173,plain,
! [SV1601: $i,SV963: $i,SV223: $i] :
( ( ! [SY4577: $i,SY4578: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1601 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SY4577 @ SY4578 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SY4577 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV1601 @ SY4578 @ SV223 ) @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4174,plain,
! [SV964: $i,SV224: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV224 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV964 @ SV224 ) @ SV224 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV964 @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(4175,plain,
! [SV1602: $i,SV965: $i,SV225: $i] :
( ( ! [SY4579: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ SV965 @ SV1602 @ SV225 ) @ SY4579 @ SV225 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ SV965 @ SY4579 @ SV225 ) @ ( c_HOL_Oplus__class_Oplus @ SV1602 @ SY4579 @ SV225 ) @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(4176,plain,
! [SV966: $i,SV226: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV226 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV966 @ SV966 @ SV226 ) @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(4177,plain,
! [SV1603: $i,SV967: $i,SV227: $i] :
( ( ! [SY4580: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ SV967 @ ( c_HOL_Oplus__class_Oplus @ SV1603 @ SY4580 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1603 @ SV227 ) @ SY4580 @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4178,plain,
! [SV1604: $i,SV968: $i,SV228: $i] :
( ( ! [SY4581: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ SV968 @ ( c_HOL_Oplus__class_Oplus @ SV1604 @ SY4581 @ SV228 ) @ SV228 )
= ( c_HOL_Oplus__class_Oplus @ SV1604 @ ( c_HOL_Oplus__class_Oplus @ SV968 @ SY4581 @ SV228 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4179,plain,
! [SV1605: $i,SV969: $i,SV229: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV229 @ SV969 @ tc_nat ) @ SV1605 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV229 @ ( c_HOL_Oplus__class_Oplus @ SV969 @ SV1605 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4180,plain,
! [SV1606: $i,SV970: $i,SV230: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV230 @ ( c_HOL_Oplus__class_Oplus @ SV970 @ SV1606 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV970 @ ( c_HOL_Oplus__class_Oplus @ SV230 @ SV1606 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4181,plain,
! [SV1607: $i,SV971: $i,SV231: $i] :
( ( ! [SY4582: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV971 @ SV1607 @ SV231 ) @ SY4582 @ SV231 )
= ( c_HOL_Oplus__class_Oplus @ SV971 @ ( c_HOL_Oplus__class_Oplus @ SV1607 @ SY4582 @ SV231 ) @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(4182,plain,
! [SV1608: $i,SV972: $i,SV232: $i] :
( ( ! [SY4583: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ SV972 @ ( c_HOL_Oplus__class_Oplus @ SV1608 @ SY4583 @ SV232 ) @ SV232 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV972 @ SV1608 @ SV232 ) @ SY4583 @ SV232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4183,plain,
! [SV1609: $i,SV973: $i,SV233: $i] :
( ( ! [SY4584: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV1609 @ SV233 ) @ SY4584 @ SV233 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SY4584 @ SV233 ) @ SV1609 @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4184,plain,
! [SV1610: $i,SV974: $i,SV234: $i] :
( ( ! [SY4585: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ SV974 @ ( c_HOL_Oplus__class_Oplus @ SV1610 @ SY4585 @ SV234 ) @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV1610 @ ( c_HOL_Oplus__class_Oplus @ SV974 @ SY4585 @ SV234 ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4185,plain,
! [SV1611: $i,SV975: $i,SV235: $i] :
( ( ! [SY4586: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SV1611 @ SV235 ) @ SY4586 @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV975 @ ( c_HOL_Oplus__class_Oplus @ SV1611 @ SY4586 @ SV235 ) @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(4186,plain,
! [SV976: $i,SV236: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV236 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV976 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV976 @ SV236 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3467]) ).
thf(4187,plain,
! [SV1612: $i,SV977: $i,SV238: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV238 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ SV977 @ SV1612 @ SV238 ) @ SV238 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV977 @ SV238 ) @ ( c_HOL_Oabs__class_Oabs @ SV1612 @ SV238 ) @ SV238 ) @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4188,plain,
! [SV1613: $i,SV978: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ ( c_HOL_Oplus__class_Oplus @ SV978 @ SV1613 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV239 @ SV978 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4189,plain,
! [SV1614: $i,SV979: $i,SV240: $i] :
( ( ( c_lessequals @ SV240 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SV1614 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV240 @ SV1614 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4190,plain,
! [SV1615: $i,SV980: $i,SV241: $i] :
( ( ( c_lessequals @ SV241 @ SV980 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SV1615 @ tc_nat ) @ SV980 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(4191,plain,
! [SV1616: $i,SV981: $i,SV242: $i] :
( ( ( c_lessequals @ SV242 @ SV981 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV242 @ tc_nat ) @ SV981 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(4192,plain,
! [SV1617: $i,SV982: $i,SV243: $i] :
( ( ( c_lessequals @ SV243 @ ( c_HOL_Oplus__class_Oplus @ SV982 @ SV1617 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV243 @ SV982 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(4193,plain,
! [SV1618: $i,SV983: $i,SV244: $i] :
( ( ( c_lessequals @ SV244 @ ( c_HOL_Oplus__class_Oplus @ SV983 @ SV1618 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV244 @ SV1618 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(4194,plain,
! [SV1619: $i,SV984: $i,SV246: $i] :
( ( ! [SY4587: $i] :
( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ SV1619 @ SV246 ) @ SY4587 @ SV246 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ ( c_Divides_Odiv__class_Omod @ SV1619 @ SY4587 @ SV246 ) @ SV246 ) @ SY4587 @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4195,plain,
! [SV1620: $i,SV985: $i,SV247: $i] :
( ( ! [SY4588: $i] :
( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV985 @ SV1620 @ SV247 ) @ SY4588 @ SV247 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV985 @ SY4588 @ SV247 ) @ SV1620 @ SV247 ) @ SY4588 @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4196,plain,
! [SV1621: $i,SV986: $i,SV248: $i] :
( ( ! [SY4589: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SY4589 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SY4589 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4197,plain,
! [SV1622: $i,SV988: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV250 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV988 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV1622 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4198,plain,
! [SV1623: $i,SV989: $i,SV251: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV251 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV989 @ SV251 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1623 @ SV251 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4199,plain,
! [SV1624: $i,SV990: $i,SV252: $i] :
( ( ! [SY4590: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
| ( c_lessequals @ SV990 @ SV1624 @ SV252 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SY4590 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SY4590 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SY4590 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3482]) ).
thf(4200,plain,
! [SV1625: $i,SV991: $i,SV253: $i] :
( ( ! [SY4591: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
| ( c_lessequals @ SV991 @ SV1625 @ SV253 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SY4591 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4591 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SY4591 @ SV1625 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(4201,plain,
! [SV1626: $i,SV992: $i,SV254: $i] :
( ( ! [SY4592: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SY4592 @ SV254 ) @ SV254 )
| ~ ( c_lessequals @ SV1626 @ SY4592 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(4202,plain,
! [SV1627: $i,SV993: $i,SV255: $i] :
( ( ! [SY4593: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
| ( c_lessequals @ SV993 @ SV1627 @ SV255 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4593 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SY4593 @ SV1627 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SY4593 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(4203,plain,
! [SV1628: $i,SV994: $i,SV256: $i] :
( ( ! [SY4594: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SY4594 @ SV256 ) @ SV256 )
| ~ ( c_lessequals @ SY4594 @ SV1628 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4204,plain,
! [SV1629: $i,SV995: $i,SV257: $i] :
( ( ! [SY4595: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
| ( c_lessequals @ SV995 @ SV1629 @ SV257 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SY4595 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SY4595 @ SV995 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SY4595 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(4205,plain,
! [SV1630: $i,SV996: $i,SV258: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV996 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV1630 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV996 @ SV1630 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4206,plain,
! [SV1631: $i,SV997: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ SV997 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV997 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1631 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4207,plain,
! [SV1632: $i,SV998: $i,SV260: $i] :
( ( ( c_lessequals @ SV260 @ SV998 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1632 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV998 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(4208,plain,
! [SV1633: $i,SV999: $i,SV261: $i] :
( ( ( c_lessequals @ SV261 @ SV999 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1633 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SV1633 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV999 @ SV1633 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(4209,plain,
! [SV262: $i] :
( ( ( SV262
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV262 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
= $true )
| ( ( SV262
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(4210,plain,
! [SV1634: $i,SV1000: $i,SV263: $i] :
( ( ! [SY4596: $i,SY4597: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV263 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1634 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SY4596 @ SY4597 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SY4596 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SY4597 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SY4596 @ SV263 ) @ SY4597 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SY4596 @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SY4597 @ SV263 ) @ SV263 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4211,plain,
! [SV1635: $i,SV1001: $i,SV266: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV266 )
| ( ( c_Orderings_Oord__class_Omin @ SV1001 @ SV1635 @ SV266 )
= ( c_Orderings_Oord__class_Omin @ SV1635 @ SV1001 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4212,plain,
! [SV1636: $i,SV1002: $i,SV267: $i] :
( ( ! [SY4598: $i,SY4599: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV267 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1636 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4598 @ SV1636 @ SV267 ) @ SY4599 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV1002 @ SY4598 @ SV267 ) @ SV1636 @ SV267 ) @ SY4599 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4213,plain,
! [SV1637: $i,SV1003: $i,SV268: $i] :
( ( ! [SY4600: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1003 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1637 @ SV1003 @ tc_nat ) @ SY4600 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV268 @ SV1637 @ tc_nat ) @ SV1003 @ tc_nat ) @ SY4600 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4214,plain,
! [SV1004: $i,SV269: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV269 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV269 @ SV1004 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3497]) ).
thf(4215,plain,
! [SV1005: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV270 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV270 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3498]) ).
thf(4216,plain,
! [SV1638: $i,SV1006: $i,SV271: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4217,plain,
! [SV1639: $i,SV1007: $i,SV272: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV272 )
| ( SV1007
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1639 @ SV1639 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SV1007 @ SV1007 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(4218,plain,
! [SV1640: $i,SV1008: $i,SV273: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV273 )
| ( SV1008
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1008 @ SV1008 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1640 @ SV1640 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4219,plain,
! [SV1641: $i,SV1009: $i,SV275: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV275 @ SV1009 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1641 ) @ SV275 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1641 ) @ SV1009 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4220,plain,
! [SV1642: $i,SV1010: $i,SV276: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1010 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1642 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SV1642 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4221,plain,
! [SV1011: $i,SV277: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV277 ) @ SV1011 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1011 @ SV277 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3504]) ).
thf(4222,plain,
! [SV1012: $i,SV278: $i] :
( ( ( ~ ( c_lessequals @ SV278 @ SV1012 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV1012 ) @ SV278 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3505]) ).
thf(4223,plain,
! [SV1643: $i,SV1014: $i,SV281: $i] :
( ( ( c_lessequals @ SV281 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1014 @ SV281 @ tc_nat ) @ SV1643 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1643 @ SV1014 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4224,plain,
! [SV1015: $i,SV282: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV282 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1015 @ SV282 )
= SV1015 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV1015 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(4225,plain,
! [SV1644: $i,SV1016: $i,SV283: $i] :
( ( ! [SY4601: $i] :
( ~ ( class_Divides_Osemiring__div @ SV283 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ SV1644 @ SV283 ) @ SY4601 @ SV283 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ ( c_Divides_Odiv__class_Omod @ SV1644 @ SY4601 @ SV283 ) @ SV283 ) @ SY4601 @ SV283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(4226,plain,
! [SV1645: $i,SV1017: $i,SV284: $i] :
( ( ! [SY4602: $i] :
( ~ ( class_Divides_Osemiring__div @ SV284 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1017 @ SV1645 @ SV284 ) @ SY4602 @ SV284 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1017 @ SY4602 @ SV284 ) @ SV1645 @ SV284 ) @ SY4602 @ SV284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(4227,plain,
! [SV1646: $i,SV1018: $i,SV285: $i] :
( ( ( c_lessequals @ SV285 @ SV1018 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1646 ) @ SV285 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1646 ) @ SV1018 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(4228,plain,
! [SV1647: $i,SV1019: $i,SV286: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1019 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1647 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1019 @ SV1647 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4229,plain,
! [SV1648: $i,SV1020: $i,SV287: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV287 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV287 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1020 @ SV1020 @ SV287 ) @ ( c_HOL_Otimes__class_Otimes @ SV1648 @ SV1648 @ SV287 ) @ SV287 ) @ SV287 )
| ( SV1648
= ( c_HOL_Ozero__class_Ozero @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(4230,plain,
! [SV1649: $i,SV1021: $i,SV288: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV288 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV288 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1021 @ SV1021 @ SV288 ) @ ( c_HOL_Otimes__class_Otimes @ SV1649 @ SV1649 @ SV288 ) @ SV288 ) @ SV288 )
| ( SV1021
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4231,plain,
! [SV1022: $i,SV289: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV289 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1022 @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV289 ) @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(4232,plain,
! [SV291: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV291 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ SV291 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(4233,plain,
! [SV293: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV293 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV293
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(4234,plain,
! [SV1650: $i,SV1024: $i,SV296: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV296 @ SV1024 @ tc_nat ) @ SV1650 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV296 @ SV1650 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1024 @ SV1650 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4235,plain,
! [SV1651: $i,SV1025: $i,SV297: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV297 @ ( c_Divides_Odiv__class_Omod @ SV1025 @ SV1651 @ tc_nat ) @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV297 @ SV1025 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV297 @ SV1651 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4236,plain,
! [SV1652: $i,SV1026: $i,SV298: $i] :
( ( ! [SY4603: $i] :
( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SY4603 @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SY4603 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4237,plain,
! [SV1653: $i,SV1027: $i,SV299: $i] :
( ( ! [SY4604: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SY4604 @ SV1653 @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SY4604 @ SV1027 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4238,plain,
! [SV1654: $i,SV1028: $i,SV300: $i] :
( ( ! [SY4605: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SY4605 @ SV1654 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SY4605 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4239,plain,
! [SV1655: $i,SV1029: $i,SV301: $i] :
( ( ! [SY4606: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SY4606 @ SV1655 @ SV301 ) @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SY4606 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4240,plain,
! [SV1656: $i,SV1030: $i,SV302: $i] :
( ( ! [SY4607: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SY4607 @ SV1656 @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SY4607 @ SV1030 @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4241,plain,
! [SV1657: $i,SV1031: $i,SV303: $i] :
( ( ! [SY4608: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SY4608 @ SV303 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SY4608 @ SV1657 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(4242,plain,
! [SV1658: $i,SV1032: $i,SV304: $i] :
( ( ! [SY4609: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SY4609 @ SV304 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV1658 @ SY4609 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4243,plain,
! [SV1659: $i,SV1033: $i,SV305: $i] :
( ( ! [SY4610: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SY4610 @ SV305 ) @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SY4610 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4244,plain,
! [SV1660: $i,SV1034: $i,SV306: $i] :
( ( ! [SY4611: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SY4611 @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SY4611 @ SV1660 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(4245,plain,
! [SV1661: $i,SV1035: $i,SV307: $i] :
( ( ! [SY4612: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SY4612 @ SV307 ) @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV1661 @ SY4612 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(4246,plain,
! [SV1662: $i,SV1036: $i,SV308: $i] :
( ( ! [SY4613: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
| ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4613 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SY4613 @ SV1662 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SY4613 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4247,plain,
! [SV1663: $i,SV1037: $i,SV309: $i] :
( ( ! [SY4614: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SY4614 @ SV309 ) @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SY4614 @ SV1663 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4248,plain,
! [SV1664: $i,SV1038: $i,SV310: $i] :
( ( ! [SY4615: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4615 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SY4615 @ SV1038 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SY4615 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(4249,plain,
! [SV1665: $i,SV1039: $i,SV311: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1039 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1665 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV1665 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(4250,plain,
! [SV1666: $i,SV1040: $i,SV312: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV312 @ SV1040 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV1040 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1666 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4251,plain,
! [SV1667: $i,SV1041: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SV1041 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1667 @ SV1041 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1041 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1667 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4252,plain,
! [SV1668: $i,SV1042: $i,SV314: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1042 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1668 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1668 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4253,plain,
! [SV1669: $i,SV1043: $i,SV315: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1043 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1669 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1043 @ SV1669 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4254,plain,
! [SV1670: $i,SV1044: $i,SV316: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SV1044 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1670 @ SV1044 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV316 @ SV1670 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1044 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4255,plain,
! [SV1671: $i,SV1045: $i,SV317: $i] :
( ( ! [SY4616: $i] :
( ~ ( class_Divides_Osemiring__div @ SV317 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1045 @ ( c_HOL_Otimes__class_Otimes @ SV1671 @ SY4616 @ SV317 ) @ SV317 ) @ SV1671 @ SV317 )
= ( c_Divides_Odiv__class_Omod @ SV1045 @ SV1671 @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(4256,plain,
! [SV1672: $i,SV1046: $i,SV318: $i] :
( ( ! [SY4617: $i] :
( ~ ( class_Divides_Osemiring__div @ SV318 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1046 @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SY4617 @ SV318 ) @ SV318 ) @ SY4617 @ SV318 )
= ( c_Divides_Odiv__class_Omod @ SV1046 @ SY4617 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4257,plain,
! [SV1673: $i,SV1047: $i,SV319: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV319 @ SV1047 @ tc_nat ) @ SV1673 @ tc_nat ) @ SV1047 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1047 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4258,plain,
! [SV1674: $i,SV1048: $i,SV320: $i] :
( ( ! [SY4618: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV320 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
| ( SY4618
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SY4618 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SY4618 @ SV320 ) @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4259,plain,
! [SV1675: $i,SV1049: $i,SV321: $i] :
( ( ! [SY4619: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV321 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
| ( SY4619
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SY4619 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SY4619 @ SV1675 @ SV321 ) @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4260,plain,
! [SV1676: $i,SV1050: $i,SV322: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV322 @ SV1050 @ tc_nat )
| ( SV1676
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV322 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV1050 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4261,plain,
! [SV1677: $i,SV1051: $i,SV323: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4262,plain,
! [SV1678: $i,SV1052: $i,SV324: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 )
| ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4263,plain,
! [SV1679: $i,SV1053: $i,SV325: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4264,plain,
! [SV1680: $i,SV1054: $i,SV326: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 )
| ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4265,plain,
! [SV1681: $i,SV1055: $i,SV327: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4266,plain,
! [SV1682: $i,SV1056: $i,SV328: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 )
| ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4267,plain,
! [SV1683: $i,SV1057: $i,SV329: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(4268,plain,
! [SV330: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV330 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV330 ) @ SV330 ) @ ( c_HOL_Ozero__class_Ozero @ SV330 ) @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(4269,plain,
! [SV1684: $i,SV1058: $i,SV331: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4270,plain,
! [SV1685: $i,SV1059: $i,SV332: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4271,plain,
! [SV1686: $i,SV1060: $i,SV333: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV333 )
| ( ( c_Divides_Odiv__class_Omod @ SV1060 @ SV1686 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1686 @ SV1060 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4272,plain,
! [SV1061: $i,SV334: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 ) )
= $true )
| ( ( ( SV1061
= ( c_HOL_Ozero__class_Ozero @ SV334 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV334 ) @ SV1061 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(4273,plain,
! [SV335: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV335 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV335 )
= ( c_HOL_Ozero__class_Ozero @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3560]) ).
thf(4274,plain,
! [SV1062: $i,SV336: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV1062 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV336 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1062 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3561]) ).
thf(4275,plain,
! [SV1687: $i,SV1064: $i,SV338: $i] :
( ( ! [SY4620: $i] :
( ~ ( class_Orderings_Olinorder @ SV338 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1064 @ SV1687 @ SV338 ) @ SY4620 @ SV338 )
= ( c_Orderings_Oord__class_Omin @ SV1064 @ ( c_Orderings_Oord__class_Omin @ SV1687 @ SY4620 @ SV338 ) @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(4276,plain,
! [SV1688: $i,SV1065: $i,SV339: $i] :
( ( ! [SY4621: $i] :
( ~ ( class_Orderings_Olinorder @ SV339 )
| ( ( c_Orderings_Oord__class_Omin @ SV1065 @ ( c_Orderings_Oord__class_Omin @ SV1688 @ SY4621 @ SV339 ) @ SV339 )
= ( c_Orderings_Oord__class_Omin @ SV1688 @ ( c_Orderings_Oord__class_Omin @ SV1065 @ SY4621 @ SV339 ) @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(4277,plain,
! [SV1689: $i,SV1066: $i,SV340: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(4278,plain,
! [SV1067: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV341 @ SV1067 @ tc_nat ) @ SV1067 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1067 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(4279,plain,
! [SV1690: $i,SV1068: $i,SV342: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV342 )
| ( ( c_Orderings_Oord__class_Omin @ SV1068 @ SV1690 @ SV342 )
= SV1068 )
| ~ ( c_lessequals @ SV1068 @ SV1690 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4280,plain,
! [SV1691: $i,SV1069: $i,SV343: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV343 )
| ( ( c_Orderings_Oord__class_Omin @ SV1069 @ SV1691 @ SV343 )
= SV1691 )
| ~ ( c_lessequals @ SV1691 @ SV1069 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(4281,plain,
! [SV1070: $i,SV344: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV344 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1070 @ SV344 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(4282,plain,
! [SV1071: $i,SV345: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV345 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV1071 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(4283,plain,
! [SV1692: $i,SV1072: $i,SV346: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4284,plain,
! [SV1073: $i,SV347: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV347 @ ( c_Suc @ SV1073 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV347 @ SV1073 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(4285,plain,
! [SV1074: $i,SV348: $i] :
( ( ( c_lessequals @ SV348 @ SV1074 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV348 @ ( c_Suc @ SV1074 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(4286,plain,
! [SV349: $i] :
( ( ( c_lessequals @ SV349 @ SV349 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Suc @ SV349 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(4287,plain,
! [SV1693: $i,SV1075: $i,SV350: $i] :
( ( ! [SY4622: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1693 @ SY4622 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1075 @ SY4622 @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SV1693 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4288,plain,
! [SV1694: $i,SV1076: $i,SV351: $i] :
( ( ! [SY4623: $i,SY4624: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SY4623 @ SY4624 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SV1694 @ SY4624 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SY4623 @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4289,plain,
! [SV1695: $i,SV1077: $i,SV352: $i] :
( ( ! [SY4625: $i,SY4626: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4625 @ SV1077 @ tc_nat ) @ SY4626 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SY4625 @ tc_nat ) @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ SY4626 @ tc_nat ) )
| ~ ( c_lessequals @ SY4625 @ SV352 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4290,plain,
! [SV1696: $i,SV1078: $i,SV353: $i] :
( ( ! [SY4627: $i,SY4628: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV1078 @ tc_nat ) @ SV1696 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4627 @ SV1078 @ tc_nat ) @ SY4628 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1696 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4627 @ SV353 @ tc_nat ) @ SV1078 @ tc_nat ) @ SY4628 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV353 @ SY4627 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4291,plain,
! [SV1079: $i,SV354: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV354 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV1079 @ SV354 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ ( c_HOL_Oplus__class_Oplus @ SV1079 @ SV1079 @ SV354 ) @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(4292,plain,
! [SV1080: $i,SV355: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV355 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ ( c_HOL_Oplus__class_Oplus @ SV1080 @ SV1080 @ SV355 ) @ SV355 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ SV1080 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(4293,plain,
! [SV1697: $i,SV1081: $i,SV356: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV356 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1081 @ SV1697 @ SV356 ) @ SV1697 @ SV356 )
= ( c_Divides_Odiv__class_Omod @ SV1081 @ SV1697 @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(4294,plain,
! [SV1698: $i,SV1082: $i,SV357: $i] :
( ( ! [SY4629: $i,SY4630: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1082 @ SV1698 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SY4629 @ SY4630 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1082 @ SY4629 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1698 @ SY4630 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4295,plain,
! [SV1699: $i,SV1083: $i,SV358: $i] :
( ( ! [SY4631: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SY4631 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SY4631 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3583]) ).
thf(4296,plain,
! [SV1084: $i,SV359: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SV1084 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV359 @ SV1084 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(4297,plain,
! [SV1700: $i,SV1085: $i,SV360: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
| ~ ( c_lessequals @ SV1085 @ SV1700 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4298,plain,
! [SV1701: $i,SV1086: $i,SV361: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
| ~ ( c_lessequals @ SV1701 @ SV1086 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(4299,plain,
! [SV1702: $i,SV1087: $i,SV362: $i] :
( ( ! [SY4632: $i,SY4633: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV362 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1702 @ SV362 ) @ SY4632 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4633 @ SV1702 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SY4633 @ SV362 ) @ SV1702 @ SV362 ) @ SY4632 @ SV362 ) @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3587]) ).
thf(4300,plain,
! [SV1703: $i,SV1088: $i,SV363: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1088 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1703 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1088 @ SV1703 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(4301,plain,
! [SV1704: $i,SV1089: $i,SV364: $i] :
( ( ! [SY4634: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV364 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV1704 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SY4634 @ SV364 ) @ SV364 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1704 @ SY4634 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(4302,plain,
! [SV1705: $i,SV1090: $i,SV365: $i] :
( ( ! [SY4635: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV365 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SV1705 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SY4635 @ SV1705 @ SV365 ) @ SV365 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SY4635 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4303,plain,
! [SV1091: $i,SV366: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV366 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV1091 @ SV366 ) @ SV366 )
= ( c_HOL_Oabs__class_Oabs @ SV1091 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(4304,plain,
! [SV1094: $i,SV369: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV369 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oabs__class_Oabs @ SV1094 @ SV369 ) @ SV369 )
| ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4305,plain,
! [SV1095: $i,SV370: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV370 @ SV1095 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV1095 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4306,plain,
! [SV1096: $i,SV371: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV371 @ SV1096 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV371 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(4307,plain,
! [SV1097: $i,SV372: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV372 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1097 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 )
= SV1097 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(4308,plain,
! [SV1098: $i,SV373: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV373 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1098 @ SV1098 @ SV373 )
= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(4309,plain,
! [SV1706: $i,SV1099: $i,SV374: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV374 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1099 @ SV1706 @ SV374 )
= ( c_HOL_Oplus__class_Oplus @ SV1706 @ SV1099 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4310,plain,
! [SV1707: $i,SV1101: $i,SV376: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV376 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1101 @ SV1707 @ SV376 )
= ( c_HOL_Oplus__class_Oplus @ SV1707 @ SV1101 @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4311,plain,
! [SV1708: $i,SV1102: $i,SV377: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV377 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1102 @ SV1708 @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ SV1708 @ SV1102 @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4312,plain,
! [SV1709: $i,SV1103: $i,SV378: $i] :
( ( ! [SY4636: $i] :
( ~ ( class_Divides_Osemiring__div @ SV378 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1103 @ SV1709 @ SV378 ) @ SY4636 @ SV378 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1103 @ SY4636 @ SV378 ) @ ( c_Divides_Odiv__class_Omod @ SV1709 @ SY4636 @ SV378 ) @ SV378 ) @ SY4636 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4313,plain,
! [SV1710: $i,SV1104: $i,SV379: $i] :
( ( ! [SY4637: $i] :
( ~ ( class_Orderings_Olinorder @ SV379 )
| ( c_lessequals @ SV1104 @ SV1710 @ SV379 )
| ~ ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SV1710 @ SY4637 @ SV379 ) @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(4314,plain,
! [SV1711: $i,SV1105: $i,SV380: $i] :
( ( ! [SY4638: $i] :
( ~ ( class_Orderings_Olinorder @ SV380 )
| ( c_lessequals @ SV1105 @ SV1711 @ SV380 )
| ~ ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SY4638 @ SV1711 @ SV380 ) @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4315,plain,
! [SV1712: $i,SV1106: $i,SV381: $i] :
( ( ! [SY4639: $i] :
( ~ ( class_Orderings_Olinorder @ SV381 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SV1712 @ SV381 ) @ SY4639 @ SV381 )
| ~ ( c_lessequals @ SV1106 @ SY4639 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4316,plain,
! [SV1713: $i,SV1107: $i,SV382: $i] :
( ( ! [SY4640: $i] :
( ~ ( class_Orderings_Olinorder @ SV382 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SV1713 @ SV382 ) @ SY4640 @ SV382 )
| ~ ( c_lessequals @ SV1713 @ SY4640 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4317,plain,
! [SV1714: $i,SV1108: $i,SV383: $i] :
( ( ! [SY4641: $i] :
( ~ ( class_Orderings_Olinorder @ SV383 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SV1714 @ SV383 ) @ SY4641 @ SV383 )
| ~ ( c_lessequals @ SV1108 @ SY4641 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4318,plain,
! [SV1715: $i,SV1109: $i,SV384: $i] :
( ( ! [SY4642: $i] :
( ~ ( class_Orderings_Olinorder @ SV384 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SV1715 @ SV384 ) @ SY4642 @ SV384 )
| ~ ( c_lessequals @ SV1715 @ SY4642 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4319,plain,
! [SV1716: $i,SV1110: $i,SV385: $i] :
( ( ! [SY4643: $i] :
( ~ ( class_Orderings_Olinorder @ SV385 )
| ( c_lessequals @ SV1110 @ SV1716 @ SV385 )
| ~ ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SV1716 @ SY4643 @ SV385 ) @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4320,plain,
! [SV1717: $i,SV1111: $i,SV386: $i] :
( ( ! [SY4644: $i] :
( ~ ( class_Orderings_Olinorder @ SV386 )
| ( c_lessequals @ SV1111 @ SV1717 @ SV386 )
| ~ ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SY4644 @ SV1717 @ SV386 ) @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4321,plain,
! [SV1112: $i,SV387: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV387 ) )
= $true )
| ( ( c_lessequals @ SV1112 @ ( c_HOL_Oabs__class_Oabs @ SV1112 @ SV387 ) @ SV387 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3612]) ).
thf(4322,plain,
! [SV1718: $i,SV1113: $i,SV388: $i] :
( ( ! [SY4645: $i] :
( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
| ( c_lessequals @ SY4645 @ SV1718 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SY4645 @ SV1113 @ SV388 ) @ SV1718 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4323,plain,
! [SV1719: $i,SV1114: $i,SV389: $i] :
( ( ! [SY4646: $i] :
( ~ ( c_lessequals @ SV389 @ SV1114 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV389 @ SV1719 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1114 @ SV389 @ tc_nat ) @ SV1719 @ tc_nat ) @ SY4646 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1114 @ SV1719 @ tc_nat ) @ SY4646 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3614]) ).
thf(4324,plain,
! [SV1720: $i,SV1115: $i,SV390: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV390 @ SV1115 @ tc_nat ) @ SV1720 @ tc_nat )
| ~ ( c_lessequals @ SV390 @ ( c_HOL_Oplus__class_Oplus @ SV1720 @ SV1115 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4325,plain,
! [SV1721: $i,SV1116: $i,SV391: $i] :
( ( ( c_lessequals @ SV391 @ ( c_HOL_Oplus__class_Oplus @ SV1116 @ SV1721 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV391 @ SV1721 @ tc_nat ) @ SV1116 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4326,plain,
! [SV1722: $i,SV1117: $i,SV392: $i] :
( ( ! [SY4647: $i,SY4648: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SY4647 @ tc_nat ) @ SY4648 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SY4647 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SY4648 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4327,plain,
! [SV1723: $i,SV1118: $i,SV393: $i] :
( ( ! [SY4649: $i,SY4650: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4649 @ SV1118 @ tc_nat ) @ SY4650 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SY4649 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SY4650 @ tc_nat )
| ~ ( c_lessequals @ SY4649 @ SV393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4328,plain,
! [SV1724: $i,SV1119: $i,SV394: $i] :
( ( ! [SY4651: $i,SY4652: $i] :
( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SY4651 @ tc_nat ) @ SY4652 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SY4651 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SY4651 @ tc_nat ) @ SY4652 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1724 @ SV1119 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4329,plain,
! [SV1725: $i,SV1120: $i,SV395: $i] :
( ( ! [SY4653: $i,SY4654: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4653 @ SV1120 @ tc_nat ) @ SY4654 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4653 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SY4654 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV395 @ SY4653 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4330,plain,
! [SV1726: $i,SV1121: $i,SV396: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV396 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1726 @ tc_nat ) @ SV396 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1121 @ SV396 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1726 @ SV396 ) @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4331,plain,
! [SV1727: $i,SV1122: $i,SV397: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV397 @ SV1122 @ tc_nat ) @ SV1727 @ tc_nat ) ) @ SV1122 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV1727 ) @ SV1122 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4332,plain,
! [SV1123: $i,SV398: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV398 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1123 @ SV398 ) @ ( c_HOL_Oabs__class_Oabs @ SV1123 @ SV398 ) @ SV398 )
= ( c_HOL_Otimes__class_Otimes @ SV1123 @ SV1123 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(4333,plain,
! [SV1124: $i,SV399: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV399 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV399 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1124 @ SV399 ) @ SV399 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(4334,plain,
! [SV1125: $i,SV400: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV400 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV400 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1125 @ SV400 ) @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3625]) ).
thf(4335,plain,
! [SV1126: $i,SV401: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV401 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1126 @ ( c_HOL_Ozero__class_Ozero @ SV401 ) @ SV401 )
= SV1126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(4336,plain,
! [SV1127: $i,SV402: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV402 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV402 ) @ SV1127 @ SV402 )
= SV1127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(4337,plain,
! [SV1128: $i,SV403: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV403 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1128 @ ( c_HOL_Ozero__class_Ozero @ SV403 ) @ SV403 )
= SV1128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(4338,plain,
! [SV1129: $i,SV404: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV404 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV404 )
| ( SV1129
= ( c_HOL_Oplus__class_Oplus @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3629]) ).
thf(4339,plain,
! [SV1130: $i,SV405: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV405 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1130 @ SV405 )
= SV1130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3630]) ).
thf(4340,plain,
! [SV1131: $i,SV406: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV406 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1131 @ SV406 )
= SV1131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(4341,plain,
! [SV1132: $i,SV410: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV410 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1132 @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV410 )
= SV1132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(4342,plain,
! [SV1133: $i,SV411: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV411 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV411 ) @ SV1133 @ SV411 )
= SV1133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(4343,plain,
! [SV1728: $i,SV1134: $i,SV412: $i] :
( ( ! [SY4655: $i,SY4656: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SY4655 @ SY4656 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SV1728 @ SY4656 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SY4655 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(4344,plain,
! [SV1729: $i,SV1135: $i,SV413: $i] :
( ( ! [SY4657: $i,SY4658: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SY4657 @ SY4658 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SY4658 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SY4657 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3635]) ).
thf(4345,plain,
! [SV1730: $i,SV1136: $i,SV414: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(4346,plain,
! [SV1731: $i,SV1137: $i,SV415: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4347,plain,
! [SV1732: $i,SV1138: $i,SV416: $i] :
( ( ! [SY4659: $i] :
( ~ ( class_Orderings_Oorder @ SV416 )
| ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
| ~ ( c_lessequals @ SV1138 @ SY4659 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SY4659 @ SV1732 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4348,plain,
! [SV1733: $i,SV1139: $i,SV417: $i] :
( ( ! [SY4660: $i] :
( ~ ( class_Orderings_Oorder @ SV417 )
| ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SY4660 @ SV417 )
| ~ ( c_lessequals @ SY4660 @ SV1733 @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4349,plain,
! [SV1734: $i,SV1140: $i,SV418: $i] :
( ( ! [SY4661: $i] :
( ~ ( class_Orderings_Opreorder @ SV418 )
| ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
| ~ ( c_lessequals @ SY4661 @ SV1734 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SY4661 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4350,plain,
! [SV1735: $i,SV1141: $i,SV419: $i] :
( ( ! [SY4662: $i] :
( ~ ( class_Orderings_Opreorder @ SV419 )
| ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SY4662 @ SV1735 @ SV419 )
| ~ ( c_lessequals @ SV1141 @ SY4662 @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(4351,plain,
! [SV1736: $i,SV1142: $i,SV420: $i] :
( ( ! [SY4663: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SV1736 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SY4663 @ SV1736 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SV1142 @ SY4663 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(4352,plain,
! [SV1737: $i,SV1143: $i,SV421: $i] :
( ( ! [SY4664: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SV1737 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SY4664 @ SV1737 @ SV421 ) @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SV1143 @ SY4664 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4353,plain,
! [SV1738: $i,SV1144: $i,SV422: $i] :
( ( ! [SY4665: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_HOL_Oord__class_Oless @ SV1144 @ SV1738 @ SV422 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SY4665 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SV1738 @ SY4665 @ SV422 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(4354,plain,
! [SV1739: $i,SV1145: $i,SV423: $i] :
( ( ! [SY4666: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV1739 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SY4666 @ SV423 ) @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SY4666 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4355,plain,
! [SV1740: $i,SV1146: $i,SV424: $i] :
( ( ! [SY4667: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV1740 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SY4667 @ SV424 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SY4667 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(4356,plain,
! [SV1741: $i,SV1147: $i,SV425: $i] :
( ( ! [SY4668: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
| ( c_HOL_Oord__class_Oless @ SV1147 @ SV1741 @ SV425 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY4668 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SY4668 @ SV1741 @ SV425 ) @ SV425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(4357,plain,
! [SV1742: $i,SV1148: $i,SV426: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV426 )
| ( c_lessequals @ SV1148 @ SV1742 @ SV426 )
| ~ ( c_HOL_Oord__class_Oless @ SV1148 @ SV1742 @ SV426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(4358,plain,
! [SV1743: $i,SV1149: $i,SV427: $i] :
( ( ~ ( class_Orderings_Oorder @ SV427 )
| ( c_lessequals @ SV1149 @ SV1743 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1149 @ SV1743 @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3649]) ).
thf(4359,plain,
! [SV1744: $i,SV1150: $i,SV428: $i] :
( ( ! [SY4669: $i,SY4670: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SY4669 @ SY4670 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SY4670 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SY4669 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(4360,plain,
! [SV1745: $i,SV1151: $i,SV429: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV429 )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SV1745 @ SV429 )
| ( c_lessequals @ SV1745 @ SV1151 @ SV429 )
| ~ ( c_lessequals @ SV1151 @ SV1745 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3651]) ).
thf(4361,plain,
! [SV1746: $i,SV1152: $i,SV430: $i] :
( ( ! [SY4671: $i] :
( ~ ( class_Orderings_Olinorder @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SY4671 @ SV1746 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SY4671 @ SV1152 @ SV430 ) @ SV1746 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4362,plain,
! [SV1747: $i,SV1153: $i,SV431: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV431 )
| ( c_HOL_Oord__class_Oless @ SV1153 @ SV1747 @ SV431 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1153 @ SV431 ) @ SV1747 @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4363,plain,
! [SV1748: $i,SV1154: $i,SV432: $i] :
( ( ! [SY4672: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SY4672 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SY4672 @ SV432 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3654]) ).
thf(4364,plain,
! [SV1749: $i,SV1155: $i,SV433: $i] :
( ( ! [SY4673: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4673 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SY4673 @ SV1155 @ SV433 ) @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(4365,plain,
! [SV1750: $i,SV1156: $i,SV434: $i] :
( ( ~ ( class_Orderings_Oorder @ SV434 )
| ( c_HOL_Oord__class_Oless @ SV1156 @ SV1750 @ SV434 )
| ( SV1750 = SV1156 )
| ~ ( c_lessequals @ SV1156 @ SV1750 @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(4366,plain,
! [SV1751: $i,SV1157: $i,SV435: $i] :
( ( ~ ( class_Orderings_Oorder @ SV435 )
| ( c_HOL_Oord__class_Oless @ SV1157 @ SV1751 @ SV435 )
| ~ ( c_lessequals @ SV1157 @ SV1751 @ SV435 )
| ( SV1751 = SV1157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(4367,plain,
! [SV1752: $i,SV1158: $i,SV436: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV436 )
| ( SV1158 = SV1752 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1752 @ SV436 )
| ~ ( c_lessequals @ SV1158 @ SV1752 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4368,plain,
! [SV1753: $i,SV1159: $i,SV437: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV437 )
| ( SV1159 = SV1753 )
| ~ ( c_lessequals @ SV1159 @ SV1753 @ SV437 )
| ( c_HOL_Oord__class_Oless @ SV1159 @ SV1753 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4369,plain,
! [SV1754: $i,SV1160: $i,SV438: $i] :
( ( ~ ( class_Orderings_Oorder @ SV438 )
| ( c_HOL_Oord__class_Oless @ SV1160 @ SV1754 @ SV438 )
| ~ ( c_lessequals @ SV1160 @ SV1754 @ SV438 )
| ( SV1160 = SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(4370,plain,
! [SV1755: $i,SV1161: $i,SV439: $i] :
( ( ~ ( class_Orderings_Oorder @ SV439 )
| ( c_HOL_Oord__class_Oless @ SV1161 @ SV1755 @ SV439 )
| ( SV1161 = SV1755 )
| ~ ( c_lessequals @ SV1161 @ SV1755 @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4371,plain,
! [SV1756: $i,SV1162: $i,SV440: $i] :
( ( ~ ( class_Orderings_Oorder @ SV440 )
| ( SV1162 = SV1756 )
| ( c_HOL_Oord__class_Oless @ SV1162 @ SV1756 @ SV440 )
| ~ ( c_lessequals @ SV1162 @ SV1756 @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4372,plain,
! [SV1757: $i,SV1163: $i,SV441: $i] :
( ( ~ ( class_Orderings_Oorder @ SV441 )
| ( c_HOL_Oord__class_Oless @ SV1163 @ SV1757 @ SV441 )
| ( SV1163 = SV1757 )
| ~ ( c_lessequals @ SV1163 @ SV1757 @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3663]) ).
thf(4373,plain,
! [SV1758: $i,SV1164: $i,SV442: $i] :
( ( ! [SY4674: $i] :
( ~ ( class_Orderings_Olinorder @ SV442 )
| ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SY4674 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SY4674 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(4374,plain,
! [SV1759: $i,SV1165: $i,SV443: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV443 )
| ~ ( c_lessequals @ SV1165 @ SV1759 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ SV1759 @ SV1165 @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(4375,plain,
! [SV1760: $i,SV1166: $i,SV444: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV444 )
| ( c_HOL_Oord__class_Oless @ SV1166 @ SV1760 @ SV444 )
| ( c_lessequals @ SV1760 @ SV1166 @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(4376,plain,
! [SV1167: $i,SV445: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV445 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1167 @ SV1167 @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1167 @ SV1167 @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3667]) ).
thf(4377,plain,
! [SV1168: $i,SV446: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV446 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1168 @ SV1168 @ SV446 )
| ( c_lessequals @ SV1168 @ SV1168 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(4378,plain,
! [SV1761: $i,SV1169: $i,SV447: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1169 @ SV1761 @ SV447 )
| ~ ( c_lessequals @ SV1761 @ SV1169 @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3669]) ).
thf(4379,plain,
! [SV1762: $i,SV1170: $i,SV448: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV448 )
| ( c_lessequals @ SV1170 @ SV1762 @ SV448 )
| ( c_HOL_Oord__class_Oless @ SV1762 @ SV1170 @ SV448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4380,plain,
! [SV1763: $i,SV1171: $i,SV449: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV449 )
| ( c_HOL_Oord__class_Oless @ SV1171 @ SV1763 @ SV449 )
| ( c_lessequals @ SV1763 @ SV1171 @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4381,plain,
! [SV1764: $i,SV1172: $i,SV450: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV450 )
| ~ ( c_lessequals @ SV1172 @ SV1764 @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ SV1764 @ SV1172 @ SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4382,plain,
! [SV1765: $i,SV1173: $i,SV451: $i] :
( ( ! [SY4675: $i] :
( ~ ( class_Orderings_Olinorder @ SV451 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SV1765 @ SV451 ) @ SY4675 @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SY4675 @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4383,plain,
! [SV1766: $i,SV1174: $i,SV452: $i] :
( ( ! [SY4676: $i] :
( ~ ( class_Orderings_Olinorder @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SV1766 @ SV452 ) @ SY4676 @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SY4676 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(4384,plain,
! [SV1767: $i,SV1175: $i,SV453: $i] :
( ( ! [SY4677: $i] :
( ~ ( class_Orderings_Olinorder @ SV453 )
| ( c_HOL_Oord__class_Oless @ SV1175 @ SV1767 @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SY4677 @ SV1767 @ SV453 ) @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(4385,plain,
! [SV1768: $i,SV1176: $i,SV454: $i] :
( ( ! [SY4678: $i] :
( ~ ( class_Orderings_Olinorder @ SV454 )
| ( c_HOL_Oord__class_Oless @ SV1176 @ SV1768 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SY4678 @ SV454 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4386,plain,
! [SV1769: $i,SV1177: $i,SV455: $i] :
( ( ! [SY4679: $i] :
( ~ ( class_Orderings_Olinorder @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SV1769 @ SV455 ) @ SY4679 @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1769 @ SY4679 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(4387,plain,
! [SV1770: $i,SV1178: $i,SV456: $i] :
( ( ! [SY4680: $i] :
( ~ ( class_Orderings_Olinorder @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SV1770 @ SV456 ) @ SY4680 @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SY4680 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3678]) ).
thf(4388,plain,
! [SV1771: $i,SV1179: $i,SV457: $i] :
( ( ! [SY4681: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV457 )
| ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SV1771 @ SY4681 @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1771 @ SV457 ) @ SV457 ) @ SY4681 @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3679]) ).
thf(4389,plain,
! [SV1772: $i,SV1180: $i,SV458: $i] :
( ( ! [SY4682: $i,SY4683: $i,SY4684: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SY4682 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4683 @ SV1772 @ SV458 ) @ SY4684 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SY4682 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4683 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SY4684 @ SV458 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3680]) ).
thf(4390,plain,
! [SV1773: $i,SV1181: $i,SV459: $i] :
( ( ! [SY4685: $i,SY4686: $i,SY4687: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SY4685 @ SV459 ) @ SY4686 @ SV459 ) @ SY4687 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4685 @ SY4686 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SY4686 @ SV459 ) @ SY4687 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3681]) ).
thf(4391,plain,
! [SV1774: $i,SV1182: $i,SV460: $i] :
( ( ! [SY4688: $i,SY4689: $i,SY4690: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SY4688 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4689 @ SV1774 @ SV460 ) @ SY4690 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SY4689 @ SV460 ) @ SV1774 @ SV460 ) @ SY4688 @ SV460 ) @ SY4690 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(4392,plain,
! [SV1775: $i,SV1183: $i,SV461: $i] :
( ( ! [SY4691: $i,SY4692: $i,SY4693: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SY4691 @ SV461 ) @ SY4692 @ SV461 ) @ SY4693 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SY4691 @ SV461 ) @ SY4692 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SY4691 @ SV461 ) @ SY4693 @ SV461 ) @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3683]) ).
thf(4393,plain,
! [SV1776: $i,SV1184: $i,SV462: $i] :
( ( ! [SY4694: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV462 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SY4694 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SY4694 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SY4694 @ SV462 ) @ SV1184 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3684]) ).
thf(4394,plain,
! [SV1777: $i,SV1185: $i,SV463: $i] :
( ( ! [SY4695: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV463 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV1185 @ SV1777 @ SV463 ) @ SY4695 @ SV463 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV1185 @ SY4695 @ SV463 ) @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SY4695 @ SV463 ) @ SV463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(4395,plain,
! [SV1778: $i,SV1186: $i,SV464: $i] :
( ( ! [SY4696: $i] :
( ~ ( class_Divides_Oring__div @ SV464 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ SV1778 @ SV464 ) @ SY4696 @ SV464 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ ( c_Divides_Odiv__class_Omod @ SV1778 @ SY4696 @ SV464 ) @ SV464 ) @ SY4696 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3686]) ).
thf(4396,plain,
! [SV1779: $i,SV1187: $i,SV465: $i] :
( ( ! [SY4697: $i] :
( ~ ( class_Divides_Oring__div @ SV465 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1187 @ SV1779 @ SV465 ) @ SY4697 @ SV465 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1187 @ SY4697 @ SV465 ) @ SV1779 @ SV465 ) @ SY4697 @ SV465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4397,plain,
! [SV1780: $i,SV1188: $i,SV466: $i] :
( ( ! [SY4698: $i] :
( ~ ( class_Divides_Oring__div @ SV466 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1188 @ SV1780 @ SV466 ) @ SY4698 @ SV466 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1188 @ SY4698 @ SV466 ) @ ( c_Divides_Odiv__class_Omod @ SV1780 @ SY4698 @ SV466 ) @ SV466 ) @ SY4698 @ SV466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(4398,plain,
! [SV1781: $i,SV1189: $i,SV467: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV467 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1189 @ SV1781 @ SV467 ) @ SV467 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1781 @ SV1189 @ SV467 ) @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3689]) ).
thf(4399,plain,
! [SV1782: $i,SV1190: $i,SV468: $i] :
( ( ! [SY4699: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SY4699 @ SV468 ) @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SY4699 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(4400,plain,
! [SV1191: $i,SV469: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV469 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(4401,plain,
! [SV1192: $i,SV470: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV470 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1192 @ SV1192 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(4402,plain,
! [SV1193: $i,SV471: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV471 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1193 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= SV1193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(4403,plain,
! [SV1194: $i,SV472: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV472 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1194 @ SV1194 @ SV472 )
= ( c_HOL_Ozero__class_Ozero @ SV472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3694]) ).
thf(4404,plain,
! [SV1195: $i,SV473: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV473 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV473 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1195 @ SV1195 @ SV473 )
= ( c_HOL_Ozero__class_Ozero @ SV473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(4405,plain,
! [SV1783: $i,SV1196: $i,SV474: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV474 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1783 @ SV474 ) @ SV1783 @ SV474 )
= SV1196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(4406,plain,
! [SV1784: $i,SV1197: $i,SV475: $i] :
( ( ! [SY4700: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV475 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1197 @ ( c_HOL_Ominus__class_Ominus @ SV1784 @ SY4700 @ SV475 ) @ SV475 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV1784 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SY4700 @ SV475 ) @ SV475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(4407,plain,
! [SV1785: $i,SV1198: $i,SV476: $i] :
( ( ! [SY4701: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV476 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1198 @ ( c_HOL_Ominus__class_Ominus @ SV1785 @ SY4701 @ SV476 ) @ SV476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV1785 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SY4701 @ SV476 ) @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(4408,plain,
! [SV1786: $i,SV1199: $i,SV477: $i] :
( ( ! [SY4702: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV477 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1199 @ SV1786 @ SV477 ) @ SY4702 @ SV477 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1199 @ SY4702 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1786 @ SY4702 @ SV477 ) @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(4409,plain,
! [SV1787: $i,SV1200: $i,SV478: $i] :
( ( ! [SY4703: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV478 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1200 @ SV1787 @ SV478 ) @ SY4703 @ SV478 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1200 @ SY4703 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1787 @ SY4703 @ SV478 ) @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3700]) ).
thf(4410,plain,
! [SV1788: $i,SV1201: $i,SV479: $i] :
( ( ! [SY4704: $i,SY4705: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV479 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1201 @ SV1788 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SY4704 @ SY4705 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ SY4704 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SV1788 @ SY4705 @ SV479 ) @ SV479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(4411,plain,
! [SV1789: $i,SV1202: $i,SV480: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV480 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1789 @ SV480 ) @ SV1789 @ SV480 )
= SV1202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(4412,plain,
! [SV1790: $i,SV1203: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1203 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1790 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1203 @ SV1790 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(4413,plain,
! [SV1791: $i,SV1204: $i,SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV482 @ SV1204 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1791 @ SV482 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1791 @ SV1204 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4414,plain,
! [SV1792: $i,SV1205: $i,SV483: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV483 @ SV1205 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1792 @ SV1205 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV1792 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3705]) ).
thf(4415,plain,
! [SV1206: $i,SV484: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV484 @ SV1206 @ tc_nat ) @ SV484 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(4416,plain,
! [SV1207: $i,SV485: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV485 @ SV1207 @ tc_nat ) @ SV1207 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4417,plain,
! [SV1208: $i,SV487: $i] :
( ( ( c_lessequals @ SV487 @ SV1208 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV487 @ SV1208 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(4418,plain,
! [SV1209: $i,SV488: $i] :
( ( ( c_lessequals @ SV488 @ SV1209 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV488 @ SV1209 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3710]) ).
thf(4419,plain,
! [SV1793: $i,SV1210: $i,SV489: $i] :
( ( ! [SY4706: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1793 @ SY4706 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1210 @ SY4706 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1793 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(4420,plain,
! [SV1211: $i,SV490: $i] :
( ( ( SV490 = SV1211 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV490 @ SV1211 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV490 @ ( c_Suc @ SV1211 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(4421,plain,
! [SV1212: $i,SV491: $i] :
( ( ( SV491 = SV1212 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1212 @ ( c_Suc @ SV491 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1212 @ SV491 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3713]) ).
thf(4422,plain,
! [SV1213: $i,SV493: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV493 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1213 @ ( c_HOL_Ozero__class_Ozero @ SV493 ) @ SV493 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(4423,plain,
! [SV1214: $i,SV494: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV494 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV494 ) @ SV1214 @ SV494 )
= ( c_HOL_Ozero__class_Ozero @ SV494 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3715]) ).
thf(4424,plain,
! [SV1215: $i,SV495: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV495 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1215 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= ( c_HOL_Ozero__class_Ozero @ SV495 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(4425,plain,
! [SV1216: $i,SV496: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV496 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV496 ) @ SV1216 @ SV496 )
= ( c_HOL_Ozero__class_Ozero @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(4426,plain,
! [SV1217: $i,SV497: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV497 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV497 ) @ SV1217 @ SV497 )
= ( c_HOL_Ozero__class_Ozero @ SV497 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3718]) ).
thf(4427,plain,
! [SV1218: $i,SV500: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV500 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ SV500 ) @ SV500 )
= ( c_HOL_Ozero__class_Ozero @ SV500 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3719]) ).
thf(4428,plain,
! [SV1219: $i,SV501: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV501 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1219 @ ( c_HOL_Ozero__class_Ozero @ SV501 ) @ SV501 )
= ( c_HOL_Ozero__class_Ozero @ SV501 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(4429,plain,
! [SV1220: $i,SV502: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV502 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV502 ) @ SV1220 @ SV502 )
= ( c_HOL_Ozero__class_Ozero @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3721]) ).
thf(4430,plain,
! [SV1221: $i,SV503: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV503 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV503 ) @ SV1221 @ SV503 )
= ( c_HOL_Ozero__class_Ozero @ SV503 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3722]) ).
thf(4431,plain,
! [SV1222: $i,SV504: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV504 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1222 @ ( c_HOL_Ozero__class_Ozero @ SV504 ) @ SV504 )
= ( c_HOL_Ozero__class_Ozero @ SV504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(4432,plain,
! [SV1223: $i,SV505: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV505 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV1223 @ SV505 )
= ( c_HOL_Ozero__class_Ozero @ SV505 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(4433,plain,
! [SV1224: $i,SV506: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV506 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1224 @ ( c_HOL_Ozero__class_Ozero @ SV506 ) @ SV506 )
= ( c_HOL_Ozero__class_Ozero @ SV506 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(4434,plain,
! [SV1794: $i,SV1225: $i,SV507: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV507 @ ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1794 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV507 @ SV1794 @ tc_nat ) @ SV1225 @ tc_nat ) )
| ~ ( c_lessequals @ SV1794 @ SV1225 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(4435,plain,
! [SV1795: $i,SV1226: $i,SV509: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV509 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1226 @ SV509 ) @ SV1795 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV1226 @ SV1795 @ SV509 ) @ SV509 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SV1795 @ SV509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(4436,plain,
! [SV1227: $i,SV510: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ ( c_HOL_Oplus__class_Oplus @ SV1227 @ SV510 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ SV1227 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3728]) ).
thf(4437,plain,
! [SV1228: $i,SV511: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ SV1228 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ ( c_HOL_Oplus__class_Oplus @ SV1228 @ SV511 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(4438,plain,
! [SV1796: $i,SV1229: $i,SV512: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV512 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1229 @ SV1796 @ SV512 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1229 @ SV512 ) @ SV1796 @ SV512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(4439,plain,
! [SV1797: $i,SV1230: $i,SV513: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV513 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1230 @ SV513 ) @ SV1797 @ SV513 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1230 @ SV1797 @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(4440,plain,
! [SV1798: $i,SV1231: $i,SV514: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV514 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ SV1798 @ SV514 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ ( c_HOL_Oabs__class_Oabs @ SV1798 @ SV514 ) @ SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(4441,plain,
! [SV1799: $i,SV1232: $i,SV515: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV515 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ ( c_HOL_Oabs__class_Oabs @ SV1799 @ SV515 ) @ SV515 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ SV1799 @ SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(4442,plain,
! [SV1233: $i,SV516: $i] :
( ( ( ~ ( c_lessequals @ SV516 @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV516 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV516 @ tc_nat ) @ SV516 @ tc_nat )
= SV1233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3734]) ).
thf(4443,plain,
! [SV1800: $i,SV1234: $i,SV517: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(4444,plain,
! [SV1239: $i,SV522: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SV1239 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV522 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1239 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(4445,plain,
! [SV1801: $i,SV1240: $i,SV523: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV523 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1240 @ SV1801 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1240 @ SV1801 @ SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(4446,plain,
! [SV1802: $i,SV1241: $i,SV524: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV524 )
| ( c_lessequals @ SV1241 @ SV1802 @ SV524 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1241 @ SV1802 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(4447,plain,
! [SV1242: $i,SV525: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV525 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1242 @ SV525 ) @ ( c_HOL_Ozero__class_Ozero @ SV525 ) @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(4448,plain,
! [SV1243: $i,SV526: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV526 @ SV1243 @ tc_nat ) @ SV1243 @ tc_nat )
= SV526 )
= $true )
| ( ( ~ ( c_lessequals @ SV1243 @ SV526 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4449,plain,
! [SV1244: $i,SV527: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV527 @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV527 @ tc_nat ) @ tc_nat )
= SV1244 )
= $true )
| ( ( ~ ( c_lessequals @ SV527 @ SV1244 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(4450,plain,
! [SV1245: $i,SV528: $i] :
( ( ( ~ ( c_lessequals @ SV528 @ SV1245 @ tc_nat ) )
= $true )
| ( ( SV1245
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ SV528 @ tc_nat ) @ SV528 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(4451,plain,
! [SV1803: $i,SV1246: $i,SV529: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SV1246 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1803 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV1246 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(4452,plain,
! [SV1804: $i,SV1247: $i,SV530: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SV1247 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV1247 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1804 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(4453,plain,
! [SV1805: $i,SV1248: $i,SV531: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1248 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1805 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1248 @ SV1805 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(4454,plain,
! [SV1806: $i,SV1249: $i,SV532: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV532 @ SV1249 @ tc_nat ) @ SV1806 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV1806 @ tc_nat ) @ SV1249 @ tc_nat ) )
| ~ ( c_lessequals @ SV1249 @ SV532 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3750]) ).
thf(4455,plain,
! [SV1807: $i,SV1250: $i,SV533: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV533 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1807 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV1250 @ tc_nat ) @ SV1807 @ tc_nat ) )
| ~ ( c_lessequals @ SV1807 @ SV1250 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3751]) ).
thf(4456,plain,
! [SV1251: $i,SV534: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV534 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1251 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV534 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1251 @ SV534 ) @ SV534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3752]) ).
thf(4457,plain,
! [SV1252: $i,SV535: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV535 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1252 @ SV535 ) @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1252 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(4458,plain,
! [SV1808: $i,SV1253: $i,SV536: $i] :
( ( ! [SY4707: $i,SY4708: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SY4707 @ SY4708 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SY4708 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SY4707 @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(4459,plain,
! [SV1809: $i,SV1254: $i,SV537: $i] :
( ( ! [SY4709: $i,SY4710: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SY4709 @ SY4710 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SY4710 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SY4709 @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3755]) ).
thf(4460,plain,
! [SV1810: $i,SV1255: $i,SV538: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV538 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SV1810 @ SV538 ) @ SV538 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1255 @ SV538 ) @ ( c_HOL_Oabs__class_Oabs @ SV1810 @ SV538 ) @ SV538 ) @ SV538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(4461,plain,
! [SV1256: $i,SV539: $i] :
( ( ( c_lessequals @ SV539 @ ( c_Suc @ SV1256 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV539 @ SV1256 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(4462,plain,
! [SV1257: $i,SV540: $i] :
( ( ( c_lessequals @ SV540 @ SV1257 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV540 ) @ SV1257 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(4463,plain,
! [SV1258: $i,SV541: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV541 @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1258 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1258 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV541 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3759]) ).
thf(4464,plain,
! [SV1259: $i,SV542: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV542 @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV542 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1259 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV542 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3760]) ).
thf(4465,plain,
! [SV1811: $i,SV1260: $i,SV544: $i] :
( ( ! [SY4711: $i] :
( ~ ( class_Divides_Osemiring__div @ SV544 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SV1811 @ SV544 ) @ SY4711 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SY4711 @ SV544 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY4711 @ SV1811 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(4466,plain,
! [SV1261: $i,SV545: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV545 ) )
= $true )
| ( ( ( c_lessequals @ SV1261 @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1261 @ SV1261 @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(4467,plain,
! [SV1262: $i,SV546: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV546 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1262 @ SV1262 @ SV546 ) @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
| ~ ( c_lessequals @ SV1262 @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3764]) ).
thf(4468,plain,
! [SV1263: $i,SV547: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV547 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1263 @ SV547 )
= SV1263 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(4469,plain,
! [SV1264: $i,SV548: $i] :
( ( ( ~ ( class_Ring__and__Field_Oabs__if @ SV548 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1264 @ SV548 )
= SV1264 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ ( c_HOL_Ozero__class_Ozero @ SV548 ) @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(4470,plain,
! [SV1812: $i,SV1265: $i,SV549: $i] :
( ( ! [SY4712: $i,SY4713: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SY4712 @ SY4713 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SY4713 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SY4712 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(4471,plain,
! [SV1813: $i,SV1266: $i,SV550: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV550 )
| ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SV1813 @ SV550 ) @ SV550 ) @ SV550 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SV1813 @ SV550 ) @ SV550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(4472,plain,
! [SV552: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV552 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ SV552 ) @ SV552 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(4473,plain,
! [SV1268: $i,SV553: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV553 @ SV1268 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1268 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV553 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3771]) ).
thf(4474,plain,
! [SV1269: $i,SV554: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV554 ) )
= $true )
| ( ( c_lessequals @ SV1269 @ SV1269 @ SV554 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(4475,plain,
! [SV1270: $i,SV555: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV555 ) )
= $true )
| ( ( c_lessequals @ SV1270 @ SV1270 @ SV555 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(4476,plain,
! [SV1814: $i,SV1271: $i,SV557: $i] :
( ( ( c_lessequals @ SV557 @ SV1271 @ tc_nat )
| ~ ( c_lessequals @ SV1814 @ SV1271 @ tc_nat )
| ~ ( c_lessequals @ SV557 @ SV1814 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4477,plain,
! [SV1815: $i,SV1272: $i,SV559: $i] :
( ( ! [SY4714: $i,SY4715: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
| ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SY4714 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SY4715 @ SY4714 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SY4715 @ SV559 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(4478,plain,
! [SV1816: $i,SV1273: $i,SV560: $i] :
( ( ! [SY4716: $i] :
( ~ ( class_Orderings_Opreorder @ SV560 )
| ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SY4716 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV1273 @ SY4716 @ SV560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(4479,plain,
! [SV1817: $i,SV1274: $i,SV561: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(4480,plain,
! [SV1818: $i,SV1275: $i,SV562: $i] :
( ( ! [SY4717: $i] :
( ~ ( class_Orderings_Oorder @ SV562 )
| ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
| ~ ( c_lessequals @ SV1275 @ SY4717 @ SV562 )
| ~ ( c_lessequals @ SY4717 @ SV1818 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(4481,plain,
! [SV1276: $i,SV563: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV563 @ tc_nat )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1276 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV1276 @ SV563 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3779]) ).
thf(4482,plain,
! [SV1819: $i,SV1278: $i,SV565: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV565 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1278 @ SV1819 @ SV565 ) @ SV1278 @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4483,plain,
! [SV1820: $i,SV1279: $i,SV566: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV566 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1279 @ SV1820 @ SV566 ) @ SV1820 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4484,plain,
! [SV1280: $i,SV567: $i] :
( ( ( SV567 = SV1280 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV567 @ ( c_Suc @ SV1280 ) @ tc_nat )
| ~ ( c_lessequals @ SV1280 @ SV567 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3783]) ).
thf(4485,plain,
! [SV568: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV568 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ SV568 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ ( c_HOL_Ozero__class_Ozero @ SV568 ) @ SV568 ) @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(4486,plain,
! [SV1821: $i,SV1281: $i,SV569: $i] :
( ( ! [SY4718: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
| ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SY4718 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SY4718 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SY4718 @ SV1281 @ SV569 ) @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4487,plain,
! [SV1822: $i,SV1282: $i,SV570: $i] :
( ( ! [SY4719: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1822 @ SY4719 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SY4719 @ SV570 ) @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(4488,plain,
! [SV1823: $i,SV1283: $i,SV571: $i] :
( ( ! [SY4720: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
| ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SY4720 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SY4720 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SY4720 @ SV571 ) @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(4489,plain,
! [SV1824: $i,SV1284: $i,SV572: $i] :
( ( ! [SY4721: $i] :
( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1824 @ SY4721 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SY4721 @ SV1284 @ SV572 ) @ SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(4490,plain,
! [SV1825: $i,SV1285: $i,SV573: $i] :
( ( ! [SY4722: $i] :
( ~ ( class_Divides_Osemiring__div @ SV573 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV1825 @ SV573 ) @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SY4722 @ SV573 ) @ SV573 )
= ( c_HOL_Otimes__class_Otimes @ SV1285 @ ( c_Divides_Odiv__class_Omod @ SV1825 @ SY4722 @ SV573 ) @ SV573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(4491,plain,
! [SV1826: $i,SV1286: $i,SV574: $i] :
( ( ! [SY4723: $i] :
( ~ ( class_Divides_Osemiring__div @ SV574 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV1826 @ SV574 ) @ ( c_HOL_Otimes__class_Otimes @ SY4723 @ SV1826 @ SV574 ) @ SV574 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1286 @ SY4723 @ SV574 ) @ SV1826 @ SV574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(4492,plain,
! [SV1287: $i,SV575: $i] :
( ( ( c_lessequals @ SV575 @ SV1287 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1287 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV575 @ SV1287 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(4493,plain,
! [SV1288: $i,SV576: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV576 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ ( c_HOL_Oabs__class_Oabs @ SV1288 @ SV576 ) @ SV576 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(4494,plain,
! [SV1289: $i,SV577: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV577 ) @ ( c_Suc @ SV1289 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV577 @ SV1289 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(4495,plain,
! [SV1290: $i,SV578: $i] :
( ( ( c_lessequals @ SV578 @ SV1290 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV578 ) @ ( c_Suc @ SV1290 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(4496,plain,
! [SV1827: $i,SV1291: $i,SV579: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV579 )
| ( c_lessequals @ SV1291 @ SV1827 @ SV579 )
| ( c_lessequals @ SV1827 @ SV1291 @ SV579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(4497,plain,
! [SV1828: $i,SV1292: $i,SV580: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV1292 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV580 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1828 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4498,plain,
! [SV1829: $i,SV1293: $i,SV581: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SV1829 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1829 @ SV1293 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1829 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(4499,plain,
! [SV1294: $i,SV582: $i] :
( ( ( c_lessequals @ SV582 @ SV1294 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1294 @ SV582 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(4500,plain,
! [SV1295: $i,SV583: $i] :
( ( ( SV583 = SV1295 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV583 @ ( c_Suc @ SV1295 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV583 @ SV1295 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3799]) ).
thf(4501,plain,
! [SV1296: $i,SV586: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV586 @ ( c_Suc @ SV1296 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1296 @ SV586 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3802]) ).
thf(4502,plain,
! [SV1297: $i,SV587: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV587 @ SV1297 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1297 @ ( c_Suc @ SV587 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(4503,plain,
! [SV1298: $i,SV589: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV589 @ SV1298 @ tc_nat )
= $true )
| ( ( ( SV589 = SV1298 )
| ~ ( c_lessequals @ SV589 @ SV1298 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3805]) ).
thf(4504,plain,
! [SV1299: $i,SV590: $i] :
( ( ( SV590 = SV1299 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV1299 @ tc_nat )
| ~ ( c_lessequals @ SV590 @ SV1299 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(4505,plain,
! [SV1300: $i,SV591: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV591 @ SV1300 @ tc_nat )
= $true )
| ( ( ( SV591 = SV1300 )
| ~ ( c_lessequals @ SV591 @ SV1300 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(4506,plain,
! [SV1301: $i,SV592: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV592 @ SV1301 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV592 ) @ SV1301 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3808]) ).
thf(4507,plain,
! [SV1302: $i,SV593: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV593 @ ( c_Suc @ SV1302 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV593 @ SV1302 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3809]) ).
thf(4508,plain,
! [SV1830: $i,SV1303: $i,SV594: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV594 @ SV1303 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1830 @ SV594 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1830 @ SV1303 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(4509,plain,
! [SV1831: $i,SV1304: $i,SV595: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV595 @ SV1304 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV595 @ SV1831 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV1831 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(4510,plain,
! [SV1832: $i,SV1305: $i,SV598: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SV1305 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1832 @ SV1305 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV598 @ SV1832 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(4511,plain,
! [SV1306: $i,SV599: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV599 @ SV1306 @ tc_nat )
= SV599 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV599 @ SV1306 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3813]) ).
thf(4512,plain,
! [SV1833: $i,SV1307: $i,SV600: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV600 @ ( c_HOL_Oplus__class_Oplus @ SV1307 @ SV1833 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV1307 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3814]) ).
thf(4513,plain,
! [SV1834: $i,SV1308: $i,SV601: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV601 @ ( c_HOL_Oplus__class_Oplus @ SV1308 @ SV1834 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV601 @ SV1834 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3815]) ).
thf(4514,plain,
! [SV1835: $i,SV1309: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV1309 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV602 @ SV1835 @ tc_nat ) @ SV1309 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3816]) ).
thf(4515,plain,
! [SV1836: $i,SV1310: $i,SV603: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV603 @ ( c_HOL_Oplus__class_Oplus @ SV1310 @ SV1836 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV603 @ SV1310 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(4516,plain,
! [SV1837: $i,SV1311: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Oplus__class_Oplus @ SV1311 @ SV1837 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ SV1837 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(4517,plain,
! [SV1312: $i,SV605: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV605 ) @ SV1312 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV605 )
= SV1312 )
| ~ ( c_HOL_Oord__class_Oless @ SV605 @ SV1312 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(4518,plain,
! [SV1313: $i,SV606: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV606 ) @ ( c_Suc @ SV1313 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV606 @ SV1313 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3820]) ).
thf(4519,plain,
! [SV1314: $i,SV607: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV607 @ SV1314 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV607 ) @ ( c_Suc @ SV1314 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(4520,plain,
! [SV1315: $i,SV608: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV608 ) @ ( c_Suc @ SV1315 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV608 @ SV1315 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(4521,plain,
! [SV1838: $i,SV1316: $i,SV609: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV609 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1316 @ SV1838 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1316 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1838 @ SV609 ) @ SV609 ) )
| ~ ( c_lessequals @ SV1838 @ SV1316 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(4522,plain,
! [SV1317: $i,SV610: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV610 @ ( c_Suc @ SV1317 ) @ tc_nat ) @ SV610 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV610 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4523,plain,
! [SV611: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV611 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV611 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV611 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(4524,plain,
! [SV1839: $i,SV1319: $i,SV613: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV613 @ SV1319 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV613 @ SV1839 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1319 @ SV1839 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4525,plain,
! [SV1840: $i,SV1320: $i,SV614: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV614 @ SV1320 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1840 @ SV1320 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV614 @ SV1840 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(4526,plain,
! [SV1841: $i,SV1321: $i,SV615: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV615 ) @ SV1321 @ tc_nat ) @ ( c_Suc @ SV1841 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV615 @ SV1321 @ tc_nat ) @ SV1841 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4527,plain,
! [SV1322: $i,SV616: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_HOL_Ominus__class_Ominus @ SV616 @ SV1322 @ tc_nat ) @ tc_nat )
= SV1322 )
= $true )
| ( ( ~ ( c_lessequals @ SV1322 @ SV616 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3830]) ).
thf(4528,plain,
! [SV1842: $i,SV1323: $i,SV617: $i] :
( ( ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV617 @ SV1323 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1842 @ SV1323 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV617 @ SV1842 @ tc_nat ) @ SV1323 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4529,plain,
! [SV1843: $i,SV1324: $i,SV618: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SV1324 @ SV1843 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1843 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1324 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(4530,plain,
! [SV1844: $i,SV1325: $i,SV621: $i] :
( ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1844 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ SV1844 @ SV621 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(4531,plain,
! [SV1845: $i,SV1326: $i,SV622: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV622 @ SV1845 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV1845 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(4532,plain,
! [SV1846: $i,SV1327: $i,SV623: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV623 @ SV1327 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1846 @ SV1327 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV623 @ SV1846 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4533,plain,
! [SV1847: $i,SV1328: $i,SV624: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1328 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1847 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1847 @ SV1328 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4534,plain,
! [SV1848: $i,SV1329: $i,SV625: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV625 @ SV1329 @ tc_nat ) @ SV1848 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV625 @ ( c_HOL_Oplus__class_Oplus @ SV1329 @ SV1848 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4535,plain,
! [SV1330: $i,SV627: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV627 @ SV1330 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1330 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV627 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3838]) ).
thf(4536,plain,
! [SV1331: $i,SV628: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV628 @ SV1331 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV1331 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV628 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3839]) ).
thf(4537,plain,
! [SV1849: $i,SV1333: $i,SV630: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV630 @ SV1333 @ tc_nat ) @ SV1849 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV630 @ SV1849 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1333 @ SV1849 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4538,plain,
! [SV1850: $i,SV1334: $i,SV631: $i] :
( ( ( c_HOL_Otimes__class_Otimes @ SV631 @ ( c_HOL_Ominus__class_Ominus @ SV1334 @ SV1850 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV631 @ SV1334 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV631 @ SV1850 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4539,plain,
! [SV1851: $i,SV1335: $i,SV632: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1335 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1851 @ SV1335 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1851 @ tc_nat ) )
| ~ ( c_lessequals @ SV1335 @ SV1851 @ tc_nat )
| ~ ( c_lessequals @ SV1335 @ SV632 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(4540,plain,
! [SV1852: $i,SV1338: $i,SV635: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV635 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ SV1852 @ SV635 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1338 @ SV1852 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3846]) ).
thf(4541,plain,
! [SV1853: $i,SV1339: $i,SV636: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV636 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1339 @ SV1853 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
| ~ ( c_HOL_Oord__class_Oless @ SV1339 @ SV1853 @ SV636 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(4542,plain,
! [SV1854: $i,SV1340: $i,SV637: $i] :
( ( ! [SY4724: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV637 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SV1854 @ SV637 ) @ SY4724 @ SV637 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SY4724 @ SV1340 @ SV637 ) @ SV637 ) @ SV1854 @ SV637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(4543,plain,
! [SV1855: $i,SV1341: $i,SV638: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV638 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1341 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1855 @ SV638 ) @ SV638 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV1855 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4544,plain,
! [SV1856: $i,SV1342: $i,SV639: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( c_HOL_Oord__class_Oless @ SV1342 @ SV1856 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1342 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1856 @ SV639 ) @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4545,plain,
! [SV1343: $i,SV640: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV640 @ ( c_HOL_Ominus__class_Ominus @ SV1343 @ SV640 @ tc_nat ) @ tc_nat )
= SV1343 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1343 @ SV640 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4546,plain,
! [SV1344: $i,SV641: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV1344 @ tc_nat ) @ SV641 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV641 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1344 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3852]) ).
thf(4547,plain,
! [SV1345: $i,SV642: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat ) )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1345 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV642 @ SV1345 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SV1345 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(4548,plain,
! [SV1346: $i,SV643: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat ) )
= $true )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1346 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1346 @ SV643 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV1346 @ SV643 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3854]) ).
thf(4549,plain,
! [SV1857: $i,SV1347: $i,SV644: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV644 @ SV1347 @ tc_nat ) @ SV1857 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV644 @ ( c_HOL_Ominus__class_Ominus @ SV1857 @ SV1347 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(4550,plain,
! [SV1858: $i,SV1348: $i,SV645: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV645 @ ( c_HOL_Ominus__class_Ominus @ SV1348 @ SV1858 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV645 @ SV1858 @ tc_nat ) @ SV1348 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(4551,plain,
! [SV1859: $i,SV1349: $i,SV646: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1859 @ SV1349 @ tc_nat )
| ~ ( c_lessequals @ SV1859 @ SV646 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4552,plain,
! [SV1860: $i,SV1350: $i,SV647: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV1860 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3858]) ).
thf(4553,plain,
! [SV1352: $i,SV649: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV649 @ SV1352 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1352 @ SV649 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4554,plain,
! [SV1353: $i,SV650: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV650 @ SV1353 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1353 @ SV650 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4555,plain,
! [SV1354: $i,SV651: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV651 @ SV1354 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV651 @ SV1354 @ tc_nat ) @ SV1354 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV651 @ SV1354 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3862]) ).
thf(4556,plain,
! [SV1861: $i,SV1355: $i,SV652: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SV1355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1861 @ SV1355 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1355 @ SV652 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV652 @ SV1861 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4557,plain,
! [SV1356: $i,SV653: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV653 @ SV1356 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV653 @ SV1356 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4558,plain,
! [SV1862: $i,SV1357: $i,SV654: $i] :
( ( ~ ( class_Orderings_Oorder @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV1862 @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SV1862 @ SV1357 @ SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3865]) ).
thf(4559,plain,
! [SV1863: $i,SV1358: $i,SV655: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SV1358 @ SV1863 @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SV1863 @ SV1358 @ SV655 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4560,plain,
! [SV1864: $i,SV1359: $i,SV656: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SV1359 @ SV1864 @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SV1864 @ SV1359 @ SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4561,plain,
! [SV1865: $i,SV1360: $i,SV657: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SV1360 @ SV1865 @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SV1865 @ SV1360 @ SV657 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(4562,plain,
! [SV1361: $i,SV658: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV658 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV1361 @ SV658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3869]) ).
thf(4563,plain,
! [SV1362: $i,SV659: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV659 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1362 @ SV1362 @ SV659 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3870]) ).
thf(4564,plain,
! [SV1363: $i,SV662: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV662 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1363 @ SV1363 @ SV662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3873]) ).
thf(4565,plain,
! [SV1866: $i,SV1364: $i,SV663: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV663 @ SV1364 @ tc_nat ) @ SV1866 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV1866 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4566,plain,
! [SV1867: $i,SV1365: $i,SV664: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1867 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV664 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV1365 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(4567,plain,
! [SV1868: $i,SV1366: $i,SV665: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV665 )
| ( c_HOL_Oord__class_Oless @ SV1366 @ SV1868 @ SV665 )
| ( c_HOL_Oord__class_Oless @ SV1868 @ SV1366 @ SV665 )
| ( SV1868 = SV1366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(4568,plain,
! [SV1869: $i,SV1367: $i,SV666: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV666 )
| ( SV1367 = SV1869 )
| ( c_HOL_Oord__class_Oless @ SV1869 @ SV1367 @ SV666 )
| ( c_HOL_Oord__class_Oless @ SV1367 @ SV1869 @ SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(4569,plain,
! [SV1870: $i,SV1368: $i,SV667: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV667 )
| ( SV1368 = SV1870 )
| ( c_HOL_Oord__class_Oless @ SV1368 @ SV1870 @ SV667 )
| ( c_HOL_Oord__class_Oless @ SV1870 @ SV1368 @ SV667 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(4570,plain,
! [SV1871: $i,SV1369: $i,SV668: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV668 )
| ( c_HOL_Oord__class_Oless @ SV1369 @ SV1871 @ SV668 )
| ( SV1871 = SV1369 )
| ( c_HOL_Oord__class_Oless @ SV1871 @ SV1369 @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3879]) ).
thf(4571,plain,
! [SV1370: $i,SV669: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV669 @ SV1370 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1370 @ SV669 @ tc_nat )
| ( SV1370 = SV669 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(4572,plain,
! [SV1371: $i,SV670: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV670 @ SV1371 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1371 @ SV670 @ tc_nat )
| ( SV1371 = SV670 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4573,plain,
! [SV1872: $i,SV1372: $i,SV671: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV671 )
| ( c_HOL_Oord__class_Oless @ SV1372 @ SV1872 @ SV671 )
| ( c_HOL_Oord__class_Oless @ SV1872 @ SV1372 @ SV671 )
| ( SV1872 = SV1372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(4574,plain,
! [SV1873: $i,SV1373: $i,SV672: $i] :
( ( ! [SY4725: $i] :
( ~ ( class_Orderings_Oorder @ SV672 )
| ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SY4725 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SY4725 @ SV1873 @ SV672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(4575,plain,
! [SV1874: $i,SV1374: $i,SV673: $i] :
( ( ! [SY4726: $i] :
( ~ ( class_Orderings_Opreorder @ SV673 )
| ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SY4726 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SY4726 @ SV673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4576,plain,
! [SV1875: $i,SV1375: $i,SV674: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV674 @ SV1375 @ tc_nat ) @ SV1875 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV674 @ SV1875 @ tc_nat ) @ SV1375 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(4577,plain,
! [SV1876: $i,SV1376: $i,SV675: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1376 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1876 @ tc_nat ) )
| ( SV1376 = SV1876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(4578,plain,
! [SV1377: $i,SV677: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV677 @ SV1377 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV677
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3888]) ).
thf(4579,plain,
! [SV678: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV678 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV678 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3889]) ).
thf(4580,plain,
! [SV1378: $i,SV679: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV679 @ SV1378 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1378 @ SV679 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1378 = SV679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4581,plain,
! [SV1877: $i,SV1379: $i,SV680: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1379 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1877 @ tc_nat ) )
| ( SV1379 = SV1877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(4582,plain,
! [SV1878: $i,SV1380: $i,SV681: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV681 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1380 @ SV1380 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SV1878 @ SV1878 @ SV681 ) @ SV681 )
!= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
| ( SV1380
= ( c_HOL_Ozero__class_Ozero @ SV681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3892]) ).
thf(4583,plain,
! [SV1879: $i,SV1381: $i,SV682: $i] :
( ( ! [SY4727: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV682 )
| ~ ( class_Int_Onumber__ring @ SV682 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SY4727 @ SV682 ) )
| ( SV1879 = SY4727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3893]) ).
thf(4584,plain,
! [SV1880: $i,SV1382: $i,SV683: $i] :
( ( ! [SY4728: $i,SY4729: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV1880 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY4728 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SY4729 @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ SV683 @ SV1382 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SY4728 @ SV1382 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4585,plain,
! [SV1881: $i,SV1383: $i,SV684: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1383 @ SV684 )
!= ( c_HOL_Oabs__class_Oabs @ SV1881 @ SV684 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1383 @ SV1881 @ SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4586,plain,
! [SV1882: $i,SV1384: $i,SV685: $i] :
( ( ! [SY4730: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV1882 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SY4730 @ SV685 ) )
| ( SV1882 = SY4730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4587,plain,
! [SV1883: $i,SV1385: $i,SV686: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
!= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4588,plain,
! [SV1386: $i,SV687: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV687 @ SV1386 @ tc_nat ) )
= $true )
| ( ( ( SV687
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV687
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3898]) ).
thf(4589,plain,
! [SV1884: $i,SV1387: $i,SV688: $i] :
( ( ! [SY4731: $i,SY4732: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SY4731 @ SY4732 @ SV688 ) )
| ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SY4732 @ SY4731 @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4590,plain,
! [SV1885: $i,SV1388: $i,SV689: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SV1885 @ SV689 )
!= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1885
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4591,plain,
! [SV1886: $i,SV1389: $i,SV690: $i] :
( ( ! [SY4733: $i,SY4734: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SY4733 @ SY4734 @ SV690 ) )
| ( c_lessequals @ SY4734 @ SY4733 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4592,plain,
! [SV1887: $i,SV1390: $i,SV691: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV691 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1390 @ SV1887 @ SV691 )
!= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
| ( SV1390 = SV1887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(4593,plain,
! [SV1888: $i,SV1391: $i,SV693: $i] :
( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SV1888 @ SV693 )
!= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1888
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(4594,plain,
! [SV1392: $i,SV695: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1392 @ tc_nat ) )
= $true )
| ( ( ( SV1392
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1392
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(4595,plain,
! [SV1889: $i,SV1393: $i,SV696: $i] :
( ( ! [SY4735: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV696 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SV1889 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SY4735 @ SY4735 @ SV696 ) )
| ( SV1393 = SV1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3907]) ).
thf(4596,plain,
! [SV1394: $i,SV697: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1394 @ tc_nat ) )
= $true )
| ( ( ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV697
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3908]) ).
thf(4597,plain,
! [SV1890: $i,SV1395: $i,SV698: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV698 )
| ~ ( class_Int_Onumber__ring @ SV698 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SV1395 = SV1890 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(4598,plain,
! [SV1396: $i,SV699: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV699 @ SV1396 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV699 @ SV1396 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3910]) ).
thf(4599,plain,
! [SV701: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV701 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV701 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3912]) ).
thf(4600,plain,
! [SV1891: $i,SV1397: $i,SV702: $i] :
( ( ! [SY4736: $i,SY4737: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV702 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SY4736 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SY4737 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SY4736 @ SV702 )
= SY4737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4601,plain,
! [SV1398: $i,SV703: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV703 @ SV1398 @ tc_nat ) )
= $true )
| ( ( ( SV703
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1398
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3914]) ).
thf(4602,plain,
! [SV1892: $i,SV1399: $i,SV704: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV704 )
| ( ( c_Divides_Odiv__class_Omod @ SV1399 @ SV1892 @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1892 @ SV1399 @ SV704 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4603,plain,
! [SV1893: $i,SV1400: $i,SV705: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
!= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4604,plain,
! [SV1401: $i,SV706: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV706 @ SV1401 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( SV1401
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV706
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3917]) ).
thf(4605,plain,
! [SV1894: $i,SV1402: $i,SV708: $i] :
( ( ! [SY4738: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV708 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SV1894 @ SY4738 @ SV708 ) )
| ( SV1894 = SY4738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4606,plain,
! [SV1895: $i,SV1403: $i,SV709: $i] :
( ( ! [SY4739: $i,SY4740: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV709 )
| ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SY4739 @ SY4740 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SY4740 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SY4739 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SY4740 )
| ( SV1403 = SY4739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3920]) ).
thf(4607,plain,
! [SV1896: $i,SV1404: $i,SV710: $i] :
( ( ! [SY4741: $i,SY4742: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SY4741 @ SY4742 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SY4741 @ SY4742 @ SV710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3921]) ).
thf(4608,plain,
! [SV1405: $i,SV711: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV711 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1405 @ SV1405 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1405
= ( c_HOL_Ozero__class_Ozero @ SV711 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3922]) ).
thf(4609,plain,
! [SV1897: $i,SV1406: $i,SV712: $i] :
( ( ! [SY4743: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1897 @ SY4743 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1897 @ SV1406 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV712 @ SY4743 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4610,plain,
! [SV1898: $i,SV1407: $i,SV713: $i] :
( ( ! [SY4744: $i,SY4745: $i,SY4746: $i] :
( ~ ( class_Divides_Oring__div @ SV713 )
| ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY4744 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4745 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY4746 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4745 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4746 @ SY4744 @ SV713 ) @ SV1898 @ SV713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4611,plain,
! [SV1408: $i,SV714: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1408 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1408
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV714
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(4612,plain,
! [SV1899: $i,SV1409: $i,SV715: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV715 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1409 @ SV715 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1899 @ SV715 ) )
| ( SV1409 = SV1899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3926]) ).
thf(4613,plain,
! [SV1410: $i,SV716: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV716 @ SV1410 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV716
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(4614,plain,
! [SV1411: $i,SV717: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV717 @ SV1411 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1411
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4615,plain,
! [SV1412: $i,SV718: $i] :
( ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV718 @ SV1412 @ tc_nat ) )
!= SV1412 )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV718 ) @ SV1412 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3929]) ).
thf(4616,plain,
! [SV1413: $i,SV719: $i] :
( ( ( ( c_Suc @ SV719 )
!= ( c_Suc @ SV1413 ) )
= $true )
| ( ( SV719 = SV1413 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4617,plain,
! [SV1900: $i,SV1414: $i,SV720: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV720 @ SV1414 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV1900 @ SV1414 @ tc_nat ) )
| ( SV1414
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV720 = SV1900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(4618,plain,
! [SV1901: $i,SV1415: $i,SV721: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1415 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1901 @ tc_nat ) )
| ( SV1415 = SV1901 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4619,plain,
! [SV1902: $i,SV1416: $i,SV722: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV722 )
| ~ ( class_Int_Onumber__ring @ SV722 )
| ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
| ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4620,plain,
! [SV1417: $i,SV723: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV723 @ SV1417 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1417
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1417
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3934]) ).
thf(4621,plain,
! [SV1903: $i,SV1418: $i,SV724: $i] :
( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SV1903 @ SV724 )
!= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1903
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4622,plain,
! [SV1904: $i,SV1419: $i,SV725: $i] :
( ( ! [SY4747: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SV1904 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SY4747 @ SV1904 @ SV725 ) )
| ( SV1419 = SY4747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4623,plain,
! [SV1420: $i,SV726: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1420 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1420
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4624,plain,
! [SV1905: $i,SV1421: $i,SV727: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1421 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1905 @ tc_nat ) )
| ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1421 = SV1905 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4625,plain,
! [SV1906: $i,SV1422: $i,SV728: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV728 @ SV1422 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1906 @ SV1422 @ tc_nat ) )
| ( SV728 = SV1906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4626,plain,
! [SV1907: $i,SV1423: $i,SV729: $i] :
( ( ! [SY4748: $i,SY4749: $i,SY4750: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV729 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SY4748 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4749 @ SV1907 @ SV729 ) @ SY4750 @ SV729 ) )
| ( SY4748
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4749 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SY4750 @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4627,plain,
! [SV1424: $i,SV730: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV730 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1424 @ SV730 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ( SV1424
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4628,plain,
! [SV1425: $i,SV731: $i] :
( ( ( SV731
!= ( c_HOL_Oplus__class_Oplus @ SV731 @ SV1425 @ tc_nat ) )
= $true )
| ( ( SV1425
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3942]) ).
thf(4629,plain,
! [SV1908: $i,SV1426: $i,SV732: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV732 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1426 @ SV1908 @ SV732 )
!= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
| ( SV1426 = SV1908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4630,plain,
! [SV1427: $i,SV733: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV733 @ SV1427 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV733
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1427
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3944]) ).
thf(4631,plain,
! [SV1909: $i,SV1428: $i,SV734: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV734 )
| ( ( c_Orderings_Oord__class_Omin @ SV1428 @ SV1909 @ SV734 )
!= SV1428 )
| ( c_lessequals @ SV1428 @ SV1909 @ SV734 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4632,plain,
! [SV1910: $i,SV1429: $i,SV735: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
| ~ ( c_lessequals @ SV1429 @ SV1910 @ tc_nat )
| ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
| ( SV735 = SV1910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3946]) ).
thf(4633,plain,
! [SV1430: $i,SV736: $i] :
( ( ( ( c_Suc @ SV736 )
!= ( c_Suc @ SV1430 ) )
= $true )
| ( ( SV736 = SV1430 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(4634,plain,
! [SV1431: $i,SV737: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV737 @ SV1431 @ tc_nat )
!= SV737 )
= $true )
| ( ( SV1431
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4635,plain,
! [SV1911: $i,SV1432: $i,SV738: $i] :
( ( ! [SY4751: $i,SY4752: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4751 @ SV1432 @ tc_nat ) @ SY4752 @ tc_nat ) )
| ~ ( c_lessequals @ SV738 @ SY4751 @ tc_nat )
| ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4751 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SY4752 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4636,plain,
! [SV1433: $i,SV739: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1433 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV739
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4637,plain,
! [SV1912: $i,SV1434: $i,SV741: $i] :
( ( ! [SY4753: $i,SY4754: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SY4753 @ SY4754 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SY4753 @ SY4754 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4638,plain,
! [SV1913: $i,SV1435: $i,SV742: $i] :
( ( ! [SY4755: $i,SY4756: $i,SY4757: $i] :
( ~ ( class_Divides_Osemiring__div @ SV742 )
| ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY4755 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4756 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY4757 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4756 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4757 @ SY4755 @ SV742 ) @ SV1913 @ SV742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4639,plain,
! [SV1914: $i,SV1436: $i,SV743: $i] :
( ( ! [SY4758: $i,SY4759: $i,SY4760: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV743 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SY4758 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4759 @ SV1914 @ SV743 ) @ SY4760 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SY4759 @ SV743 ) @ SV1914 @ SV743 ) @ SY4758 @ SV743 )
= SY4760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4640,plain,
! [SV1915: $i,SV1437: $i,SV744: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1437 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1915 @ tc_nat ) )
| ( SV1437 = SV1915 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4641,plain,
! [SV1916: $i,SV1438: $i,SV745: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1438 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1916 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat )
| ( SV1438 = SV1916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3956]) ).
thf(4642,plain,
! [SV1917: $i,SV1439: $i,SV746: $i] :
( ( ! [SY4761: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV1439 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SY4761 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SY4761 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV1439 @ tc_nat ) @ tc_nat ) )
| ( SV1439 = SY4761 )
| ( SV746 = SV1917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4643,plain,
! [SV1918: $i,SV1440: $i,SV747: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1440 @ SV1440 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SV1918 @ SV1918 @ SV747 ) @ SV747 )
!= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
| ( SV1918
= ( c_HOL_Ozero__class_Ozero @ SV747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4644,plain,
! [SV1919: $i,SV1441: $i,SV748: $i] :
( ( ! [SY4762: $i,SY4763: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV748 )
| ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SY4762 @ SY4763 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SY4763 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SY4762 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SY4763 )
| ( SV1441 = SY4762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3959]) ).
thf(4645,plain,
! [SV1920: $i,SV1442: $i,SV749: $i] :
( ( ! [SY4764: $i,SY4765: $i,SY4766: $i] :
( ~ ( class_Divides_Osemiring__div @ SV749 )
| ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY4764 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4765 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY4766 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4765 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4766 @ SY4764 @ SV749 ) @ SV1920 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3960]) ).
thf(4646,plain,
! [SV1921: $i,SV1443: $i,SV750: $i] :
( ( ! [SY4767: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV1921 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SY4767 @ tc_nat ) @ tc_nat ) )
| ( SV1921 = SY4767 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3961]) ).
thf(4647,plain,
! [SV1922: $i,SV1444: $i,SV751: $i] :
( ( ! [SY4768: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV1922 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SY4768 @ SV751 ) )
| ( SV1922 = SY4768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3962]) ).
thf(4648,plain,
! [SV1923: $i,SV1445: $i,SV752: $i] :
( ( ! [SY4769: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV1445 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SY4769 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SY4769 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV1445 @ tc_nat ) @ tc_nat ) )
| ( SV1445 = SY4769 )
| ( SV752 = SV1923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3963]) ).
thf(4649,plain,
! [SV1924: $i,SV1446: $i,SV753: $i] :
( ( ! [SY4770: $i,SY4771: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4770 @ SV1446 @ tc_nat ) @ SY4771 @ tc_nat ) )
| ~ ( c_lessequals @ SY4770 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SY4770 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SY4771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4650,plain,
! [SV1925: $i,SV1447: $i,SV754: $i] :
( ( ! [SY4772: $i,SY4773: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV754 )
| ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SY4772 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SY4773 @ SV754 ) @ SV754 ) )
| ( SY4772 = SY4773 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4651,plain,
! [SV1448: $i,SV755: $i,SV1: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4652,plain,
! [SV1449: $i,SV756: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4653,plain,
! [SV1450: $i,SV759: $i,SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV5 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV759 @ SV759 @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV1450 @ SV1450 @ SV5 ) @ SV5 ) @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4654,plain,
! [SV1451: $i,SV760: $i,SV6: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4655,plain,
! [SV1452: $i,SV761: $i,SV7: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4656,plain,
! [SV1453: $i,SV762: $i,SV9: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV9 @ SV762 @ tc_nat ) @ SV1453 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV9 @ SV1453 @ tc_nat ) @ SV762 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1453 @ SV9 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3972]) ).
thf(4657,plain,
! [SV1454: $i,SV763: $i,SV10: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV10 @ SV763 @ tc_nat ) @ SV1454 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV10 @ ( c_HOL_Ominus__class_Ominus @ SV763 @ SV1454 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1454 @ SV763 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3973]) ).
thf(4658,plain,
! [SV1926: $i,SV1455: $i,SV764: $i,SV11: $i] :
( ( ! [SY4774: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1455 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1926 @ SY4774 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1926 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1455 @ SY4774 @ SV11 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4659,plain,
! [SV1927: $i,SV1456: $i,SV765: $i,SV12: $i] :
( ( ! [SY4775: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV765 @ SV1456 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SY4775 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SV765 @ ( c_HOL_Otimes__class_Otimes @ SV1456 @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SY4775 @ SV12 ) @ SV12 ) @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4660,plain,
! [SV1928: $i,SV1457: $i,SV766: $i,SV13: $i] :
( ( ! [SY4776: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV1928 @ SY4776 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SV1928 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ SY4776 @ SV13 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4661,plain,
! [SV767: $i,SV14: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV14 )
= $false )
| ( ( ( SV767
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV767 @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4662,plain,
! [SV768: $i,SV15: $i] :
( ( ( class_Orderings_Olinorder @ SV15 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV768 @ SV768 @ SV15 )
= SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3978]) ).
thf(4663,plain,
! [SV1929: $i,SV1458: $i,SV769: $i,SV16: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
| ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SV1458 @ ( c_HOL_Oabs__class_Oabs @ SV1929 @ SV16 ) @ SV16 ) @ SV16 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SV1929 @ SV16 ) @ SV1458 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3979]) ).
thf(4664,plain,
! [SV1459: $i,SV770: $i,SV18: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV18 ) )
= $true )
| ( ( ( SV770 = SV1459 )
| ~ ( c_lessequals @ SV1459 @ SV770 @ SV18 )
| ~ ( c_lessequals @ SV770 @ SV1459 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3981]) ).
thf(4665,plain,
! [SV1460: $i,SV771: $i,SV19: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV19 ) )
= $true )
| ( ( ( SV771 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV771 @ SV19 )
| ~ ( c_lessequals @ SV771 @ SV1460 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3982]) ).
thf(4666,plain,
! [SV772: $i,SV20: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV772 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV772 @ SV20 @ tc_nat )
| ( SV772 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3983]) ).
thf(4667,plain,
! [SV773: $i,SV21: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SV773 @ tc_nat )
= $false )
| ( ( ( SV773 = SV21 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV773 @ SV21 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4668,plain,
! [SV774: $i,SV22: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV22 @ SV774 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV774 @ SV22 @ tc_nat ) )
= $true )
| ( ( SV22 = SV774 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3985]) ).
thf(4669,plain,
! [SV23: $i,SV775: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV775 @ SV23 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV23 @ SV775 @ tc_nat ) )
= $true )
| ( ( SV23 = SV775 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3986]) ).
thf(4670,plain,
! [SV776: $i,SV24: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV24 @ SV776 @ tc_nat )
= $false )
| ( ( ( SV776 = SV24 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV776 @ SV24 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3987]) ).
thf(4671,plain,
! [SV25: $i,SV777: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV777 @ SV25 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV25 @ SV777 @ tc_nat ) )
= $true )
| ( ( SV25 = SV777 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3988]) ).
thf(4672,plain,
! [SV26: $i,SV778: $i] :
( ( ( ~ ( c_lessequals @ SV778 @ SV26 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV26 @ SV778 @ tc_nat ) )
= $true )
| ( ( SV26 = SV778 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3989]) ).
thf(4673,plain,
! [SV27: $i,SV779: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV779 @ SV27 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV27 @ SV779 @ tc_nat ) )
= $true )
| ( ( SV27 = SV779 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3990]) ).
thf(4674,plain,
! [SV1461: $i,SV780: $i,SV28: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV28 ) )
= $true )
| ( ( ( SV780 = SV1461 )
| ~ ( c_lessequals @ SV780 @ SV1461 @ SV28 )
| ~ ( c_lessequals @ SV1461 @ SV780 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3991]) ).
thf(4675,plain,
! [SV781: $i,SV29: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV29 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV781 @ SV29 )
= SV781 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV781 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4676,plain,
! [SV1462: $i,SV782: $i,SV30: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV782 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1462 @ SV782 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV1462 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3993]) ).
thf(4677,plain,
! [SV1463: $i,SV783: $i,SV31: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4678,plain,
! [SV784: $i,SV32: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV32 @ SV784 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV784 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4679,plain,
! [SV785: $i,SV34: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV34 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV785 @ SV785 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4680,plain,
! [SV1930: $i,SV1464: $i,SV786: $i,SV35: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4681,plain,
! [SV1465: $i,SV787: $i,SV36: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV36 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV787 @ SV1465 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SV1465 @ tc_nat ) @ ( c_Suc @ SV787 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1465 @ SV787 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3998]) ).
thf(4682,plain,
! [SV1466: $i,SV789: $i,SV38: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV38 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV789 @ SV38 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV1466 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3999]) ).
thf(4683,plain,
! [SV1467: $i,SV790: $i,SV39: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV39 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV790 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ ( c_HOL_Otimes__class_Otimes @ SV1467 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4000]) ).
thf(4684,plain,
! [SV1468: $i,SV791: $i,SV40: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV791 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV1468 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV791 @ SV1468 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4001]) ).
thf(4685,plain,
! [SV1469: $i,SV792: $i,SV41: $i] :
( ( ( c_lessequals @ SV41 @ SV792 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1469 @ SV41 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1469 @ SV792 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4002]) ).
thf(4686,plain,
! [SV1470: $i,SV793: $i,SV42: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV42 @ SV793 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1470 @ SV793 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV42 @ SV1470 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4003]) ).
thf(4687,plain,
! [SV1931: $i,SV1471: $i,SV794: $i,SV43: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1471 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1931 @ SV43 ) @ SV43 )
| ~ ( c_lessequals @ SV1471 @ SV1931 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4688,plain,
! [SV1932: $i,SV1472: $i,SV795: $i,SV44: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SV1472 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SV1932 @ SV1472 @ SV44 ) @ SV44 )
| ~ ( c_lessequals @ SV795 @ SV1932 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4689,plain,
! [SV1933: $i,SV1473: $i,SV796: $i,SV45: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
| ( c_lessequals @ SV796 @ SV1473 @ SV45 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV1473 @ SV45 ) @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4006]) ).
thf(4690,plain,
! [SV1934: $i,SV1474: $i,SV797: $i,SV46: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1474 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1934 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ SV1474 @ SV1934 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4691,plain,
! [SV1935: $i,SV1475: $i,SV798: $i,SV47: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
| ( c_lessequals @ SV798 @ SV1475 @ SV47 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SV1935 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SV1475 @ SV1935 @ SV47 ) @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4008]) ).
thf(4692,plain,
! [SV1936: $i,SV1476: $i,SV799: $i,SV48: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SV1476 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SV1936 @ SV1476 @ SV48 ) @ SV48 )
| ~ ( c_lessequals @ SV799 @ SV1936 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4009]) ).
thf(4693,plain,
! [SV1477: $i,SV800: $i,SV49: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV49 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV1477 @ SV49 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV800 @ SV49 ) @ ( c_HOL_Oabs__class_Oabs @ SV1477 @ SV49 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4694,plain,
! [SV1478: $i,SV801: $i,SV50: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV50 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4011]) ).
thf(4695,plain,
! [SV1479: $i,SV802: $i,SV51: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV51 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
| ~ ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4696,plain,
! [SV1480: $i,SV803: $i,SV52: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV52 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 )
| ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4697,plain,
! [SV1481: $i,SV804: $i,SV53: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ SV53 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
| ~ ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
| ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4014]) ).
thf(4698,plain,
! [SV1482: $i,SV805: $i,SV54: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV54 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV805 @ ( c_HOL_Otimes__class_Otimes @ SV805 @ SV1482 @ SV54 ) @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV805 @ SV1482 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4699,plain,
! [SV1483: $i,SV806: $i,SV56: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV56 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1483 @ SV56 ) @ SV806 @ SV56 )
= ( c_Divides_Odiv__class_Omod @ SV1483 @ SV806 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4700,plain,
! [SV1484: $i,SV807: $i,SV57: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV57 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1484 @ SV57 ) @ SV1484 @ SV57 )
= ( c_Divides_Odiv__class_Omod @ SV807 @ SV1484 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4018]) ).
thf(4701,plain,
! [SV1485: $i,SV808: $i,SV58: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV58 ) )
= $true )
| ( ( ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SV1485 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4702,plain,
! [SV1486: $i,SV809: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV59 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV1486 @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4703,plain,
! [SV1487: $i,SV810: $i,SV60: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV60 ) )
= $true )
| ( ( ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ( c_lessequals @ SV1487 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV1487 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4021]) ).
thf(4704,plain,
! [SV1488: $i,SV811: $i,SV61: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV61 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
| ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1488 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4022]) ).
thf(4705,plain,
! [SV1489: $i,SV812: $i,SV62: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4706,plain,
! [SV1490: $i,SV813: $i,SV63: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4024]) ).
thf(4707,plain,
! [SV1491: $i,SV814: $i,SV64: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4025]) ).
thf(4708,plain,
! [SV1492: $i,SV815: $i,SV65: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4026]) ).
thf(4709,plain,
! [SV1493: $i,SV816: $i,SV66: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV66 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4710,plain,
! [SV67: $i,SV817: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV817 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV67 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV67 @ SV817 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4711,plain,
! [SV818: $i,SV68: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV68 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV818 @ SV818 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ SV818 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4029]) ).
thf(4712,plain,
! [SV819: $i,SV69: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV819 @ SV819 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4030]) ).
thf(4713,plain,
! [SV820: $i,SV70: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV70 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV820 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4031]) ).
thf(4714,plain,
! [SV821: $i,SV71: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV71 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV821 @ SV71 ) @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4032]) ).
thf(4715,plain,
! [SV73: $i,SV822: $i] :
( ( ( c_lessequals @ SV822 @ SV73 @ tc_nat )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV73 @ SV822 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV73 @ SV822 @ tc_nat ) @ SV822 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4716,plain,
! [SV1937: $i,SV1494: $i,SV823: $i,SV76: $i] :
( ( ~ ( c_lessequals @ SV76 @ SV823 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1494 @ tc_nat ) @ SV1937 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV76 @ SV1494 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV823 @ SV76 @ tc_nat ) @ SV1494 @ tc_nat ) @ SV1937 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(4717,plain,
! [SV1938: $i,SV1495: $i,SV824: $i,SV77: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
| ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4718,plain,
! [SV1939: $i,SV1496: $i,SV825: $i,SV78: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
| ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4719,plain,
! [SV1940: $i,SV1497: $i,SV826: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV79 )
| ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4720,plain,
! [SV1941: $i,SV1498: $i,SV827: $i,SV80: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV80 )
| ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4038]) ).
thf(4721,plain,
! [SV81: $i,SV828: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV828 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV81 @ SV828 @ tc_nat ) @ SV828 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4722,plain,
! [SV1499: $i,SV829: $i,SV82: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV82 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV829 @ SV82 ) @ ( c_HOL_Otimes__class_Otimes @ SV1499 @ SV1499 @ SV82 ) @ SV82 ) @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4723,plain,
! [SV83: $i,SV830: $i] :
( ( ( c_lessequals @ SV830 @ SV83 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV83 ) @ SV830 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV83 @ SV830 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4041]) ).
thf(4724,plain,
! [SV1942: $i,SV1500: $i,SV831: $i,SV84: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV84 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4725,plain,
! [SV1943: $i,SV1501: $i,SV832: $i,SV85: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV85 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4726,plain,
! [SV1944: $i,SV1502: $i,SV833: $i,SV86: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV86 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4044]) ).
thf(4727,plain,
! [SV1945: $i,SV1503: $i,SV834: $i,SV87: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV87 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4728,plain,
! [SV1946: $i,SV1504: $i,SV835: $i,SV88: $i] :
( ( ! [SY4777: $i,SY4778: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4777 @ SV1504 @ SV88 ) @ SY4778 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4777 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SY4778 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4046]) ).
thf(4729,plain,
! [SV1947: $i,SV1505: $i,SV836: $i,SV89: $i] :
( ( ! [SY4779: $i,SY4780: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 )
| ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SY4779 @ SV89 ) @ SY4780 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SY4779 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SY4779 @ SV89 ) @ SY4780 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4730,plain,
! [SV1948: $i,SV1506: $i,SV837: $i,SV90: $i] :
( ( ! [SY4781: $i,SY4782: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4781 @ SV1506 @ SV90 ) @ SY4782 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SY4781 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SY4782 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4048]) ).
thf(4731,plain,
! [SV1949: $i,SV1507: $i,SV838: $i,SV91: $i] :
( ( ! [SY4783: $i,SY4784: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SY4783 @ SV91 ) @ SY4784 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SY4783 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SY4784 @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4049]) ).
thf(4732,plain,
! [SV839: $i,SV92: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV92 @ SV839 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV92 ) @ SV839 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4733,plain,
! [SV840: $i,SV93: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV93 ) @ SV840 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV93 @ SV840 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4734,plain,
! [SV841: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV94 @ SV841 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV94 ) @ SV841 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4735,plain,
! [SV842: $i,SV95: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV95 ) @ SV842 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV95 @ SV842 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4736,plain,
! [SV1950: $i,SV1508: $i,SV843: $i,SV96: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4737,plain,
! [SV1951: $i,SV1509: $i,SV844: $i,SV97: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
| ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4055]) ).
thf(4738,plain,
! [SV1510: $i,SV845: $i,SV98: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SV845 @ tc_nat ) @ SV1510 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SV1510 @ SV845 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV845 @ SV1510 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4056]) ).
thf(4739,plain,
! [SV1511: $i,SV846: $i,SV99: $i] :
( ( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1511 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SV1511 @ tc_nat ) @ SV846 @ tc_nat )
| ~ ( c_lessequals @ SV1511 @ SV846 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4740,plain,
! [SV1952: $i,SV1512: $i,SV850: $i,SV103: $i] :
( ( ! [SY4785: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1952 @ SV850 @ tc_nat ) @ SY4785 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1952 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SY4785 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV103 @ SV1952 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4741,plain,
! [SV1953: $i,SV1513: $i,SV851: $i,SV104: $i] :
( ( ! [SY4786: $i] :
( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SV1953 @ tc_nat ) @ SY4786 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SV1953 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SV1953 @ tc_nat ) @ SY4786 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1513 @ SV851 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4059]) ).
thf(4742,plain,
! [SV1954: $i,SV1514: $i,SV852: $i,SV105: $i] :
( ( ! [SY4787: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1954 @ SV852 @ tc_nat ) @ SY4787 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SV1954 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SY4787 @ tc_nat )
| ~ ( c_lessequals @ SV1954 @ SV105 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4743,plain,
! [SV1955: $i,SV1515: $i,SV853: $i,SV106: $i] :
( ( ! [SY4788: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ SY4788 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SY4788 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4061]) ).
thf(4744,plain,
! [SV1956: $i,SV1516: $i,SV854: $i,SV107: $i] :
( ( ! [SY4789: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV107 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV1516 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1956 @ SV854 @ SV107 ) @ SV1516 @ SV107 ) @ SY4789 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1956 @ SV1516 @ SV107 ) @ SY4789 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4745,plain,
! [SV1517: $i,SV855: $i,SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Olordered__ring @ SV108 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV855 @ SV1517 @ SV108 ) @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV855 @ SV108 ) @ ( c_HOL_Oabs__class_Oabs @ SV1517 @ SV108 ) @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4746,plain,
! [SV1518: $i,SV856: $i,SV109: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 ) )
= $true )
| ( ( ( c_lessequals @ SV856 @ SV1518 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV856 @ SV109 ) @ SV1518 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4064]) ).
thf(4747,plain,
! [SV1957: $i,SV1519: $i,SV857: $i,SV110: $i] :
( ( ! [SY4790: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SY4790 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SY4790 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4748,plain,
! [SV1958: $i,SV1520: $i,SV858: $i,SV111: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV858 @ SV1520 @ SV111 ) @ SV1958 @ SV111 ) @ SV1520 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV858 @ SV1958 @ SV111 ) @ SV1520 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(4749,plain,
! [SV1959: $i,SV1521: $i,SV859: $i,SV112: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV112 )
| ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1959 @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4750,plain,
! [SV1960: $i,SV1522: $i,SV860: $i,SV113: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV113 )
| ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1960 @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4068]) ).
thf(4751,plain,
! [SV1961: $i,SV1523: $i,SV861: $i,SV114: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV114 )
| ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1961 @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4752,plain,
! [SV1524: $i,SV862: $i,SV115: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV115 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV862 @ SV1524 @ SV115 ) @ SV1524 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4070]) ).
thf(4753,plain,
! [SV1525: $i,SV863: $i,SV116: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV116 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV863 @ SV1525 @ SV116 ) @ SV863 @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4071]) ).
thf(4754,plain,
! [SV1526: $i,SV864: $i,SV117: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV864 @ tc_nat ) ) @ SV1526 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV117 ) @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SV1526 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV864 @ SV117 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4755,plain,
! [SV1527: $i,SV865: $i,SV118: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV865 @ ( c_HOL_Otimes__class_Otimes @ SV1527 @ SV865 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4073]) ).
thf(4756,plain,
! [SV1528: $i,SV866: $i,SV119: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV119 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV866 @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV1528 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4757,plain,
! [SV1529: $i,SV867: $i,SV120: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV120 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV867 @ ( c_HOL_Otimes__class_Otimes @ SV867 @ SV1529 @ SV120 ) @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4075]) ).
thf(4758,plain,
! [SV1530: $i,SV868: $i,SV121: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV121 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV868 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1530 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ SV868 @ SV1530 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4076]) ).
thf(4759,plain,
! [SV1531: $i,SV869: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV122 ) )
= $true )
| ( ( ( c_lessequals @ SV869 @ SV1531 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV869 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1531 @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4760,plain,
! [SV870: $i,SV123: $i] :
( ( ( class_Divides_Osemiring__div @ SV123 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV870 @ SV123 )
= ( c_HOL_Ozero__class_Ozero @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4761,plain,
! [SV1962: $i,SV1532: $i,SV871: $i,SV124: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV124 )
| ~ ( class_Int_Onumber__ring @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4079]) ).
thf(4762,plain,
! [SV1963: $i,SV1533: $i,SV872: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV125 )
| ~ ( class_Int_Onumber__ring @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4763,plain,
! [SV1536: $i,SV875: $i,SV129: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV129 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV875 @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ SV1536 @ SV129 ) @ SV129 ) @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV875 @ SV1536 @ SV129 ) @ SV129 ) @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4764,plain,
! [SV1537: $i,SV876: $i,SV130: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV130 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV876 @ ( c_Orderings_Oord__class_Omin @ SV876 @ SV1537 @ SV130 ) @ SV130 )
= ( c_Orderings_Oord__class_Omin @ SV876 @ SV1537 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4765,plain,
! [SV1964: $i,SV1538: $i,SV877: $i,SV131: $i] :
( ( ! [SY4791: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV131 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SY4791 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SY4791 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4086]) ).
thf(4766,plain,
! [SV1539: $i,SV879: $i,SV133: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SV879 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV133 @ SV1539 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV133 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4767,plain,
! [SV1540: $i,SV880: $i,SV134: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV134 @ SV880 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1540 @ SV880 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV880 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4089]) ).
thf(4768,plain,
! [SV135: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4769,plain,
! [SV1541: $i,SV881: $i,SV136: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV881 @ SV1541 @ SV136 )
= ( c_HOL_Otimes__class_Otimes @ SV1541 @ SV881 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4770,plain,
! [SV1542: $i,SV883: $i,SV139: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV139 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV883 @ SV1542 @ SV139 )
= ( c_HOL_Otimes__class_Otimes @ SV1542 @ SV883 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4093]) ).
thf(4771,plain,
! [SV1965: $i,SV1543: $i,SV884: $i,SV140: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV140 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV884 @ SV1543 @ SV140 ) @ SV1965 @ SV140 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV884 @ SV1965 @ SV140 ) @ ( c_Divides_Odiv__class_Omod @ SV1543 @ SV1965 @ SV140 ) @ SV140 ) @ SV1965 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4094]) ).
thf(4772,plain,
! [SV1966: $i,SV1544: $i,SV885: $i,SV142: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV142 )
| ( ( c_HOL_Oplus__class_Oplus @ SV885 @ ( c_HOL_Oplus__class_Oplus @ SV1544 @ SV1966 @ SV142 ) @ SV142 )
= ( c_HOL_Oplus__class_Oplus @ SV1544 @ ( c_HOL_Oplus__class_Oplus @ SV885 @ SV1966 @ SV142 ) @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4773,plain,
! [SV1967: $i,SV1545: $i,SV886: $i,SV143: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV143 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV886 @ SV1545 @ SV143 ) @ SV1967 @ SV143 )
= ( c_HOL_Oplus__class_Oplus @ SV886 @ ( c_HOL_Oplus__class_Oplus @ SV1545 @ SV1967 @ SV143 ) @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4097]) ).
thf(4774,plain,
! [SV1968: $i,SV1546: $i,SV887: $i,SV144: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SV1546 @ SV1968 @ SV144 ) @ SV144 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SV1968 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4775,plain,
! [SV1969: $i,SV1547: $i,SV888: $i,SV145: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SV1547 @ SV1969 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SV1547 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4776,plain,
! [SV1970: $i,SV1548: $i,SV889: $i,SV146: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SV1548 @ SV146 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SV1970 @ SV146 ) @ SV1548 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4777,plain,
! [SV1971: $i,SV1549: $i,SV890: $i,SV147: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SV1549 @ SV147 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1971 @ SV890 @ SV147 ) @ SV1549 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4778,plain,
! [SV1972: $i,SV1550: $i,SV891: $i,SV148: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 )
| ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4779,plain,
! [SV1973: $i,SV1551: $i,SV894: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SV1551 @ tc_nat ) @ tc_nat ) @ SV1973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SV1551 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1973 @ SV151 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1551 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(4780,plain,
! [SV1974: $i,SV1552: $i,SV895: $i,SV152: $i] :
( ( ~ ( class_Ring__and__Field_Omult__mono1 @ SV152 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
| ~ ( c_lessequals @ SV1552 @ SV1974 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4104]) ).
thf(4781,plain,
! [SV1975: $i,SV1553: $i,SV896: $i,SV153: $i] :
( ( ~ ( class_Ring__and__Field_Omult__mono @ SV153 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
| ~ ( c_lessequals @ SV1553 @ SV1975 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4782,plain,
! [SV1976: $i,SV1554: $i,SV897: $i,SV154: $i] :
( ( ~ ( class_Ring__and__Field_Omult__mono @ SV154 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
| ~ ( c_lessequals @ SV897 @ SV1976 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4783,plain,
! [SV1977: $i,SV1555: $i,SV898: $i,SV155: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV155 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV1977 @ SV1555 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4107]) ).
thf(4784,plain,
! [SV1978: $i,SV1556: $i,SV899: $i,SV156: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV156 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1978 @ SV899 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4108]) ).
thf(4785,plain,
! [SV900: $i,SV157: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV157 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV900 @ SV900 @ SV157 )
= SV900 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4109]) ).
thf(4786,plain,
! [SV1979: $i,SV1557: $i,SV901: $i,SV158: $i] :
( ( ! [SY4792: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SY4792 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SY4792 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4110]) ).
thf(4787,plain,
! [SV1558: $i,SV902: $i,SV159: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV159 @ SV902 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1558 @ SV902 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV159 @ SV1558 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4788,plain,
! [SV1559: $i,SV903: $i,SV160: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV903 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV1559 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV903 @ SV1559 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4789,plain,
! [SV1560: $i,SV904: $i,SV161: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV904 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV1560 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV904 @ SV1560 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4790,plain,
! [SV1561: $i,SV905: $i,SV162: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV162 @ SV905 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1561 @ SV905 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV162 @ SV1561 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4791,plain,
! [SV1562: $i,SV906: $i,SV163: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV163 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV906 @ SV1562 @ tc_nat ) @ SV163 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV906 @ SV163 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1562 @ SV163 ) @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4792,plain,
! [SV1980: $i,SV1563: $i,SV907: $i,SV164: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV164 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ ( c_Divides_Odiv__class_Omod @ SV1563 @ SV1980 @ SV164 ) @ SV164 ) @ SV1980 @ SV164 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ SV1563 @ SV164 ) @ SV1980 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4793,plain,
! [SV1981: $i,SV1564: $i,SV908: $i,SV165: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV165 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV908 @ SV1564 @ SV165 ) @ SV1981 @ SV165 ) @ SV1564 @ SV165 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV908 @ SV1981 @ SV165 ) @ SV1564 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4794,plain,
! [SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ! [SY4793: $i,SY4794: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV166 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SY4793 @ SV166 ) @ SV166 ) @ SY4794 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SY4794 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SY4793 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4795,plain,
! [SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ! [SY4795: $i,SY4796: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV167 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SY4795 @ SY4796 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SY4796 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(4796,plain,
! [SV1567: $i,SV911: $i,SV168: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV168 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4797,plain,
! [SV1568: $i,SV912: $i,SV169: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV169 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4798,plain,
! [SV1569: $i,SV913: $i,SV170: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV170 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4799,plain,
! [SV914: $i,SV171: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV171 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV171 ) @ ( c_HOL_Otimes__class_Otimes @ SV914 @ SV914 @ SV171 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4123]) ).
thf(4800,plain,
! [SV1570: $i,SV915: $i,SV172: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV172 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4801,plain,
! [SV1571: $i,SV916: $i,SV173: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV173 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4125]) ).
thf(4802,plain,
! [SV1572: $i,SV917: $i,SV174: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4803,plain,
! [SV1573: $i,SV918: $i,SV175: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV175 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV918 @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ SV1573 @ SV175 ) @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1573 @ SV175 ) @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4804,plain,
! [SV1984: $i,SV1574: $i,SV919: $i,SV176: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV176 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1574 @ SV176 ) @ SV1984 @ SV176 )
= ( c_HOL_Otimes__class_Otimes @ SV919 @ ( c_HOL_Otimes__class_Otimes @ SV1574 @ SV1984 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(4805,plain,
! [SV1985: $i,SV1575: $i,SV920: $i,SV177: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV177 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1575 @ SV177 ) @ SV1985 @ SV177 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1985 @ SV177 ) @ SV1575 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4806,plain,
! [SV1986: $i,SV1576: $i,SV921: $i,SV178: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV178 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1576 @ SV178 ) @ SV1986 @ SV178 )
= ( c_HOL_Otimes__class_Otimes @ SV921 @ ( c_HOL_Otimes__class_Otimes @ SV1576 @ SV1986 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4807,plain,
! [SV1987: $i,SV1577: $i,SV922: $i,SV179: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV179 )
| ( ( c_HOL_Otimes__class_Otimes @ SV922 @ ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV1987 @ SV179 ) @ SV179 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV922 @ SV1577 @ SV179 ) @ SV1987 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4808,plain,
! [SV1988: $i,SV1578: $i,SV923: $i,SV180: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV180 )
| ( ( c_HOL_Otimes__class_Otimes @ SV923 @ ( c_HOL_Otimes__class_Otimes @ SV1578 @ SV1988 @ SV180 ) @ SV180 )
= ( c_HOL_Otimes__class_Otimes @ SV1578 @ ( c_HOL_Otimes__class_Otimes @ SV923 @ SV1988 @ SV180 ) @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4809,plain,
! [SV1989: $i,SV1580: $i,SV925: $i,SV182: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV182 )
| ( ( c_HOL_Otimes__class_Otimes @ SV925 @ ( c_HOL_Otimes__class_Otimes @ SV1580 @ SV1989 @ SV182 ) @ SV182 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV925 @ SV1580 @ SV182 ) @ SV1989 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4810,plain,
! [SV1990: $i,SV1581: $i,SV926: $i,SV183: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV926 @ SV1581 @ SV183 ) @ SV1990 @ SV183 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV926 @ SV1990 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV1581 @ SV1990 @ SV183 ) @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4811,plain,
! [SV1991: $i,SV1582: $i,SV927: $i,SV184: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV184 )
| ( ( c_HOL_Otimes__class_Otimes @ SV927 @ ( c_HOL_Oplus__class_Oplus @ SV1582 @ SV1991 @ SV184 ) @ SV184 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1582 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1991 @ SV184 ) @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4812,plain,
! [SV1992: $i,SV1583: $i,SV928: $i,SV185: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV185 )
| ( ( c_HOL_Otimes__class_Otimes @ SV928 @ ( c_HOL_Oplus__class_Oplus @ SV1583 @ SV1992 @ SV185 ) @ SV185 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1583 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1992 @ SV185 ) @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4813,plain,
! [SV1993: $i,SV1584: $i,SV929: $i,SV186: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV929 @ SV1584 @ SV186 ) @ SV1993 @ SV186 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SV1993 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV1584 @ SV1993 @ SV186 ) @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4814,plain,
! [SV1994: $i,SV1585: $i,SV930: $i,SV187: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV187 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV930 @ SV1585 @ SV187 ) @ SV1994 @ SV187 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV930 @ SV1994 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV1585 @ SV1994 @ SV187 ) @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4815,plain,
! [SV1995: $i,SV1588: $i,SV933: $i,SV190: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV190 )
| ( ( c_HOL_Otimes__class_Otimes @ SV933 @ ( c_HOL_Oplus__class_Oplus @ SV1588 @ SV1995 @ SV190 ) @ SV190 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1588 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1995 @ SV190 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4142]) ).
thf(4816,plain,
! [SV1996: $i,SV1589: $i,SV934: $i,SV191: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV191 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV934 @ SV1589 @ SV191 ) @ SV1996 @ SV191 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV1996 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV1589 @ SV1996 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(4817,plain,
! [SV192: $i,SV935: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV935 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV192 @ SV935 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4818,plain,
! [SV936: $i,SV193: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV193 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV193 @ SV936 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4819,plain,
! [SV937: $i,SV194: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV194 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV937 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV937 @ SV194 ) @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4146]) ).
thf(4820,plain,
! [SV938: $i,SV195: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV195 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV938 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV938 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4821,plain,
! [SV1590: $i,SV939: $i,SV196: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV196 ) )
= $true )
| ( ( ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SV1590 @ SV196 ) @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4148]) ).
thf(4822,plain,
! [SV1591: $i,SV940: $i,SV197: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV197 ) )
= $true )
| ( ( ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1591 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SV1591 @ SV940 @ SV197 ) @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4149]) ).
thf(4823,plain,
! [SV1592: $i,SV941: $i,SV198: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV198 ) )
= $true )
| ( ( ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1592 @ SV198 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SV1592 @ SV198 ) @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4824,plain,
! [SV1593: $i,SV942: $i,SV199: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV199 ) )
= $true )
| ( ( ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SV1593 @ SV942 @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4825,plain,
! [SV200: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV200 ) @ SV200 ) @ SV200 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4152]) ).
thf(4826,plain,
! [SV1997: $i,SV1594: $i,SV943: $i,SV201: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV943 @ SV1594 @ SV201 ) @ ( c_HOL_Otimes__class_Otimes @ SV1997 @ SV1594 @ SV201 ) @ SV201 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV943 @ SV1997 @ SV201 ) @ SV1594 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4827,plain,
! [SV1998: $i,SV1595: $i,SV944: $i,SV202: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1595 @ SV1998 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV944 @ SV1998 @ tc_nat )
| ~ ( c_lessequals @ SV202 @ SV1595 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4828,plain,
! [SV1999: $i,SV1596: $i,SV945: $i,SV204: $i] :
( ( ! [SY4797: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV204 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SY4797 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SY4797 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4155]) ).
thf(4829,plain,
! [SV2000: $i,SV1597: $i,SV946: $i,SV205: $i] :
( ( ! [SY4798: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ SV205 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SY4798 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SY4798 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4156]) ).
thf(4830,plain,
! [SV206: $i,SV947: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV947 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV206 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV206 @ SV947 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4157]) ).
thf(4831,plain,
! [SV207: $i,SV948: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV948 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV207 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV207 @ SV948 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4158]) ).
thf(4832,plain,
! [SV949: $i,SV208: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV208 @ tc_nat )
= $false )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV949 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV208 @ SV949 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4833,plain,
! [SV950: $i,SV209: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV209 @ tc_nat )
= $false )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV950 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV950 @ SV209 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4834,plain,
! [SV210: $i,SV951: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV951 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV210 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SV951 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4161]) ).
thf(4835,plain,
! [SV211: $i,SV952: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV952 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV211 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV211 @ SV952 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4836,plain,
! [SV212: $i,SV953: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV953 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV212 @ SV953 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV212 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4163]) ).
thf(4837,plain,
! [SV213: $i,SV954: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV954 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV954 @ SV213 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV213 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4838,plain,
! [SV955: $i,SV214: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV214 @ SV955 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV955 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ SV214 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4165]) ).
thf(4839,plain,
! [SV956: $i,SV215: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV215 @ SV956 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV956 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ SV215 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4166]) ).
thf(4840,plain,
! [SV216: $i,SV957: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV957 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV216 @ SV957 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV216 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4167]) ).
thf(4841,plain,
! [SV958: $i,SV217: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV217 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV958 @ tc_nat )
| ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV217 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4168]) ).
thf(4842,plain,
! [SV959: $i,SV218: $i] :
( ( ( c_lessequals @ SV218 @ SV959 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV218 @ ( c_Suc @ SV959 ) @ tc_nat ) )
= $true )
| ( ( SV218
= ( c_Suc @ SV959 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4169]) ).
thf(4843,plain,
! [SV2001: $i,SV1598: $i,SV960: $i,SV219: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV2001 @ SV219 ) @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4844,plain,
! [SV2002: $i,SV1599: $i,SV961: $i,SV220: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SV2002 @ SV961 @ SV220 ) @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4845,plain,
! [SV2003: $i,SV1600: $i,SV962: $i,SV221: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4846,plain,
! [SV2004: $i,SV1601: $i,SV963: $i,SV223: $i] :
( ( ! [SY4799: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1601 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV2004 @ SY4799 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV2004 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV1601 @ SY4799 @ SV223 ) @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4847,plain,
! [SV964: $i,SV224: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV224 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV964 @ SV224 ) @ SV224 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV964 @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4848,plain,
! [SV2005: $i,SV1602: $i,SV965: $i,SV225: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ SV965 @ SV1602 @ SV225 ) @ SV2005 @ SV225 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ SV965 @ SV2005 @ SV225 ) @ ( c_HOL_Oplus__class_Oplus @ SV1602 @ SV2005 @ SV225 ) @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4849,plain,
! [SV966: $i,SV226: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV226 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV966 @ SV966 @ SV226 ) @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4850,plain,
! [SV2006: $i,SV1603: $i,SV967: $i,SV227: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
| ( ( c_HOL_Oplus__class_Oplus @ SV967 @ ( c_HOL_Oplus__class_Oplus @ SV1603 @ SV2006 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1603 @ SV227 ) @ SV2006 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4851,plain,
! [SV2007: $i,SV1604: $i,SV968: $i,SV228: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV228 )
| ( ( c_HOL_Oplus__class_Oplus @ SV968 @ ( c_HOL_Oplus__class_Oplus @ SV1604 @ SV2007 @ SV228 ) @ SV228 )
= ( c_HOL_Oplus__class_Oplus @ SV1604 @ ( c_HOL_Oplus__class_Oplus @ SV968 @ SV2007 @ SV228 ) @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4852,plain,
! [SV2008: $i,SV1607: $i,SV971: $i,SV231: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV231 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV971 @ SV1607 @ SV231 ) @ SV2008 @ SV231 )
= ( c_HOL_Oplus__class_Oplus @ SV971 @ ( c_HOL_Oplus__class_Oplus @ SV1607 @ SV2008 @ SV231 ) @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4853,plain,
! [SV2009: $i,SV1608: $i,SV972: $i,SV232: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV232 )
| ( ( c_HOL_Oplus__class_Oplus @ SV972 @ ( c_HOL_Oplus__class_Oplus @ SV1608 @ SV2009 @ SV232 ) @ SV232 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV972 @ SV1608 @ SV232 ) @ SV2009 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(4854,plain,
! [SV2010: $i,SV1609: $i,SV973: $i,SV233: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV1609 @ SV233 ) @ SV2010 @ SV233 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV2010 @ SV233 ) @ SV1609 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4183]) ).
thf(4855,plain,
! [SV2011: $i,SV1610: $i,SV974: $i,SV234: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
| ( ( c_HOL_Oplus__class_Oplus @ SV974 @ ( c_HOL_Oplus__class_Oplus @ SV1610 @ SV2011 @ SV234 ) @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV1610 @ ( c_HOL_Oplus__class_Oplus @ SV974 @ SV2011 @ SV234 ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4184]) ).
thf(4856,plain,
! [SV2012: $i,SV1611: $i,SV975: $i,SV235: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SV1611 @ SV235 ) @ SV2012 @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV975 @ ( c_HOL_Oplus__class_Oplus @ SV1611 @ SV2012 @ SV235 ) @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4857,plain,
! [SV236: $i,SV976: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV976 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV976 @ SV236 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV236 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4858,plain,
! [SV1612: $i,SV977: $i,SV238: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV238 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ SV977 @ SV1612 @ SV238 ) @ SV238 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV977 @ SV238 ) @ ( c_HOL_Oabs__class_Oabs @ SV1612 @ SV238 ) @ SV238 ) @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4187]) ).
thf(4859,plain,
! [SV1613: $i,SV978: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ ( c_HOL_Oplus__class_Oplus @ SV978 @ SV1613 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV239 @ SV978 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4860,plain,
! [SV1614: $i,SV979: $i,SV240: $i] :
( ( ( c_lessequals @ SV240 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SV1614 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV240 @ SV1614 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4189]) ).
thf(4861,plain,
! [SV1615: $i,SV980: $i,SV241: $i] :
( ( ( c_lessequals @ SV241 @ SV980 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SV1615 @ tc_nat ) @ SV980 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4190]) ).
thf(4862,plain,
! [SV1616: $i,SV981: $i,SV242: $i] :
( ( ( c_lessequals @ SV242 @ SV981 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV242 @ tc_nat ) @ SV981 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4863,plain,
! [SV1617: $i,SV982: $i,SV243: $i] :
( ( ( c_lessequals @ SV243 @ ( c_HOL_Oplus__class_Oplus @ SV982 @ SV1617 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV243 @ SV982 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4192]) ).
thf(4864,plain,
! [SV1618: $i,SV983: $i,SV244: $i] :
( ( ( c_lessequals @ SV244 @ ( c_HOL_Oplus__class_Oplus @ SV983 @ SV1618 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV244 @ SV1618 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4193]) ).
thf(4865,plain,
! [SV2013: $i,SV1619: $i,SV984: $i,SV246: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV246 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ SV1619 @ SV246 ) @ SV2013 @ SV246 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ ( c_Divides_Odiv__class_Omod @ SV1619 @ SV2013 @ SV246 ) @ SV246 ) @ SV2013 @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4194]) ).
thf(4866,plain,
! [SV2014: $i,SV1620: $i,SV985: $i,SV247: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV247 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV985 @ SV1620 @ SV247 ) @ SV2014 @ SV247 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV985 @ SV2014 @ SV247 ) @ SV1620 @ SV247 ) @ SV2014 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4867,plain,
! [SV2015: $i,SV1621: $i,SV986: $i,SV248: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4868,plain,
! [SV1622: $i,SV988: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV250 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV988 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV1622 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(4869,plain,
! [SV1623: $i,SV989: $i,SV251: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV251 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV989 @ SV251 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1623 @ SV251 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4198]) ).
thf(4870,plain,
! [SV2016: $i,SV1624: $i,SV990: $i,SV252: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
| ( c_lessequals @ SV990 @ SV1624 @ SV252 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(4871,plain,
! [SV2017: $i,SV1625: $i,SV991: $i,SV253: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
| ( c_lessequals @ SV991 @ SV1625 @ SV253 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(4872,plain,
! [SV2018: $i,SV1626: $i,SV992: $i,SV254: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
| ~ ( c_lessequals @ SV1626 @ SV2018 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(4873,plain,
! [SV2019: $i,SV1627: $i,SV993: $i,SV255: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
| ( c_lessequals @ SV993 @ SV1627 @ SV255 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(4874,plain,
! [SV2020: $i,SV1628: $i,SV994: $i,SV256: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
| ~ ( c_lessequals @ SV2020 @ SV1628 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4875,plain,
! [SV2021: $i,SV1629: $i,SV995: $i,SV257: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
| ( c_lessequals @ SV995 @ SV1629 @ SV257 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4204]) ).
thf(4876,plain,
! [SV1630: $i,SV996: $i,SV258: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV996 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV1630 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV996 @ SV1630 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4205]) ).
thf(4877,plain,
! [SV1631: $i,SV997: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ SV997 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV997 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1631 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4206]) ).
thf(4878,plain,
! [SV1632: $i,SV998: $i,SV260: $i] :
( ( ( c_lessequals @ SV260 @ SV998 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1632 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV998 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4207]) ).
thf(4879,plain,
! [SV1633: $i,SV999: $i,SV261: $i] :
( ( ( c_lessequals @ SV261 @ SV999 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1633 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SV1633 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV999 @ SV1633 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4880,plain,
! [SV262: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV262 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= $false )
| ( ( SV262
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV262
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4209]) ).
thf(4881,plain,
! [SV2022: $i,SV1634: $i,SV1000: $i,SV263: $i] :
( ( ! [SY4800: $i] :
( ~ ( class_RealVector_Oreal__normed__algebra @ SV263 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1634 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ SY4800 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SY4800 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ SY4800 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SY4800 @ SV263 ) @ SV263 ) @ SV263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4210]) ).
thf(4882,plain,
! [SV1635: $i,SV1001: $i,SV266: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV266 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1001 @ SV1635 @ SV266 )
= ( c_Orderings_Oord__class_Omin @ SV1635 @ SV1001 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4883,plain,
! [SV2023: $i,SV1636: $i,SV1002: $i,SV267: $i] :
( ( ! [SY4801: $i] :
( ~ ( class_Ring__and__Field_Osemiring @ SV267 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1636 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2023 @ SV1636 @ SV267 ) @ SY4801 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV1002 @ SV2023 @ SV267 ) @ SV1636 @ SV267 ) @ SY4801 @ SV267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4884,plain,
! [SV2024: $i,SV1637: $i,SV1003: $i,SV268: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV268 @ SV1003 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1637 @ SV1003 @ tc_nat ) @ SV2024 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV268 @ SV1637 @ tc_nat ) @ SV1003 @ tc_nat ) @ SV2024 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4885,plain,
! [SV1004: $i,SV269: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV269 @ SV1004 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV269 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4214]) ).
thf(4886,plain,
! [SV270: $i,SV1005: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1005 @ SV270 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV270 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4887,plain,
! [SV1638: $i,SV1006: $i,SV271: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4216]) ).
thf(4888,plain,
! [SV1639: $i,SV1007: $i,SV272: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV272 ) )
= $true )
| ( ( ( SV1007
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1639 @ SV1639 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SV1007 @ SV1007 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4217]) ).
thf(4889,plain,
! [SV1640: $i,SV1008: $i,SV273: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV273 ) )
= $true )
| ( ( ( SV1008
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1008 @ SV1008 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1640 @ SV1640 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4218]) ).
thf(4890,plain,
! [SV1641: $i,SV1009: $i,SV275: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV275 @ SV1009 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1641 ) @ SV275 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1641 ) @ SV1009 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4891,plain,
! [SV1642: $i,SV1010: $i,SV276: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1010 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1642 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SV1642 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4892,plain,
! [SV1012: $i,SV278: $i] :
( ( ( c_lessequals @ SV278 @ SV1012 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV1012 ) @ SV278 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4893,plain,
! [SV1643: $i,SV1014: $i,SV281: $i] :
( ( ( c_lessequals @ SV281 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1014 @ SV281 @ tc_nat ) @ SV1643 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1643 @ SV1014 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4894,plain,
! [SV1015: $i,SV282: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV282 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1015 @ SV282 )
= SV1015 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV1015 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(4895,plain,
! [SV2025: $i,SV1644: $i,SV1016: $i,SV283: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV283 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ SV1644 @ SV283 ) @ SV2025 @ SV283 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ ( c_Divides_Odiv__class_Omod @ SV1644 @ SV2025 @ SV283 ) @ SV283 ) @ SV2025 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4225]) ).
thf(4896,plain,
! [SV2026: $i,SV1645: $i,SV1017: $i,SV284: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV284 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1017 @ SV1645 @ SV284 ) @ SV2026 @ SV284 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1017 @ SV2026 @ SV284 ) @ SV1645 @ SV284 ) @ SV2026 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4226]) ).
thf(4897,plain,
! [SV1646: $i,SV1018: $i,SV285: $i] :
( ( ( c_lessequals @ SV285 @ SV1018 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1646 ) @ SV285 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1646 ) @ SV1018 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4227]) ).
thf(4898,plain,
! [SV1647: $i,SV1019: $i,SV286: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1019 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1647 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1019 @ SV1647 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4228]) ).
thf(4899,plain,
! [SV1648: $i,SV1020: $i,SV287: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV287 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV287 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1020 @ SV1020 @ SV287 ) @ ( c_HOL_Otimes__class_Otimes @ SV1648 @ SV1648 @ SV287 ) @ SV287 ) @ SV287 )
| ( SV1648
= ( c_HOL_Ozero__class_Ozero @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4229]) ).
thf(4900,plain,
! [SV1649: $i,SV1021: $i,SV288: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV288 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV288 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1021 @ SV1021 @ SV288 ) @ ( c_HOL_Otimes__class_Otimes @ SV1649 @ SV1649 @ SV288 ) @ SV288 ) @ SV288 )
| ( SV1021
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4230]) ).
thf(4901,plain,
! [SV1022: $i,SV289: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV289 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1022 @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV289 ) @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4902,plain,
! [SV291: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_Suc @ SV291 ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV291 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4903,plain,
! [SV2027: $i,SV1652: $i,SV1026: $i,SV298: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4904,plain,
! [SV2028: $i,SV1653: $i,SV1027: $i,SV299: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(4905,plain,
! [SV2029: $i,SV1654: $i,SV1028: $i,SV300: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(4906,plain,
! [SV2030: $i,SV1655: $i,SV1029: $i,SV301: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(4907,plain,
! [SV2031: $i,SV1656: $i,SV1030: $i,SV302: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(4908,plain,
! [SV2032: $i,SV1657: $i,SV1031: $i,SV303: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4241]) ).
thf(4909,plain,
! [SV2033: $i,SV1658: $i,SV1032: $i,SV304: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4242]) ).
thf(4910,plain,
! [SV2034: $i,SV1659: $i,SV1033: $i,SV305: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4243]) ).
thf(4911,plain,
! [SV2035: $i,SV1660: $i,SV1034: $i,SV306: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(4912,plain,
! [SV2036: $i,SV1661: $i,SV1035: $i,SV307: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4245]) ).
thf(4913,plain,
! [SV2037: $i,SV1662: $i,SV1036: $i,SV308: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
| ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4246]) ).
thf(4914,plain,
! [SV2038: $i,SV1663: $i,SV1037: $i,SV309: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(4915,plain,
! [SV2039: $i,SV1664: $i,SV1038: $i,SV310: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(4916,plain,
! [SV1665: $i,SV1039: $i,SV311: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1039 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1665 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV1665 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4249]) ).
thf(4917,plain,
! [SV1666: $i,SV1040: $i,SV312: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV312 @ SV1040 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV1040 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1666 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4918,plain,
! [SV1667: $i,SV1041: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SV1041 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1667 @ SV1041 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1041 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1667 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4919,plain,
! [SV1668: $i,SV1042: $i,SV314: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1042 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1668 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1668 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4920,plain,
! [SV1669: $i,SV1043: $i,SV315: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1043 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1669 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1043 @ SV1669 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4253]) ).
thf(4921,plain,
! [SV1670: $i,SV1044: $i,SV316: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SV1044 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1670 @ SV1044 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV316 @ SV1670 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1044 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4254]) ).
thf(4922,plain,
! [SV2040: $i,SV1671: $i,SV1045: $i,SV317: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV317 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1045 @ ( c_HOL_Otimes__class_Otimes @ SV1671 @ SV2040 @ SV317 ) @ SV317 ) @ SV1671 @ SV317 )
= ( c_Divides_Odiv__class_Omod @ SV1045 @ SV1671 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4255]) ).
thf(4923,plain,
! [SV2041: $i,SV1672: $i,SV1046: $i,SV318: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV318 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1046 @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2041 @ SV318 ) @ SV318 ) @ SV2041 @ SV318 )
= ( c_Divides_Odiv__class_Omod @ SV1046 @ SV2041 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(4924,plain,
! [SV2042: $i,SV1674: $i,SV1048: $i,SV320: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV320 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
| ( SV2042
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SV2042 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SV2042 @ SV320 ) @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4925,plain,
! [SV2043: $i,SV1675: $i,SV1049: $i,SV321: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV321 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
| ( SV2043
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1675 @ SV321 ) @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4259]) ).
thf(4926,plain,
! [SV1676: $i,SV1050: $i,SV322: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV322 @ SV1050 @ tc_nat )
= $true )
| ( ( ( SV1676
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV322 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV1050 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4927,plain,
! [SV1677: $i,SV1051: $i,SV323: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV323 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4928,plain,
! [SV1678: $i,SV1052: $i,SV324: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV324 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 )
| ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4262]) ).
thf(4929,plain,
! [SV1679: $i,SV1053: $i,SV325: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4263]) ).
thf(4930,plain,
! [SV1680: $i,SV1054: $i,SV326: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 )
| ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4264]) ).
thf(4931,plain,
! [SV1681: $i,SV1055: $i,SV327: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4932,plain,
! [SV1682: $i,SV1056: $i,SV328: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 )
| ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4933,plain,
! [SV1683: $i,SV1057: $i,SV329: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4934,plain,
! [SV1684: $i,SV1058: $i,SV331: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4269]) ).
thf(4935,plain,
! [SV1685: $i,SV1059: $i,SV332: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4270]) ).
thf(4936,plain,
! [SV1686: $i,SV1060: $i,SV333: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV333 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1060 @ SV1686 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1686 @ SV1060 @ SV333 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4937,plain,
! [SV1061: $i,SV334: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 )
= $false )
| ( ( ( SV1061
= ( c_HOL_Ozero__class_Ozero @ SV334 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV334 ) @ SV1061 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4938,plain,
! [SV1062: $i,SV336: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV336 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1062 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV1062 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4274]) ).
thf(4939,plain,
! [SV2044: $i,SV1687: $i,SV1064: $i,SV338: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV338 )
| ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1064 @ SV1687 @ SV338 ) @ SV2044 @ SV338 )
= ( c_Orderings_Oord__class_Omin @ SV1064 @ ( c_Orderings_Oord__class_Omin @ SV1687 @ SV2044 @ SV338 ) @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4275]) ).
thf(4940,plain,
! [SV2045: $i,SV1688: $i,SV1065: $i,SV339: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV339 )
| ( ( c_Orderings_Oord__class_Omin @ SV1065 @ ( c_Orderings_Oord__class_Omin @ SV1688 @ SV2045 @ SV339 ) @ SV339 )
= ( c_Orderings_Oord__class_Omin @ SV1688 @ ( c_Orderings_Oord__class_Omin @ SV1065 @ SV2045 @ SV339 ) @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4276]) ).
thf(4941,plain,
! [SV1689: $i,SV1066: $i,SV340: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4277]) ).
thf(4942,plain,
! [SV341: $i,SV1067: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1067 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV341 @ SV1067 @ tc_nat ) @ SV1067 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(4943,plain,
! [SV1690: $i,SV1068: $i,SV342: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV342 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1068 @ SV1690 @ SV342 )
= SV1068 )
| ~ ( c_lessequals @ SV1068 @ SV1690 @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4944,plain,
! [SV1691: $i,SV1069: $i,SV343: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV343 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1069 @ SV1691 @ SV343 )
= SV1691 )
| ~ ( c_lessequals @ SV1691 @ SV1069 @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4280]) ).
thf(4945,plain,
! [SV344: $i,SV1070: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV1070 @ SV344 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV344 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4281]) ).
thf(4946,plain,
! [SV1071: $i,SV345: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV345 @ SV1071 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV345 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4282]) ).
thf(4947,plain,
! [SV1692: $i,SV1072: $i,SV346: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4948,plain,
! [SV1073: $i,SV347: $i] :
( ( ( c_lessequals @ SV347 @ SV1073 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV347 @ ( c_Suc @ SV1073 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4284]) ).
thf(4949,plain,
! [SV1074: $i,SV348: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV348 @ ( c_Suc @ SV1074 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV348 @ SV1074 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4285]) ).
thf(4950,plain,
! [SV2046: $i,SV1693: $i,SV1075: $i,SV350: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1693 @ SV2046 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1075 @ SV2046 @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SV1693 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(4951,plain,
! [SV2047: $i,SV1694: $i,SV1076: $i,SV351: $i] :
( ( ! [SY4802: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SY4802 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SV1694 @ SY4802 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(4952,plain,
! [SV2048: $i,SV1695: $i,SV1077: $i,SV352: $i] :
( ( ! [SY4803: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2048 @ SV1077 @ tc_nat ) @ SY4803 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SV2048 @ tc_nat ) @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ SY4803 @ tc_nat ) )
| ~ ( c_lessequals @ SV2048 @ SV352 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(4953,plain,
! [SV2049: $i,SV1696: $i,SV1078: $i,SV353: $i] :
( ( ! [SY4804: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV1078 @ tc_nat ) @ SV1696 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2049 @ SV1078 @ tc_nat ) @ SY4804 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1696 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2049 @ SV353 @ tc_nat ) @ SV1078 @ tc_nat ) @ SY4804 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV353 @ SV2049 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4954,plain,
! [SV1079: $i,SV354: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV354 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV1079 @ SV354 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ ( c_HOL_Oplus__class_Oplus @ SV1079 @ SV1079 @ SV354 ) @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4955,plain,
! [SV1080: $i,SV355: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV355 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ ( c_HOL_Oplus__class_Oplus @ SV1080 @ SV1080 @ SV355 ) @ SV355 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ SV1080 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4956,plain,
! [SV1697: $i,SV1081: $i,SV356: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV356 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1081 @ SV1697 @ SV356 ) @ SV1697 @ SV356 )
= ( c_Divides_Odiv__class_Omod @ SV1081 @ SV1697 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4293]) ).
thf(4957,plain,
! [SV2050: $i,SV1698: $i,SV1082: $i,SV357: $i] :
( ( ! [SY4805: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1082 @ SV1698 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SV2050 @ SY4805 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1082 @ SV2050 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1698 @ SY4805 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4294]) ).
thf(4958,plain,
! [SV2051: $i,SV1699: $i,SV1083: $i,SV358: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4295]) ).
thf(4959,plain,
! [SV1084: $i,SV359: $i] :
( ( ( c_lessequals @ SV359 @ SV1084 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV359 @ SV1084 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4296]) ).
thf(4960,plain,
! [SV1700: $i,SV1085: $i,SV360: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1085 @ SV1700 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4297]) ).
thf(4961,plain,
! [SV1701: $i,SV1086: $i,SV361: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1701 @ SV1086 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4298]) ).
thf(4962,plain,
! [SV2052: $i,SV1702: $i,SV1087: $i,SV362: $i] :
( ( ! [SY4806: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV362 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1702 @ SV362 ) @ SV2052 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4806 @ SV1702 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SY4806 @ SV362 ) @ SV1702 @ SV362 ) @ SV2052 @ SV362 ) @ SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4299]) ).
thf(4963,plain,
! [SV1703: $i,SV1088: $i,SV363: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1088 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1703 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1088 @ SV1703 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(4964,plain,
! [SV2053: $i,SV1704: $i,SV1089: $i,SV364: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV364 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV1704 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV2053 @ SV364 ) @ SV364 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1704 @ SV2053 @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4301]) ).
thf(4965,plain,
! [SV2054: $i,SV1705: $i,SV1090: $i,SV365: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV365 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SV1705 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SV2054 @ SV1705 @ SV365 ) @ SV365 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SV2054 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4302]) ).
thf(4966,plain,
! [SV1091: $i,SV366: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV366 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ SV1091 @ SV366 ) @ SV366 )
= ( c_HOL_Oabs__class_Oabs @ SV1091 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4303]) ).
thf(4967,plain,
! [SV1094: $i,SV369: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV369 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oabs__class_Oabs @ SV1094 @ SV369 ) @ SV369 )
| ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4968,plain,
! [SV370: $i,SV1095: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1095 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV370 @ SV1095 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4305]) ).
thf(4969,plain,
! [SV1096: $i,SV371: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV371 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV371 @ SV1096 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4306]) ).
thf(4970,plain,
! [SV1097: $i,SV372: $i] :
( ( ( class_Divides_Osemiring__div @ SV372 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1097 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 )
= SV1097 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4971,plain,
! [SV1098: $i,SV373: $i] :
( ( ( class_Divides_Osemiring__div @ SV373 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1098 @ SV1098 @ SV373 )
= ( c_HOL_Ozero__class_Ozero @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4308]) ).
thf(4972,plain,
! [SV1706: $i,SV1099: $i,SV374: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV374 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1099 @ SV1706 @ SV374 )
= ( c_HOL_Oplus__class_Oplus @ SV1706 @ SV1099 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4973,plain,
! [SV1707: $i,SV1101: $i,SV376: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV376 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1101 @ SV1707 @ SV376 )
= ( c_HOL_Oplus__class_Oplus @ SV1707 @ SV1101 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4310]) ).
thf(4974,plain,
! [SV1708: $i,SV1102: $i,SV377: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV377 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1102 @ SV1708 @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ SV1708 @ SV1102 @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4311]) ).
thf(4975,plain,
! [SV2055: $i,SV1709: $i,SV1103: $i,SV378: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV378 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1103 @ SV1709 @ SV378 ) @ SV2055 @ SV378 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1103 @ SV2055 @ SV378 ) @ ( c_Divides_Odiv__class_Omod @ SV1709 @ SV2055 @ SV378 ) @ SV378 ) @ SV2055 @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4312]) ).
thf(4976,plain,
! [SV2056: $i,SV1710: $i,SV1104: $i,SV379: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV379 )
| ( c_lessequals @ SV1104 @ SV1710 @ SV379 )
| ~ ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SV1710 @ SV2056 @ SV379 ) @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4977,plain,
! [SV2057: $i,SV1711: $i,SV1105: $i,SV380: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV380 )
| ( c_lessequals @ SV1105 @ SV1711 @ SV380 )
| ~ ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SV2057 @ SV1711 @ SV380 ) @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4978,plain,
! [SV2058: $i,SV1712: $i,SV1106: $i,SV381: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV381 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SV1712 @ SV381 ) @ SV2058 @ SV381 )
| ~ ( c_lessequals @ SV1106 @ SV2058 @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4315]) ).
thf(4979,plain,
! [SV2059: $i,SV1713: $i,SV1107: $i,SV382: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV382 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SV1713 @ SV382 ) @ SV2059 @ SV382 )
| ~ ( c_lessequals @ SV1713 @ SV2059 @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4316]) ).
thf(4980,plain,
! [SV2060: $i,SV1714: $i,SV1108: $i,SV383: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV383 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SV1714 @ SV383 ) @ SV2060 @ SV383 )
| ~ ( c_lessequals @ SV1108 @ SV2060 @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(4981,plain,
! [SV2061: $i,SV1715: $i,SV1109: $i,SV384: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV384 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SV1715 @ SV384 ) @ SV2061 @ SV384 )
| ~ ( c_lessequals @ SV1715 @ SV2061 @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4982,plain,
! [SV2062: $i,SV1716: $i,SV1110: $i,SV385: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV385 )
| ( c_lessequals @ SV1110 @ SV1716 @ SV385 )
| ~ ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SV1716 @ SV2062 @ SV385 ) @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4319]) ).
thf(4983,plain,
! [SV2063: $i,SV1717: $i,SV1111: $i,SV386: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV386 )
| ( c_lessequals @ SV1111 @ SV1717 @ SV386 )
| ~ ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SV2063 @ SV1717 @ SV386 ) @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4320]) ).
thf(4984,plain,
! [SV1112: $i,SV387: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV387 )
= $false )
| ( ( c_lessequals @ SV1112 @ ( c_HOL_Oabs__class_Oabs @ SV1112 @ SV387 ) @ SV387 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4985,plain,
! [SV2064: $i,SV1718: $i,SV1113: $i,SV388: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
| ( c_lessequals @ SV2064 @ SV1718 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2064 @ SV1113 @ SV388 ) @ SV1718 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(4986,plain,
! [SV2065: $i,SV1719: $i,SV1114: $i,SV389: $i] :
( ( ~ ( c_lessequals @ SV389 @ SV1114 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV389 @ SV1719 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1114 @ SV389 @ tc_nat ) @ SV1719 @ tc_nat ) @ SV2065 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1114 @ SV1719 @ tc_nat ) @ SV2065 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4323]) ).
thf(4987,plain,
! [SV1720: $i,SV1115: $i,SV390: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV390 @ SV1115 @ tc_nat ) @ SV1720 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV390 @ ( c_HOL_Oplus__class_Oplus @ SV1720 @ SV1115 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(4988,plain,
! [SV1721: $i,SV1116: $i,SV391: $i] :
( ( ( c_lessequals @ SV391 @ ( c_HOL_Oplus__class_Oplus @ SV1116 @ SV1721 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV391 @ SV1721 @ tc_nat ) @ SV1116 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4325]) ).
thf(4989,plain,
! [SV2066: $i,SV1722: $i,SV1117: $i,SV392: $i] :
( ( ! [SY4807: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ SY4807 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SY4807 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4990,plain,
! [SV2067: $i,SV1723: $i,SV1118: $i,SV393: $i] :
( ( ! [SY4808: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2067 @ SV1118 @ tc_nat ) @ SY4808 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SV2067 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SY4808 @ tc_nat )
| ~ ( c_lessequals @ SV2067 @ SV393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4327]) ).
thf(4991,plain,
! [SV2068: $i,SV1724: $i,SV1119: $i,SV394: $i] :
( ( ! [SY4809: $i] :
( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SV2068 @ tc_nat ) @ SY4809 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SV2068 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SV2068 @ tc_nat ) @ SY4809 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1724 @ SV1119 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4328]) ).
thf(4992,plain,
! [SV2069: $i,SV1725: $i,SV1120: $i,SV395: $i] :
( ( ! [SY4810: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2069 @ SV1120 @ tc_nat ) @ SY4810 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2069 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SY4810 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV395 @ SV2069 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4329]) ).
thf(4993,plain,
! [SV1726: $i,SV1121: $i,SV396: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV396 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1726 @ tc_nat ) @ SV396 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1121 @ SV396 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1726 @ SV396 ) @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4994,plain,
! [SV1123: $i,SV398: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV398 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1123 @ SV398 ) @ ( c_HOL_Oabs__class_Oabs @ SV1123 @ SV398 ) @ SV398 )
= ( c_HOL_Otimes__class_Otimes @ SV1123 @ SV1123 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4995,plain,
! [SV1124: $i,SV399: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV399 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV399 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1124 @ SV399 ) @ SV399 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4333]) ).
thf(4996,plain,
! [SV1125: $i,SV400: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV400 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV400 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1125 @ SV400 ) @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4997,plain,
! [SV1126: $i,SV401: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV401 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1126 @ ( c_HOL_Ozero__class_Ozero @ SV401 ) @ SV401 )
= SV1126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4335]) ).
thf(4998,plain,
! [SV1127: $i,SV402: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV402 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV402 ) @ SV1127 @ SV402 )
= SV1127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4336]) ).
thf(4999,plain,
! [SV1128: $i,SV403: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV403 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1128 @ ( c_HOL_Ozero__class_Ozero @ SV403 ) @ SV403 )
= SV1128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4337]) ).
thf(5000,plain,
! [SV1129: $i,SV404: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV404 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV404 )
| ( SV1129
= ( c_HOL_Oplus__class_Oplus @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(5001,plain,
! [SV1130: $i,SV405: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV405 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV1130 @ SV405 )
= SV1130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4339]) ).
thf(5002,plain,
! [SV1131: $i,SV406: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV406 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1131 @ SV406 )
= SV1131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(5003,plain,
! [SV1132: $i,SV410: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV410 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1132 @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV410 )
= SV1132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4341]) ).
thf(5004,plain,
! [SV1133: $i,SV411: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV411 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV411 ) @ SV1133 @ SV411 )
= SV1133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(5005,plain,
! [SV2070: $i,SV1728: $i,SV1134: $i,SV412: $i] :
( ( ! [SY4811: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SY4811 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SV1728 @ SY4811 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(5006,plain,
! [SV2071: $i,SV1729: $i,SV1135: $i,SV413: $i] :
( ( ! [SY4812: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SY4812 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SY4812 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(5007,plain,
! [SV1730: $i,SV1136: $i,SV414: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(5008,plain,
! [SV1731: $i,SV1137: $i,SV415: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(5009,plain,
! [SV2072: $i,SV1732: $i,SV1138: $i,SV416: $i] :
( ( ~ ( class_Orderings_Oorder @ SV416 )
| ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
| ~ ( c_lessequals @ SV1138 @ SV2072 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(5010,plain,
! [SV2073: $i,SV1733: $i,SV1139: $i,SV417: $i] :
( ( ~ ( class_Orderings_Oorder @ SV417 )
| ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 )
| ~ ( c_lessequals @ SV2073 @ SV1733 @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4348]) ).
thf(5011,plain,
! [SV2074: $i,SV1734: $i,SV1140: $i,SV418: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV418 )
| ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
| ~ ( c_lessequals @ SV2074 @ SV1734 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4349]) ).
thf(5012,plain,
! [SV2075: $i,SV1735: $i,SV1141: $i,SV419: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV419 )
| ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 )
| ~ ( c_lessequals @ SV1141 @ SV2075 @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4350]) ).
thf(5013,plain,
! [SV2076: $i,SV1736: $i,SV1142: $i,SV420: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SV1736 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SV2076 @ SV1736 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SV1142 @ SV2076 @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(5014,plain,
! [SV2077: $i,SV1737: $i,SV1143: $i,SV421: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SV1737 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SV2077 @ SV1737 @ SV421 ) @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SV1143 @ SV2077 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(5015,plain,
! [SV2078: $i,SV1738: $i,SV1144: $i,SV422: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
| ( c_HOL_Oord__class_Oless @ SV1144 @ SV1738 @ SV422 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SV2078 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SV1738 @ SV2078 @ SV422 ) @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(5016,plain,
! [SV2079: $i,SV1739: $i,SV1145: $i,SV423: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV1739 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV2079 @ SV423 ) @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SV2079 @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(5017,plain,
! [SV2080: $i,SV1740: $i,SV1146: $i,SV424: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV1740 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV2080 @ SV424 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SV2080 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(5018,plain,
! [SV2081: $i,SV1741: $i,SV1147: $i,SV425: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
| ( c_HOL_Oord__class_Oless @ SV1147 @ SV1741 @ SV425 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1741 @ SV425 ) @ SV425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4356]) ).
thf(5019,plain,
! [SV1742: $i,SV1148: $i,SV426: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV426 ) )
= $true )
| ( ( ( c_lessequals @ SV1148 @ SV1742 @ SV426 )
| ~ ( c_HOL_Oord__class_Oless @ SV1148 @ SV1742 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(5020,plain,
! [SV1743: $i,SV1149: $i,SV427: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV427 ) )
= $true )
| ( ( ( c_lessequals @ SV1149 @ SV1743 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1149 @ SV1743 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4358]) ).
thf(5021,plain,
! [SV2082: $i,SV1744: $i,SV1150: $i,SV428: $i] :
( ( ! [SY4813: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SY4813 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SY4813 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(5022,plain,
! [SV1745: $i,SV1151: $i,SV429: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV429 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1745 @ SV429 )
| ( c_lessequals @ SV1745 @ SV1151 @ SV429 )
| ~ ( c_lessequals @ SV1151 @ SV1745 @ SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4360]) ).
thf(5023,plain,
! [SV2083: $i,SV1746: $i,SV1152: $i,SV430: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV2083 @ SV1746 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2083 @ SV1152 @ SV430 ) @ SV1746 @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(5024,plain,
! [SV1747: $i,SV1153: $i,SV431: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV431 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1153 @ SV1747 @ SV431 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1153 @ SV431 ) @ SV1747 @ SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4362]) ).
thf(5025,plain,
! [SV2084: $i,SV1748: $i,SV1154: $i,SV432: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SV2084 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SV2084 @ SV432 ) @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4363]) ).
thf(5026,plain,
! [SV2085: $i,SV1749: $i,SV1155: $i,SV433: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1155 @ SV433 ) @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(5027,plain,
! [SV1750: $i,SV1156: $i,SV434: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV434 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1750 @ SV434 )
| ( SV1750 = SV1156 )
| ~ ( c_lessequals @ SV1156 @ SV1750 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(5028,plain,
! [SV1751: $i,SV1157: $i,SV435: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV435 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1751 @ SV435 )
| ~ ( c_lessequals @ SV1157 @ SV1751 @ SV435 )
| ( SV1751 = SV1157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4366]) ).
thf(5029,plain,
! [SV1752: $i,SV1158: $i,SV436: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV436 ) )
= $true )
| ( ( ( SV1158 = SV1752 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1752 @ SV436 )
| ~ ( c_lessequals @ SV1158 @ SV1752 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(5030,plain,
! [SV1753: $i,SV1159: $i,SV437: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV437 ) )
= $true )
| ( ( ( SV1159 = SV1753 )
| ~ ( c_lessequals @ SV1159 @ SV1753 @ SV437 )
| ( c_HOL_Oord__class_Oless @ SV1159 @ SV1753 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4368]) ).
thf(5031,plain,
! [SV1754: $i,SV1160: $i,SV438: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV438 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV1754 @ SV438 )
| ~ ( c_lessequals @ SV1160 @ SV1754 @ SV438 )
| ( SV1160 = SV1754 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4369]) ).
thf(5032,plain,
! [SV1755: $i,SV1161: $i,SV439: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV439 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1755 @ SV439 )
| ( SV1161 = SV1755 )
| ~ ( c_lessequals @ SV1161 @ SV1755 @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4370]) ).
thf(5033,plain,
! [SV1756: $i,SV1162: $i,SV440: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV440 ) )
= $true )
| ( ( ( SV1162 = SV1756 )
| ( c_HOL_Oord__class_Oless @ SV1162 @ SV1756 @ SV440 )
| ~ ( c_lessequals @ SV1162 @ SV1756 @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4371]) ).
thf(5034,plain,
! [SV1757: $i,SV1163: $i,SV441: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV441 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV1757 @ SV441 )
| ( SV1163 = SV1757 )
| ~ ( c_lessequals @ SV1163 @ SV1757 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4372]) ).
thf(5035,plain,
! [SV2086: $i,SV1758: $i,SV1164: $i,SV442: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV442 )
| ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(5036,plain,
! [SV1759: $i,SV1165: $i,SV443: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV443 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1165 @ SV1759 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ SV1759 @ SV1165 @ SV443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4374]) ).
thf(5037,plain,
! [SV1760: $i,SV1166: $i,SV444: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV444 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1166 @ SV1760 @ SV444 )
| ( c_lessequals @ SV1760 @ SV1166 @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4375]) ).
thf(5038,plain,
! [SV1167: $i,SV445: $i] :
( ( ( class_Orderings_Olinorder @ SV445 )
= $false )
| ( ( ~ ( c_lessequals @ SV1167 @ SV1167 @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1167 @ SV1167 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(5039,plain,
! [SV1168: $i,SV446: $i] :
( ( ( class_Orderings_Olinorder @ SV446 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1168 @ SV1168 @ SV446 )
| ( c_lessequals @ SV1168 @ SV1168 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(5040,plain,
! [SV1761: $i,SV1169: $i,SV447: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV447 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1169 @ SV1761 @ SV447 )
| ~ ( c_lessequals @ SV1761 @ SV1169 @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4378]) ).
thf(5041,plain,
! [SV1762: $i,SV1170: $i,SV448: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV448 ) )
= $true )
| ( ( ( c_lessequals @ SV1170 @ SV1762 @ SV448 )
| ( c_HOL_Oord__class_Oless @ SV1762 @ SV1170 @ SV448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4379]) ).
thf(5042,plain,
! [SV1763: $i,SV1171: $i,SV449: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV449 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1171 @ SV1763 @ SV449 )
| ( c_lessequals @ SV1763 @ SV1171 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4380]) ).
thf(5043,plain,
! [SV1764: $i,SV1172: $i,SV450: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV450 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1172 @ SV1764 @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ SV1764 @ SV1172 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4381]) ).
thf(5044,plain,
! [SV2087: $i,SV1765: $i,SV1173: $i,SV451: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV451 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SV1765 @ SV451 ) @ SV2087 @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2087 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(5045,plain,
! [SV2088: $i,SV1766: $i,SV1174: $i,SV452: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SV1766 @ SV452 ) @ SV2088 @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2088 @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(5046,plain,
! [SV2089: $i,SV1767: $i,SV1175: $i,SV453: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV453 )
| ( c_HOL_Oord__class_Oless @ SV1175 @ SV1767 @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SV2089 @ SV1767 @ SV453 ) @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(5047,plain,
! [SV2090: $i,SV1768: $i,SV1176: $i,SV454: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV454 )
| ( c_HOL_Oord__class_Oless @ SV1176 @ SV1768 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2090 @ SV454 ) @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(5048,plain,
! [SV2091: $i,SV1769: $i,SV1177: $i,SV455: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SV1769 @ SV455 ) @ SV2091 @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1769 @ SV2091 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(5049,plain,
! [SV2092: $i,SV1770: $i,SV1178: $i,SV456: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SV1770 @ SV456 ) @ SV2092 @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV2092 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4387]) ).
thf(5050,plain,
! [SV2093: $i,SV1771: $i,SV1179: $i,SV457: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV457 )
| ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SV1771 @ SV2093 @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1771 @ SV457 ) @ SV457 ) @ SV2093 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4388]) ).
thf(5051,plain,
! [SV2094: $i,SV1772: $i,SV1180: $i,SV458: $i] :
( ( ! [SY4814: $i,SY4815: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4814 @ SV1772 @ SV458 ) @ SY4815 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4814 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SY4815 @ SV458 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4389]) ).
thf(5052,plain,
! [SV2095: $i,SV1773: $i,SV1181: $i,SV459: $i] :
( ( ! [SY4816: $i,SY4817: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SY4816 @ SV459 ) @ SY4817 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SY4816 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SY4816 @ SV459 ) @ SY4817 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4390]) ).
thf(5053,plain,
! [SV2096: $i,SV1774: $i,SV1182: $i,SV460: $i] :
( ( ! [SY4818: $i,SY4819: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4818 @ SV1774 @ SV460 ) @ SY4819 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SY4818 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SY4819 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4391]) ).
thf(5054,plain,
! [SV2097: $i,SV1775: $i,SV1183: $i,SV461: $i] :
( ( ! [SY4820: $i,SY4821: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SY4820 @ SV461 ) @ SY4821 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SY4820 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SY4821 @ SV461 ) @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4392]) ).
thf(5055,plain,
! [SV2098: $i,SV1776: $i,SV1184: $i,SV462: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV462 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(5056,plain,
! [SV2099: $i,SV1777: $i,SV1185: $i,SV463: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV463 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV1185 @ SV1777 @ SV463 ) @ SV2099 @ SV463 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV1185 @ SV2099 @ SV463 ) @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2099 @ SV463 ) @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4394]) ).
thf(5057,plain,
! [SV2100: $i,SV1778: $i,SV1186: $i,SV464: $i] :
( ( ~ ( class_Divides_Oring__div @ SV464 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ SV1778 @ SV464 ) @ SV2100 @ SV464 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ ( c_Divides_Odiv__class_Omod @ SV1778 @ SV2100 @ SV464 ) @ SV464 ) @ SV2100 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(5058,plain,
! [SV2101: $i,SV1779: $i,SV1187: $i,SV465: $i] :
( ( ~ ( class_Divides_Oring__div @ SV465 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1187 @ SV1779 @ SV465 ) @ SV2101 @ SV465 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1187 @ SV2101 @ SV465 ) @ SV1779 @ SV465 ) @ SV2101 @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4396]) ).
thf(5059,plain,
! [SV2102: $i,SV1780: $i,SV1188: $i,SV466: $i] :
( ( ~ ( class_Divides_Oring__div @ SV466 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1188 @ SV1780 @ SV466 ) @ SV2102 @ SV466 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1188 @ SV2102 @ SV466 ) @ ( c_Divides_Odiv__class_Omod @ SV1780 @ SV2102 @ SV466 ) @ SV466 ) @ SV2102 @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(5060,plain,
! [SV1781: $i,SV1189: $i,SV467: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV467 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1189 @ SV1781 @ SV467 ) @ SV467 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1781 @ SV1189 @ SV467 ) @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4398]) ).
thf(5061,plain,
! [SV2103: $i,SV1782: $i,SV1190: $i,SV468: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(5062,plain,
! [SV1191: $i,SV469: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV469 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1191 @ SV1191 @ SV469 )
= ( c_HOL_Ozero__class_Ozero @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(5063,plain,
! [SV1192: $i,SV470: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV470 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1192 @ SV1192 @ SV470 )
= ( c_HOL_Ozero__class_Ozero @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(5064,plain,
! [SV1193: $i,SV471: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV471 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1193 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= SV1193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(5065,plain,
! [SV1194: $i,SV472: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV472 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1194 @ SV1194 @ SV472 )
= ( c_HOL_Ozero__class_Ozero @ SV472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(5066,plain,
! [SV1195: $i,SV473: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV473 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV473 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1195 @ SV1195 @ SV473 )
= ( c_HOL_Ozero__class_Ozero @ SV473 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4404]) ).
thf(5067,plain,
! [SV1783: $i,SV1196: $i,SV474: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV474 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1783 @ SV474 ) @ SV1783 @ SV474 )
= SV1196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4405]) ).
thf(5068,plain,
! [SV2104: $i,SV1784: $i,SV1197: $i,SV475: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV475 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1197 @ ( c_HOL_Ominus__class_Ominus @ SV1784 @ SV2104 @ SV475 ) @ SV475 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV1784 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV2104 @ SV475 ) @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4406]) ).
thf(5069,plain,
! [SV2105: $i,SV1785: $i,SV1198: $i,SV476: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV476 )
| ( ( c_HOL_Otimes__class_Otimes @ SV1198 @ ( c_HOL_Ominus__class_Ominus @ SV1785 @ SV2105 @ SV476 ) @ SV476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV1785 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV2105 @ SV476 ) @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(5070,plain,
! [SV2106: $i,SV1786: $i,SV1199: $i,SV477: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV477 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1199 @ SV1786 @ SV477 ) @ SV2106 @ SV477 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1199 @ SV2106 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1786 @ SV2106 @ SV477 ) @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(5071,plain,
! [SV2107: $i,SV1787: $i,SV1200: $i,SV478: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV478 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1200 @ SV1787 @ SV478 ) @ SV2107 @ SV478 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1200 @ SV2107 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1787 @ SV2107 @ SV478 ) @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4409]) ).
thf(5072,plain,
! [SV2108: $i,SV1788: $i,SV1201: $i,SV479: $i] :
( ( ! [SY4822: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV479 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1201 @ SV1788 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SV2108 @ SY4822 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ SV2108 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SV1788 @ SY4822 @ SV479 ) @ SV479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4410]) ).
thf(5073,plain,
! [SV1789: $i,SV1202: $i,SV480: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV480 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1789 @ SV480 ) @ SV1789 @ SV480 )
= SV1202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4411]) ).
thf(5074,plain,
! [SV1790: $i,SV1203: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1203 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1790 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1203 @ SV1790 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(5075,plain,
! [SV1791: $i,SV1204: $i,SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV482 @ SV1204 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1791 @ SV482 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1791 @ SV1204 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4413]) ).
thf(5076,plain,
! [SV1792: $i,SV1205: $i,SV483: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV483 @ SV1205 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1792 @ SV1205 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV1792 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4414]) ).
thf(5077,plain,
! [SV1208: $i,SV487: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV487 @ SV1208 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV487 @ SV1208 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4417]) ).
thf(5078,plain,
! [SV1209: $i,SV488: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV488 @ SV1209 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV488 @ SV1209 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(5079,plain,
! [SV2109: $i,SV1793: $i,SV1210: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1793 @ SV2109 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1210 @ SV2109 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1793 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4419]) ).
thf(5080,plain,
! [SV1211: $i,SV490: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV490 @ SV1211 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV490 @ ( c_Suc @ SV1211 ) @ tc_nat ) )
= $true )
| ( ( SV490 = SV1211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(5081,plain,
! [SV491: $i,SV1212: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1212 @ ( c_Suc @ SV491 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1212 @ SV491 @ tc_nat )
= $true )
| ( ( SV491 = SV1212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(5082,plain,
! [SV1213: $i,SV493: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV493 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1213 @ ( c_HOL_Ozero__class_Ozero @ SV493 ) @ SV493 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(5083,plain,
! [SV1214: $i,SV494: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV494 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV494 ) @ SV1214 @ SV494 )
= ( c_HOL_Ozero__class_Ozero @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(5084,plain,
! [SV1215: $i,SV495: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV495 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1215 @ ( c_HOL_Ozero__class_Ozero @ SV495 ) @ SV495 )
= ( c_HOL_Ozero__class_Ozero @ SV495 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4424]) ).
thf(5085,plain,
! [SV1216: $i,SV496: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV496 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV496 ) @ SV1216 @ SV496 )
= ( c_HOL_Ozero__class_Ozero @ SV496 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4425]) ).
thf(5086,plain,
! [SV1217: $i,SV497: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV497 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV497 ) @ SV1217 @ SV497 )
= ( c_HOL_Ozero__class_Ozero @ SV497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4426]) ).
thf(5087,plain,
! [SV1218: $i,SV500: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV500 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ SV500 ) @ SV500 )
= ( c_HOL_Ozero__class_Ozero @ SV500 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4427]) ).
thf(5088,plain,
! [SV1219: $i,SV501: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV501 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1219 @ ( c_HOL_Ozero__class_Ozero @ SV501 ) @ SV501 )
= ( c_HOL_Ozero__class_Ozero @ SV501 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(5089,plain,
! [SV1220: $i,SV502: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV502 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV502 ) @ SV1220 @ SV502 )
= ( c_HOL_Ozero__class_Ozero @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4429]) ).
thf(5090,plain,
! [SV1221: $i,SV503: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV503 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV503 ) @ SV1221 @ SV503 )
= ( c_HOL_Ozero__class_Ozero @ SV503 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(5091,plain,
! [SV1222: $i,SV504: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV504 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1222 @ ( c_HOL_Ozero__class_Ozero @ SV504 ) @ SV504 )
= ( c_HOL_Ozero__class_Ozero @ SV504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4431]) ).
thf(5092,plain,
! [SV1223: $i,SV505: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV505 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV505 ) @ SV1223 @ SV505 )
= ( c_HOL_Ozero__class_Ozero @ SV505 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4432]) ).
thf(5093,plain,
! [SV1224: $i,SV506: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV506 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1224 @ ( c_HOL_Ozero__class_Ozero @ SV506 ) @ SV506 )
= ( c_HOL_Ozero__class_Ozero @ SV506 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4433]) ).
thf(5094,plain,
! [SV1794: $i,SV1225: $i,SV507: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV507 @ ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1794 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV507 @ SV1794 @ tc_nat ) @ SV1225 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1794 @ SV1225 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4434]) ).
thf(5095,plain,
! [SV1795: $i,SV1226: $i,SV509: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV509 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1226 @ SV509 ) @ SV1795 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV1226 @ SV1795 @ SV509 ) @ SV509 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SV1795 @ SV509 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(5096,plain,
! [SV1227: $i,SV510: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ SV1227 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV510 @ ( c_HOL_Oplus__class_Oplus @ SV1227 @ SV510 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(5097,plain,
! [SV1228: $i,SV511: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ ( c_HOL_Oplus__class_Oplus @ SV1228 @ SV511 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV511 @ SV1228 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(5098,plain,
! [SV1796: $i,SV1229: $i,SV512: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV512 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1229 @ SV1796 @ SV512 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1229 @ SV512 ) @ SV1796 @ SV512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(5099,plain,
! [SV1797: $i,SV1230: $i,SV513: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV513 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1230 @ SV513 ) @ SV1797 @ SV513 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1230 @ SV1797 @ SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(5100,plain,
! [SV1798: $i,SV1231: $i,SV514: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV514 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ SV1798 @ SV514 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ ( c_HOL_Oabs__class_Oabs @ SV1798 @ SV514 ) @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(5101,plain,
! [SV1799: $i,SV1232: $i,SV515: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV515 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ ( c_HOL_Oabs__class_Oabs @ SV1799 @ SV515 ) @ SV515 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ SV1799 @ SV515 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4441]) ).
thf(5102,plain,
! [SV1233: $i,SV516: $i] :
( ( ( c_lessequals @ SV516 @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV516 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1233 @ SV516 @ tc_nat ) @ SV516 @ tc_nat )
= SV1233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4442]) ).
thf(5103,plain,
! [SV1800: $i,SV1234: $i,SV517: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(5104,plain,
! [SV1239: $i,SV522: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SV1239 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV522 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1239 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(5105,plain,
! [SV1801: $i,SV1240: $i,SV523: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV523 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1240 @ SV1801 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1240 @ SV1801 @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(5106,plain,
! [SV1802: $i,SV1241: $i,SV524: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV524 ) )
= $true )
| ( ( ( c_lessequals @ SV1241 @ SV1802 @ SV524 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1241 @ SV1802 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(5107,plain,
! [SV1242: $i,SV525: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV525 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1242 @ SV525 ) @ ( c_HOL_Ozero__class_Ozero @ SV525 ) @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4447]) ).
thf(5108,plain,
! [SV526: $i,SV1243: $i] :
( ( ( c_lessequals @ SV1243 @ SV526 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV526 @ SV1243 @ tc_nat ) @ SV1243 @ tc_nat )
= SV526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(5109,plain,
! [SV1244: $i,SV527: $i] :
( ( ( c_lessequals @ SV527 @ SV1244 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV527 @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV527 @ tc_nat ) @ tc_nat )
= SV1244 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4449]) ).
thf(5110,plain,
! [SV1245: $i,SV528: $i] :
( ( ( c_lessequals @ SV528 @ SV1245 @ tc_nat )
= $false )
| ( ( SV1245
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1245 @ SV528 @ tc_nat ) @ SV528 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4450]) ).
thf(5111,plain,
! [SV1803: $i,SV1246: $i,SV529: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SV1246 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1803 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV1246 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(5112,plain,
! [SV1804: $i,SV1247: $i,SV530: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SV1247 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV1247 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1804 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4452]) ).
thf(5113,plain,
! [SV1805: $i,SV1248: $i,SV531: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1248 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1805 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1248 @ SV1805 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4453]) ).
thf(5114,plain,
! [SV1806: $i,SV1249: $i,SV532: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV532 @ SV1249 @ tc_nat ) @ SV1806 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV1806 @ tc_nat ) @ SV1249 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1249 @ SV532 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(5115,plain,
! [SV1807: $i,SV1250: $i,SV533: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV533 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1807 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV1250 @ tc_nat ) @ SV1807 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1807 @ SV1250 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(5116,plain,
! [SV1251: $i,SV534: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV534 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1251 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV534 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1251 @ SV534 ) @ SV534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(5117,plain,
! [SV1252: $i,SV535: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV535 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1252 @ SV535 ) @ SV535 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1252 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4457]) ).
thf(5118,plain,
! [SV2110: $i,SV1808: $i,SV1253: $i,SV536: $i] :
( ( ! [SY4823: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SY4823 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SY4823 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4458]) ).
thf(5119,plain,
! [SV2111: $i,SV1809: $i,SV1254: $i,SV537: $i] :
( ( ! [SY4824: $i] :
( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SY4824 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SY4824 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4459]) ).
thf(5120,plain,
! [SV1810: $i,SV1255: $i,SV538: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV538 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SV1810 @ SV538 ) @ SV538 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1255 @ SV538 ) @ ( c_HOL_Oabs__class_Oabs @ SV1810 @ SV538 ) @ SV538 ) @ SV538 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(5121,plain,
! [SV1256: $i,SV539: $i] :
( ( ( c_lessequals @ SV539 @ SV1256 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV539 @ ( c_Suc @ SV1256 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4461]) ).
thf(5122,plain,
! [SV1257: $i,SV540: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV540 ) @ SV1257 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV540 @ SV1257 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(5123,plain,
! [SV541: $i,SV1258: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1258 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV541 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV541 @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1258 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4463]) ).
thf(5124,plain,
! [SV542: $i,SV1259: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1259 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV542 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV542 @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV542 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4464]) ).
thf(5125,plain,
! [SV2112: $i,SV1811: $i,SV1260: $i,SV544: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV544 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SV1811 @ SV544 ) @ SV2112 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SV2112 @ SV544 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV2112 @ SV1811 @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4465]) ).
thf(5126,plain,
! [SV1261: $i,SV545: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV545 )
= $false )
| ( ( ( c_lessequals @ SV1261 @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1261 @ SV1261 @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4466]) ).
thf(5127,plain,
! [SV1262: $i,SV546: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV546 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1262 @ SV1262 @ SV546 ) @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
| ~ ( c_lessequals @ SV1262 @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4467]) ).
thf(5128,plain,
! [SV1263: $i,SV547: $i] :
( ( ( class_Orderings_Olinorder @ SV547 )
= $false )
| ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 )
| ( ( c_HOL_Oabs__class_Oabs @ SV1263 @ SV547 )
= SV1263 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(5129,plain,
! [SV1264: $i,SV548: $i] :
( ( ( class_Ring__and__Field_Oabs__if @ SV548 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1264 @ SV548 )
= SV1264 )
| ( c_HOL_Oord__class_Oless @ SV1264 @ ( c_HOL_Ozero__class_Ozero @ SV548 ) @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(5130,plain,
! [SV2113: $i,SV1812: $i,SV1265: $i,SV549: $i] :
( ( ! [SY4825: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SY4825 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SY4825 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4470]) ).
thf(5131,plain,
! [SV1813: $i,SV1266: $i,SV550: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV550 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SV1813 @ SV550 ) @ SV550 ) @ SV550 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SV1813 @ SV550 ) @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(5132,plain,
! [SV552: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ SV552 ) @ SV552 ) @ SV552 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4472]) ).
thf(5133,plain,
! [SV553: $i,SV1268: $i] :
( ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1268 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV553 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV553 @ SV1268 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(5134,plain,
! [SV1269: $i,SV554: $i] :
( ( ( class_Orderings_Opreorder @ SV554 )
= $false )
| ( ( c_lessequals @ SV1269 @ SV1269 @ SV554 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4474]) ).
thf(5135,plain,
! [SV1270: $i,SV555: $i] :
( ( ( class_Orderings_Oorder @ SV555 )
= $false )
| ( ( c_lessequals @ SV1270 @ SV1270 @ SV555 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4475]) ).
thf(5136,plain,
! [SV1814: $i,SV1271: $i,SV557: $i] :
( ( ( c_lessequals @ SV557 @ SV1271 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1814 @ SV1271 @ tc_nat )
| ~ ( c_lessequals @ SV557 @ SV1814 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(5137,plain,
! [SV2114: $i,SV1815: $i,SV1272: $i,SV559: $i] :
( ( ! [SY4826: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
| ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SY4826 @ SV2114 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SY4826 @ SV559 ) @ SV559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4477]) ).
thf(5138,plain,
! [SV2115: $i,SV1816: $i,SV1273: $i,SV560: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV560 )
| ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV2115 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV1273 @ SV2115 @ SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4478]) ).
thf(5139,plain,
! [SV1817: $i,SV1274: $i,SV561: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4479]) ).
thf(5140,plain,
! [SV2116: $i,SV1818: $i,SV1275: $i,SV562: $i] :
( ( ~ ( class_Orderings_Oorder @ SV562 )
| ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
| ~ ( c_lessequals @ SV1275 @ SV2116 @ SV562 )
| ~ ( c_lessequals @ SV2116 @ SV1818 @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4480]) ).
thf(5141,plain,
! [SV563: $i,SV1276: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1276 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV1276 @ SV563 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV563 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4481]) ).
thf(5142,plain,
! [SV1819: $i,SV1278: $i,SV565: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV565 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1278 @ SV1819 @ SV565 ) @ SV1278 @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(5143,plain,
! [SV1820: $i,SV1279: $i,SV566: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV566 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1279 @ SV1820 @ SV566 ) @ SV1820 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(5144,plain,
! [SV1280: $i,SV567: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV567 @ ( c_Suc @ SV1280 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1280 @ SV567 @ tc_nat ) )
= $true )
| ( ( SV567 = SV1280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4484]) ).
thf(5145,plain,
! [SV2117: $i,SV1821: $i,SV1281: $i,SV569: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
| ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV2117 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1281 @ SV569 ) @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4486]) ).
thf(5146,plain,
! [SV2118: $i,SV1822: $i,SV1282: $i,SV570: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1822 @ SV2118 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV2118 @ SV570 ) @ SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4487]) ).
thf(5147,plain,
! [SV2119: $i,SV1823: $i,SV1283: $i,SV571: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
| ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SV2119 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV2119 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SV2119 @ SV571 ) @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4488]) ).
thf(5148,plain,
! [SV2120: $i,SV1824: $i,SV1284: $i,SV572: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1824 @ SV2120 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SV2120 @ SV1284 @ SV572 ) @ SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4489]) ).
thf(5149,plain,
! [SV2121: $i,SV1825: $i,SV1285: $i,SV573: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV573 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV1825 @ SV573 ) @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV2121 @ SV573 ) @ SV573 )
= ( c_HOL_Otimes__class_Otimes @ SV1285 @ ( c_Divides_Odiv__class_Omod @ SV1825 @ SV2121 @ SV573 ) @ SV573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4490]) ).
thf(5150,plain,
! [SV2122: $i,SV1826: $i,SV1286: $i,SV574: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV574 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV1826 @ SV574 ) @ ( c_HOL_Otimes__class_Otimes @ SV2122 @ SV1826 @ SV574 ) @ SV574 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1286 @ SV2122 @ SV574 ) @ SV1826 @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4491]) ).
thf(5151,plain,
! [SV575: $i,SV1287: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1287 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV575 @ SV1287 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV575 @ SV1287 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4492]) ).
thf(5152,plain,
! [SV1288: $i,SV576: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV576 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV576 ) @ ( c_HOL_Oabs__class_Oabs @ SV1288 @ SV576 ) @ SV576 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4493]) ).
thf(5153,plain,
! [SV1289: $i,SV577: $i] :
( ( ( c_lessequals @ SV577 @ SV1289 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV577 ) @ ( c_Suc @ SV1289 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(5154,plain,
! [SV1290: $i,SV578: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV578 ) @ ( c_Suc @ SV1290 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV578 @ SV1290 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(5155,plain,
! [SV1827: $i,SV1291: $i,SV579: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV579 ) )
= $true )
| ( ( ( c_lessequals @ SV1291 @ SV1827 @ SV579 )
| ( c_lessequals @ SV1827 @ SV1291 @ SV579 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4496]) ).
thf(5156,plain,
! [SV1828: $i,SV1292: $i,SV580: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV1292 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV580 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1828 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4497]) ).
thf(5157,plain,
! [SV1829: $i,SV1293: $i,SV581: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SV1829 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1829 @ SV1293 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1829 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4498]) ).
thf(5158,plain,
! [SV1295: $i,SV583: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV583 @ ( c_Suc @ SV1295 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV583 @ SV1295 @ tc_nat )
= $true )
| ( ( SV583 = SV1295 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(5159,plain,
! [SV1297: $i,SV587: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV587 @ SV1297 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1297 @ ( c_Suc @ SV587 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(5160,plain,
! [SV1298: $i,SV589: $i] :
( ( ( SV589 = SV1298 )
= $true )
| ( ( ~ ( c_lessequals @ SV589 @ SV1298 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV589 @ SV1298 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4503]) ).
thf(5161,plain,
! [SV1299: $i,SV590: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV590 @ SV1299 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV590 @ SV1299 @ tc_nat ) )
= $true )
| ( ( SV590 = SV1299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(5162,plain,
! [SV1300: $i,SV591: $i] :
( ( ( SV591 = SV1300 )
= $true )
| ( ( ~ ( c_lessequals @ SV591 @ SV1300 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV591 @ SV1300 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(5163,plain,
! [SV1301: $i,SV592: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV592 ) @ SV1301 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV592 @ SV1301 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4506]) ).
thf(5164,plain,
! [SV1302: $i,SV593: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV593 @ SV1302 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV593 @ ( c_Suc @ SV1302 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(5165,plain,
! [SV1830: $i,SV1303: $i,SV594: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV594 @ SV1303 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1830 @ SV594 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1830 @ SV1303 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4508]) ).
thf(5166,plain,
! [SV1831: $i,SV1304: $i,SV595: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV595 @ SV1304 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV595 @ SV1831 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV1831 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(5167,plain,
! [SV1832: $i,SV1305: $i,SV598: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SV1305 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1832 @ SV1305 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV598 @ SV1832 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(5168,plain,
! [SV1306: $i,SV599: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV599 @ SV1306 @ tc_nat )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV599 @ SV1306 @ tc_nat )
= SV599 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(5169,plain,
! [SV1833: $i,SV1307: $i,SV600: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV600 @ ( c_HOL_Oplus__class_Oplus @ SV1307 @ SV1833 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV600 @ SV1307 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(5170,plain,
! [SV1834: $i,SV1308: $i,SV601: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV601 @ ( c_HOL_Oplus__class_Oplus @ SV1308 @ SV1834 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV601 @ SV1834 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4513]) ).
thf(5171,plain,
! [SV1835: $i,SV1309: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV1309 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV602 @ SV1835 @ tc_nat ) @ SV1309 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4514]) ).
thf(5172,plain,
! [SV1836: $i,SV1310: $i,SV603: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV603 @ ( c_HOL_Oplus__class_Oplus @ SV1310 @ SV1836 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV603 @ SV1310 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4515]) ).
thf(5173,plain,
! [SV1837: $i,SV1311: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Oplus__class_Oplus @ SV1311 @ SV1837 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV604 @ SV1837 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4516]) ).
thf(5174,plain,
! [SV1312: $i,SV605: $i] :
( ( ( ( c_Suc @ SV605 )
= SV1312 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV605 @ SV1312 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV605 ) @ SV1312 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4517]) ).
thf(5175,plain,
! [SV1313: $i,SV606: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV606 @ SV1313 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV606 ) @ ( c_Suc @ SV1313 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4518]) ).
thf(5176,plain,
! [SV1314: $i,SV607: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV607 ) @ ( c_Suc @ SV1314 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV607 @ SV1314 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(5177,plain,
! [SV1315: $i,SV608: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV608 @ SV1315 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV608 ) @ ( c_Suc @ SV1315 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(5178,plain,
! [SV1838: $i,SV1316: $i,SV609: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV609 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1316 @ SV1838 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1316 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1838 @ SV609 ) @ SV609 ) )
| ~ ( c_lessequals @ SV1838 @ SV1316 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4521]) ).
thf(5179,plain,
! [SV1317: $i,SV610: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV610 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV610 @ ( c_Suc @ SV1317 ) @ tc_nat ) @ SV610 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(5180,plain,
! [SV616: $i,SV1322: $i] :
( ( ( c_lessequals @ SV1322 @ SV616 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_HOL_Ominus__class_Ominus @ SV616 @ SV1322 @ tc_nat ) @ tc_nat )
= SV1322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(5181,plain,
! [SV1843: $i,SV1324: $i,SV618: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SV1324 @ SV1843 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1843 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1324 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(5182,plain,
! [SV1844: $i,SV1325: $i,SV621: $i] :
( ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1844 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ SV1844 @ SV621 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(5183,plain,
! [SV1845: $i,SV1326: $i,SV622: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV622 @ SV1845 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV1845 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(5184,plain,
! [SV1846: $i,SV1327: $i,SV623: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV623 @ SV1327 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1846 @ SV1327 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV623 @ SV1846 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4532]) ).
thf(5185,plain,
! [SV1847: $i,SV1328: $i,SV624: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1328 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1847 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1847 @ SV1328 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4533]) ).
thf(5186,plain,
! [SV627: $i,SV1330: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1330 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV627 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV627 @ SV1330 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(5187,plain,
! [SV628: $i,SV1331: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV1331 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV628 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV628 @ SV1331 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4536]) ).
thf(5188,plain,
! [SV1851: $i,SV1335: $i,SV632: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1335 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1851 @ SV1335 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1851 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1335 @ SV1851 @ tc_nat )
| ~ ( c_lessequals @ SV1335 @ SV632 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4539]) ).
thf(5189,plain,
! [SV1852: $i,SV1338: $i,SV635: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV635 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1338 @ SV1852 @ SV635 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1338 @ SV1852 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4540]) ).
thf(5190,plain,
! [SV1853: $i,SV1339: $i,SV636: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV636 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1339 @ SV1853 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
| ~ ( c_HOL_Oord__class_Oless @ SV1339 @ SV1853 @ SV636 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(5191,plain,
! [SV2123: $i,SV1854: $i,SV1340: $i,SV637: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV637 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SV1854 @ SV637 ) @ SV2123 @ SV637 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV2123 @ SV1340 @ SV637 ) @ SV637 ) @ SV1854 @ SV637 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4542]) ).
thf(5192,plain,
! [SV1855: $i,SV1341: $i,SV638: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV638 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1341 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1855 @ SV638 ) @ SV638 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV1855 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(5193,plain,
! [SV1856: $i,SV1342: $i,SV639: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1342 @ SV1856 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1342 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1856 @ SV639 ) @ SV639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(5194,plain,
! [SV1344: $i,SV641: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV641 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1344 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV1344 @ tc_nat ) @ SV641 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(5195,plain,
! [SV1345: $i,SV642: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat )
= $false )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1345 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV642 @ SV1345 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SV1345 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(5196,plain,
! [SV1346: $i,SV643: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat )
= $false )
| ( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1346 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1346 @ SV643 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV1346 @ SV643 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4548]) ).
thf(5197,plain,
! [SV1857: $i,SV1347: $i,SV644: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV644 @ SV1347 @ tc_nat ) @ SV1857 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV644 @ ( c_HOL_Ominus__class_Ominus @ SV1857 @ SV1347 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4549]) ).
thf(5198,plain,
! [SV1858: $i,SV1348: $i,SV645: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV645 @ ( c_HOL_Ominus__class_Ominus @ SV1348 @ SV1858 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV645 @ SV1858 @ tc_nat ) @ SV1348 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4550]) ).
thf(5199,plain,
! [SV1859: $i,SV1349: $i,SV646: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1859 @ SV1349 @ tc_nat )
| ~ ( c_lessequals @ SV1859 @ SV646 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4551]) ).
thf(5200,plain,
! [SV1860: $i,SV1350: $i,SV647: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV1860 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4552]) ).
thf(5201,plain,
! [SV649: $i,SV1352: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1352 @ SV649 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV649 @ SV1352 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4553]) ).
thf(5202,plain,
! [SV650: $i,SV1353: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1353 @ SV650 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV650 @ SV1353 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(5203,plain,
! [SV1861: $i,SV1355: $i,SV652: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SV1355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1861 @ SV1355 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1355 @ SV652 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV652 @ SV1861 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4556]) ).
thf(5204,plain,
! [SV1356: $i,SV653: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV653 @ SV1356 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV653 @ SV1356 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(5205,plain,
! [SV1862: $i,SV1357: $i,SV654: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV654 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV1862 @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SV1862 @ SV1357 @ SV654 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4558]) ).
thf(5206,plain,
! [SV1863: $i,SV1358: $i,SV655: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV655 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1358 @ SV1863 @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SV1863 @ SV1358 @ SV655 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(5207,plain,
! [SV1864: $i,SV1359: $i,SV656: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV656 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1359 @ SV1864 @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SV1864 @ SV1359 @ SV656 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(5208,plain,
! [SV1865: $i,SV1360: $i,SV657: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV657 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1360 @ SV1865 @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SV1865 @ SV1360 @ SV657 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4561]) ).
thf(5209,plain,
! [SV1361: $i,SV658: $i] :
( ( ( class_Orderings_Opreorder @ SV658 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV1361 @ SV658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(5210,plain,
! [SV1362: $i,SV659: $i] :
( ( ( class_Orderings_Olinorder @ SV659 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1362 @ SV1362 @ SV659 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4563]) ).
thf(5211,plain,
! [SV1363: $i,SV662: $i] :
( ( ( class_Orderings_Oorder @ SV662 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1363 @ SV1363 @ SV662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4564]) ).
thf(5212,plain,
! [SV1866: $i,SV1364: $i,SV663: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV663 @ SV1364 @ tc_nat ) @ SV1866 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV663 @ SV1866 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(5213,plain,
! [SV1867: $i,SV1365: $i,SV664: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1867 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV664 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV1365 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4566]) ).
thf(5214,plain,
! [SV1868: $i,SV1366: $i,SV665: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV665 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1366 @ SV1868 @ SV665 )
| ( c_HOL_Oord__class_Oless @ SV1868 @ SV1366 @ SV665 )
| ( SV1868 = SV1366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4567]) ).
thf(5215,plain,
! [SV1869: $i,SV1367: $i,SV666: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV666 ) )
= $true )
| ( ( ( SV1367 = SV1869 )
| ( c_HOL_Oord__class_Oless @ SV1869 @ SV1367 @ SV666 )
| ( c_HOL_Oord__class_Oless @ SV1367 @ SV1869 @ SV666 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4568]) ).
thf(5216,plain,
! [SV1870: $i,SV1368: $i,SV667: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV667 ) )
= $true )
| ( ( ( SV1368 = SV1870 )
| ( c_HOL_Oord__class_Oless @ SV1368 @ SV1870 @ SV667 )
| ( c_HOL_Oord__class_Oless @ SV1870 @ SV1368 @ SV667 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(5217,plain,
! [SV1871: $i,SV1369: $i,SV668: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV668 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1369 @ SV1871 @ SV668 )
| ( SV1871 = SV1369 )
| ( c_HOL_Oord__class_Oless @ SV1871 @ SV1369 @ SV668 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(5218,plain,
! [SV669: $i,SV1370: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1370 @ SV669 @ tc_nat )
= $true )
| ( ( SV1370 = SV669 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV669 @ SV1370 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(5219,plain,
! [SV670: $i,SV1371: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1371 @ SV670 @ tc_nat )
= $true )
| ( ( SV1371 = SV670 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV670 @ SV1371 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(5220,plain,
! [SV1872: $i,SV1372: $i,SV671: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV671 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1372 @ SV1872 @ SV671 )
| ( c_HOL_Oord__class_Oless @ SV1872 @ SV1372 @ SV671 )
| ( SV1872 = SV1372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(5221,plain,
! [SV2124: $i,SV1873: $i,SV1373: $i,SV672: $i] :
( ( ~ ( class_Orderings_Oorder @ SV672 )
| ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4574]) ).
thf(5222,plain,
! [SV2125: $i,SV1874: $i,SV1374: $i,SV673: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV673 )
| ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4575]) ).
thf(5223,plain,
! [SV1876: $i,SV1376: $i,SV675: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1376 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1876 @ tc_nat ) )
= $true )
| ( ( SV1376 = SV1876 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(5224,plain,
! [SV1377: $i,SV677: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV677 @ SV1377 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV677
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(5225,plain,
! [SV678: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV678 @ tc_nat )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV678 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(5226,plain,
! [SV1378: $i,SV679: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV679 @ SV1378 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1378 @ SV679 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1378 = SV679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(5227,plain,
! [SV1877: $i,SV1379: $i,SV680: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1379 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1877 @ tc_nat ) )
= $true )
| ( ( SV1379 = SV1877 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(5228,plain,
! [SV1878: $i,SV1380: $i,SV681: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV681 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1380 @ SV1380 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SV1878 @ SV1878 @ SV681 ) @ SV681 )
!= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
| ( SV1380
= ( c_HOL_Ozero__class_Ozero @ SV681 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(5229,plain,
! [SV2126: $i,SV1879: $i,SV1381: $i,SV682: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV682 )
| ~ ( class_Int_Onumber__ring @ SV682 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
| ( SV1879 = SV2126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4583]) ).
thf(5230,plain,
! [SV2127: $i,SV1880: $i,SV1382: $i,SV683: $i] :
( ( ! [SY4827: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV1880 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV2127 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SY4827 @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ SV683 @ SV1382 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SV2127 @ SV1382 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4584]) ).
thf(5231,plain,
! [SV1881: $i,SV1383: $i,SV684: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV684 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1383 @ SV684 )
!= ( c_HOL_Oabs__class_Oabs @ SV1881 @ SV684 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1383 @ SV1881 @ SV684 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4585]) ).
thf(5232,plain,
! [SV2128: $i,SV1882: $i,SV1384: $i,SV685: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV1882 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV2128 @ SV685 ) )
| ( SV1882 = SV2128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4586]) ).
thf(5233,plain,
! [SV1883: $i,SV1385: $i,SV686: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
!= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4587]) ).
thf(5234,plain,
! [SV1386: $i,SV687: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV687 @ SV1386 @ tc_nat ) )
= $false )
| ( ( ( SV687
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV687
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(5235,plain,
! [SV2129: $i,SV1884: $i,SV1387: $i,SV688: $i] :
( ( ! [SY4828: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SY4828 @ SV688 ) )
| ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SY4828 @ SV2129 @ SV688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(5236,plain,
! [SV1885: $i,SV1388: $i,SV689: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV689 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SV1885 @ SV689 )
!= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1885
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4590]) ).
thf(5237,plain,
! [SV2130: $i,SV1886: $i,SV1389: $i,SV690: $i] :
( ( ! [SY4829: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SY4829 @ SV690 ) )
| ( c_lessequals @ SY4829 @ SV2130 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4591]) ).
thf(5238,plain,
! [SV1887: $i,SV1390: $i,SV691: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV691 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1390 @ SV1887 @ SV691 )
!= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
| ( SV1390 = SV1887 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4592]) ).
thf(5239,plain,
! [SV1888: $i,SV1391: $i,SV693: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV693 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SV1888 @ SV693 )
!= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1888
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4593]) ).
thf(5240,plain,
! [SV1392: $i,SV695: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1392 @ tc_nat ) )
= $false )
| ( ( ( SV1392
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1392
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4594]) ).
thf(5241,plain,
! [SV2131: $i,SV1889: $i,SV1393: $i,SV696: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV696 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SV1889 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SV2131 @ SV2131 @ SV696 ) )
| ( SV1393 = SV1889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(5242,plain,
! [SV1394: $i,SV697: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1394 @ tc_nat ) )
= $false )
| ( ( ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV697
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4596]) ).
thf(5243,plain,
! [SV1890: $i,SV1395: $i,SV698: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV698 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV698 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SV1395 = SV1890 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4597]) ).
thf(5244,plain,
! [SV1396: $i,SV699: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV699 @ SV1396 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( c_lessequals @ SV699 @ SV1396 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4598]) ).
thf(5245,plain,
! [SV2132: $i,SV1891: $i,SV1397: $i,SV702: $i] :
( ( ! [SY4830: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV702 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2132 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SY4830 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SV2132 @ SV702 )
= SY4830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4600]) ).
thf(5246,plain,
! [SV1398: $i,SV703: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV703 @ SV1398 @ tc_nat ) )
= $false )
| ( ( ( SV703
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1398
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(5247,plain,
! [SV1892: $i,SV1399: $i,SV704: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV704 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1399 @ SV1892 @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1892 @ SV1399 @ SV704 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(5248,plain,
! [SV1893: $i,SV1400: $i,SV705: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
!= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(5249,plain,
! [SV1401: $i,SV706: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV706 @ SV1401 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( SV1401
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV706
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(5250,plain,
! [SV2133: $i,SV1894: $i,SV1402: $i,SV708: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV708 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SV1894 @ SV2133 @ SV708 ) )
| ( SV1894 = SV2133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4605]) ).
thf(5251,plain,
! [SV2134: $i,SV1895: $i,SV1403: $i,SV709: $i] :
( ( ! [SY4831: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV709 )
| ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SY4831 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SY4831 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SY4831 )
| ( SV1403 = SV2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(5252,plain,
! [SV2135: $i,SV1896: $i,SV1404: $i,SV710: $i] :
( ( ! [SY4832: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SY4832 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SY4832 @ SV710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4607]) ).
thf(5253,plain,
! [SV1405: $i,SV711: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV711 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1405 @ SV1405 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
| ( SV1405
= ( c_HOL_Ozero__class_Ozero @ SV711 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(5254,plain,
! [SV2136: $i,SV1897: $i,SV1406: $i,SV712: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1897 @ SV2136 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1897 @ SV1406 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV712 @ SV2136 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4609]) ).
thf(5255,plain,
! [SV2137: $i,SV1898: $i,SV1407: $i,SV713: $i] :
( ( ! [SY4833: $i,SY4834: $i] :
( ~ ( class_Divides_Oring__div @ SV713 )
| ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4833 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY4834 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4833 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4834 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4610]) ).
thf(5256,plain,
! [SV1408: $i,SV714: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1408 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1408
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV714
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(5257,plain,
! [SV1899: $i,SV1409: $i,SV715: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV715 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1409 @ SV715 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1899 @ SV715 ) )
| ( SV1409 = SV1899 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(5258,plain,
! [SV1410: $i,SV716: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV716 @ SV1410 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV716
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(5259,plain,
! [SV1411: $i,SV717: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV717 @ SV1411 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1411
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4614]) ).
thf(5260,plain,
! [SV1412: $i,SV718: $i] :
( ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV718 @ SV1412 @ tc_nat ) )
= SV1412 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV718 ) @ SV1412 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4615]) ).
thf(5261,plain,
! [SV1413: $i,SV719: $i] :
( ( ( ( c_Suc @ SV719 )
= ( c_Suc @ SV1413 ) )
= $false )
| ( ( SV719 = SV1413 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4616]) ).
thf(5262,plain,
! [SV1900: $i,SV1414: $i,SV720: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV720 @ SV1414 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV1900 @ SV1414 @ tc_nat ) )
= $true )
| ( ( ( SV1414
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV720 = SV1900 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(5263,plain,
! [SV1901: $i,SV1415: $i,SV721: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1415 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1901 @ tc_nat ) )
= $true )
| ( ( SV1415 = SV1901 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4618]) ).
thf(5264,plain,
! [SV1902: $i,SV1416: $i,SV722: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV722 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV722 )
| ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
| ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4619]) ).
thf(5265,plain,
! [SV1417: $i,SV723: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV723 @ SV1417 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1417
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1417
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(5266,plain,
! [SV1903: $i,SV1418: $i,SV724: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 ) )
= $true )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SV1903 @ SV724 )
!= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1903
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4621]) ).
thf(5267,plain,
! [SV2138: $i,SV1904: $i,SV1419: $i,SV725: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SV1904 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SV2138 @ SV1904 @ SV725 ) )
| ( SV1419 = SV2138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4622]) ).
thf(5268,plain,
! [SV1420: $i,SV726: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV726 @ SV1420 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( SV1420
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4623]) ).
thf(5269,plain,
! [SV1905: $i,SV1421: $i,SV727: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1421 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1905 @ tc_nat ) )
= $true )
| ( ( ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1421 = SV1905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4624]) ).
thf(5270,plain,
! [SV1906: $i,SV1422: $i,SV728: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV728 @ SV1422 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1906 @ SV1422 @ tc_nat ) )
= $true )
| ( ( SV728 = SV1906 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4625]) ).
thf(5271,plain,
! [SV2139: $i,SV1907: $i,SV1423: $i,SV729: $i] :
( ( ! [SY4835: $i,SY4836: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV729 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4835 @ SV1907 @ SV729 ) @ SY4836 @ SV729 ) )
| ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SY4835 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SY4836 @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4626]) ).
thf(5272,plain,
! [SV1424: $i,SV730: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV730 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1424 @ SV730 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
| ( SV1424
= ( c_HOL_Ozero__class_Ozero @ SV730 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(5273,plain,
! [SV1425: $i,SV731: $i] :
( ( ( SV731
= ( c_HOL_Oplus__class_Oplus @ SV731 @ SV1425 @ tc_nat ) )
= $false )
| ( ( SV1425
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(5274,plain,
! [SV1908: $i,SV1426: $i,SV732: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV732 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1426 @ SV1908 @ SV732 )
!= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
| ( SV1426 = SV1908 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4629]) ).
thf(5275,plain,
! [SV1427: $i,SV733: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV733 @ SV1427 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV733
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1427
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(5276,plain,
! [SV1909: $i,SV1428: $i,SV734: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV734 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1428 @ SV1909 @ SV734 )
!= SV1428 )
| ( c_lessequals @ SV1428 @ SV1909 @ SV734 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(5277,plain,
! [SV1910: $i,SV1429: $i,SV735: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1429 @ SV1910 @ tc_nat )
| ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
| ( SV735 = SV1910 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(5278,plain,
! [SV1430: $i,SV736: $i] :
( ( ( ( c_Suc @ SV736 )
= ( c_Suc @ SV1430 ) )
= $false )
| ( ( SV736 = SV1430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(5279,plain,
! [SV1431: $i,SV737: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV737 @ SV1431 @ tc_nat )
= SV737 )
= $false )
| ( ( SV1431
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(5280,plain,
! [SV2140: $i,SV1911: $i,SV1432: $i,SV738: $i] :
( ( ! [SY4837: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2140 @ SV1432 @ tc_nat ) @ SY4837 @ tc_nat ) )
| ~ ( c_lessequals @ SV738 @ SV2140 @ tc_nat )
| ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2140 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SY4837 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4635]) ).
thf(5281,plain,
! [SV1433: $i,SV739: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV739 @ SV1433 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( SV739
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4636]) ).
thf(5282,plain,
! [SV2141: $i,SV1912: $i,SV1434: $i,SV741: $i] :
( ( ! [SY4838: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SY4838 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SV2141 @ SY4838 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4637]) ).
thf(5283,plain,
! [SV2142: $i,SV1913: $i,SV1435: $i,SV742: $i] :
( ( ! [SY4839: $i,SY4840: $i] :
( ~ ( class_Divides_Osemiring__div @ SV742 )
| ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4839 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY4840 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4839 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4840 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4638]) ).
thf(5284,plain,
! [SV2143: $i,SV1914: $i,SV1436: $i,SV743: $i] :
( ( ! [SY4841: $i,SY4842: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV743 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SY4841 @ SV1914 @ SV743 ) @ SY4842 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SY4841 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SY4842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4639]) ).
thf(5285,plain,
! [SV1915: $i,SV1437: $i,SV744: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1437 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1915 @ tc_nat ) )
= $true )
| ( ( ( SV1437 = SV1915 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(5286,plain,
! [SV1916: $i,SV1438: $i,SV745: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1438 @ tc_nat )
!= ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1916 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat )
| ( SV1438 = SV1916 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(5287,plain,
! [SV2144: $i,SV1917: $i,SV1439: $i,SV746: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV1439 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV2144 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV2144 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV1439 @ tc_nat ) @ tc_nat ) )
| ( SV1439 = SV2144 )
| ( SV746 = SV1917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4642]) ).
thf(5288,plain,
! [SV1918: $i,SV1440: $i,SV747: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV747 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1440 @ SV1440 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SV1918 @ SV1918 @ SV747 ) @ SV747 )
!= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
| ( SV1918
= ( c_HOL_Ozero__class_Ozero @ SV747 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(5289,plain,
! [SV2145: $i,SV1919: $i,SV1441: $i,SV748: $i] :
( ( ! [SY4843: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV748 )
| ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SY4843 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SY4843 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SY4843 )
| ( SV1441 = SV2145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(5290,plain,
! [SV2146: $i,SV1920: $i,SV1442: $i,SV749: $i] :
( ( ! [SY4844: $i,SY4845: $i] :
( ~ ( class_Divides_Osemiring__div @ SV749 )
| ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY4844 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY4845 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4844 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4845 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4645]) ).
thf(5291,plain,
! [SV2147: $i,SV1921: $i,SV1443: $i,SV750: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV1921 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV2147 @ tc_nat ) @ tc_nat ) )
| ( SV1921 = SV2147 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4646]) ).
thf(5292,plain,
! [SV2148: $i,SV1922: $i,SV1444: $i,SV751: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV1922 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV2148 @ SV751 ) )
| ( SV1922 = SV2148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4647]) ).
thf(5293,plain,
! [SV2149: $i,SV1923: $i,SV1445: $i,SV752: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV1445 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV2149 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV2149 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV1445 @ tc_nat ) @ tc_nat ) )
| ( SV1445 = SV2149 )
| ( SV752 = SV1923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4648]) ).
thf(5294,plain,
! [SV2150: $i,SV1924: $i,SV1446: $i,SV753: $i] :
( ( ! [SY4846: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2150 @ SV1446 @ tc_nat ) @ SY4846 @ tc_nat ) )
| ~ ( c_lessequals @ SV2150 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV2150 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SY4846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4649]) ).
thf(5295,plain,
! [SV2151: $i,SV1925: $i,SV1447: $i,SV754: $i] :
( ( ! [SY4847: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV754 )
| ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SY4847 @ SV754 ) @ SV754 ) )
| ( SV2151 = SY4847 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4650]) ).
thf(5296,plain,
! [SV1448: $i,SV755: $i,SV1: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(5297,plain,
! [SV1449: $i,SV756: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4652]) ).
thf(5298,plain,
! [SV1450: $i,SV759: $i,SV5: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV5 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV759 @ SV759 @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV1450 @ SV1450 @ SV5 ) @ SV5 ) @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(5299,plain,
! [SV1451: $i,SV760: $i,SV6: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(5300,plain,
! [SV1452: $i,SV761: $i,SV7: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(5301,plain,
! [SV762: $i,SV9: $i,SV1453: $i] :
( ( ( c_lessequals @ SV1453 @ SV9 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV9 @ SV762 @ tc_nat ) @ SV1453 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV9 @ SV1453 @ tc_nat ) @ SV762 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4656]) ).
thf(5302,plain,
! [SV10: $i,SV763: $i,SV1454: $i] :
( ( ( c_lessequals @ SV1454 @ SV763 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV10 @ SV763 @ tc_nat ) @ SV1454 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV10 @ ( c_HOL_Ominus__class_Ominus @ SV763 @ SV1454 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(5303,plain,
! [SV2152: $i,SV1926: $i,SV1455: $i,SV764: $i,SV11: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1455 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1926 @ SV2152 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1926 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1455 @ SV2152 @ SV11 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4658]) ).
thf(5304,plain,
! [SV2153: $i,SV1927: $i,SV1456: $i,SV765: $i,SV12: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV765 @ SV1456 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SV2153 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SV765 @ ( c_HOL_Otimes__class_Otimes @ SV1456 @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SV2153 @ SV12 ) @ SV12 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4659]) ).
thf(5305,plain,
! [SV2154: $i,SV1928: $i,SV1457: $i,SV766: $i,SV13: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 )
| ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV1928 @ SV2154 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SV1928 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ SV2154 @ SV13 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4660]) ).
thf(5306,plain,
! [SV14: $i,SV767: $i] :
( ( ( SV767
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV767 @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV14 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(5307,plain,
! [SV1929: $i,SV1458: $i,SV769: $i,SV16: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 ) )
= $true )
| ( ( ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SV1458 @ ( c_HOL_Oabs__class_Oabs @ SV1929 @ SV16 ) @ SV16 ) @ SV16 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SV1929 @ SV16 ) @ SV1458 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(5308,plain,
! [SV1459: $i,SV770: $i,SV18: $i] :
( ( ( class_Orderings_Oorder @ SV18 )
= $false )
| ( ( ( SV770 = SV1459 )
| ~ ( c_lessequals @ SV1459 @ SV770 @ SV18 )
| ~ ( c_lessequals @ SV770 @ SV1459 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4664]) ).
thf(5309,plain,
! [SV1460: $i,SV771: $i,SV19: $i] :
( ( ( class_Orderings_Oorder @ SV19 )
= $false )
| ( ( ( SV771 = SV1460 )
| ~ ( c_lessequals @ SV1460 @ SV771 @ SV19 )
| ~ ( c_lessequals @ SV771 @ SV1460 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4665]) ).
thf(5310,plain,
! [SV20: $i,SV772: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV772 @ SV20 @ tc_nat ) )
= $true )
| ( ( SV772 = SV20 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV772 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4666]) ).
thf(5311,plain,
! [SV21: $i,SV773: $i] :
( ( ( SV773 = SV21 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV773 @ SV21 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SV773 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4667]) ).
thf(5312,plain,
! [SV774: $i,SV22: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV22 @ SV774 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV774 @ SV22 @ tc_nat ) )
= $true )
| ( ( SV22 = SV774 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(5313,plain,
! [SV23: $i,SV775: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV775 @ SV23 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV23 @ SV775 @ tc_nat ) )
= $true )
| ( ( SV23 = SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4669]) ).
thf(5314,plain,
! [SV24: $i,SV776: $i] :
( ( ( SV776 = SV24 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV776 @ SV24 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV24 @ SV776 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(5315,plain,
! [SV25: $i,SV777: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV777 @ SV25 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV25 @ SV777 @ tc_nat ) )
= $true )
| ( ( SV25 = SV777 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4671]) ).
thf(5316,plain,
! [SV26: $i,SV778: $i] :
( ( ( c_lessequals @ SV778 @ SV26 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV26 @ SV778 @ tc_nat ) )
= $true )
| ( ( SV26 = SV778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4672]) ).
thf(5317,plain,
! [SV27: $i,SV779: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV779 @ SV27 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV27 @ SV779 @ tc_nat ) )
= $true )
| ( ( SV27 = SV779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(5318,plain,
! [SV1461: $i,SV780: $i,SV28: $i] :
( ( ( class_Orderings_Oorder @ SV28 )
= $false )
| ( ( ( SV780 = SV1461 )
| ~ ( c_lessequals @ SV780 @ SV1461 @ SV28 )
| ~ ( c_lessequals @ SV1461 @ SV780 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4674]) ).
thf(5319,plain,
! [SV29: $i,SV781: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV781 @ SV29 )
= SV781 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV781 @ SV29 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(5320,plain,
! [SV30: $i,SV782: $i,SV1462: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1462 @ SV782 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV1462 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV782 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(5321,plain,
! [SV31: $i,SV1463: $i,SV783: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4677]) ).
thf(5322,plain,
! [SV784: $i,SV32: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV32 @ SV784 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV784 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(5323,plain,
! [SV1930: $i,SV1464: $i,SV786: $i,SV35: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4680]) ).
thf(5324,plain,
! [SV36: $i,SV787: $i,SV1465: $i] :
( ( ( c_lessequals @ SV1465 @ SV787 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV36 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV787 @ SV1465 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV36 @ SV1465 @ tc_nat ) @ ( c_Suc @ SV787 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(5325,plain,
! [SV1466: $i,SV789: $i,SV38: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV38 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV789 @ SV38 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV1466 @ SV38 ) @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(5326,plain,
! [SV1467: $i,SV790: $i,SV39: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV39 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV790 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ ( c_HOL_Otimes__class_Otimes @ SV1467 @ ( c_HOL_Ozero__class_Ozero @ SV39 ) @ SV39 ) @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4683]) ).
thf(5327,plain,
! [SV40: $i,SV1468: $i,SV791: $i] :
( ( ( c_lessequals @ SV791 @ SV1468 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV791 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV40 @ SV1468 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(5328,plain,
! [SV792: $i,SV41: $i,SV1469: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1469 @ SV41 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1469 @ SV792 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV41 @ SV792 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4685]) ).
thf(5329,plain,
! [SV793: $i,SV1470: $i,SV42: $i] :
( ( ( c_lessequals @ SV42 @ SV1470 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV42 @ SV793 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1470 @ SV793 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4686]) ).
thf(5330,plain,
! [SV1931: $i,SV1471: $i,SV794: $i,SV43: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1471 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1931 @ SV43 ) @ SV43 )
| ~ ( c_lessequals @ SV1471 @ SV1931 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4687]) ).
thf(5331,plain,
! [SV1932: $i,SV1472: $i,SV795: $i,SV44: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SV1472 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SV1932 @ SV1472 @ SV44 ) @ SV44 )
| ~ ( c_lessequals @ SV795 @ SV1932 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4688]) ).
thf(5332,plain,
! [SV1933: $i,SV1473: $i,SV796: $i,SV45: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 ) )
= $true )
| ( ( ( c_lessequals @ SV796 @ SV1473 @ SV45 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV1473 @ SV45 ) @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4689]) ).
thf(5333,plain,
! [SV1934: $i,SV1474: $i,SV797: $i,SV46: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1474 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1934 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ SV1474 @ SV1934 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4690]) ).
thf(5334,plain,
! [SV1935: $i,SV1475: $i,SV798: $i,SV47: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 ) )
= $true )
| ( ( ( c_lessequals @ SV798 @ SV1475 @ SV47 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SV1935 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SV1475 @ SV1935 @ SV47 ) @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4691]) ).
thf(5335,plain,
! [SV1936: $i,SV1476: $i,SV799: $i,SV48: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SV1476 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SV1936 @ SV1476 @ SV48 ) @ SV48 )
| ~ ( c_lessequals @ SV799 @ SV1936 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4692]) ).
thf(5336,plain,
! [SV1477: $i,SV800: $i,SV49: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV49 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV800 @ SV1477 @ SV49 ) @ SV49 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV800 @ SV49 ) @ ( c_HOL_Oabs__class_Oabs @ SV1477 @ SV49 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(5337,plain,
! [SV1478: $i,SV801: $i,SV50: $i] :
( ( ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(5338,plain,
! [SV1479: $i,SV802: $i,SV51: $i] :
( ( ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
| ~ ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(5339,plain,
! [SV1480: $i,SV803: $i,SV52: $i] :
( ( ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 )
| ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(5340,plain,
! [SV1481: $i,SV804: $i,SV53: $i] :
( ( ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
| ~ ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
| ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(5341,plain,
! [SV1482: $i,SV805: $i,SV54: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__idem__mult @ SV54 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV805 @ ( c_HOL_Otimes__class_Otimes @ SV805 @ SV1482 @ SV54 ) @ SV54 )
= ( c_HOL_Otimes__class_Otimes @ SV805 @ SV1482 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4698]) ).
thf(5342,plain,
! [SV1483: $i,SV806: $i,SV56: $i] :
( ( ( class_Divides_Osemiring__div @ SV56 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1483 @ SV56 ) @ SV806 @ SV56 )
= ( c_Divides_Odiv__class_Omod @ SV1483 @ SV806 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(5343,plain,
! [SV1484: $i,SV807: $i,SV57: $i] :
( ( ( class_Divides_Osemiring__div @ SV57 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1484 @ SV57 ) @ SV1484 @ SV57 )
= ( c_Divides_Odiv__class_Omod @ SV807 @ SV1484 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4700]) ).
thf(5344,plain,
! [SV1485: $i,SV808: $i,SV58: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
= $false )
| ( ( ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SV1485 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4701]) ).
thf(5345,plain,
! [SV1486: $i,SV809: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV1486 @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4702]) ).
thf(5346,plain,
! [SV1487: $i,SV810: $i,SV60: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
= $false )
| ( ( ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ( c_lessequals @ SV1487 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV1487 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(5347,plain,
! [SV1488: $i,SV811: $i,SV61: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
| ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1488 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4704]) ).
thf(5348,plain,
! [SV1489: $i,SV812: $i,SV62: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4705]) ).
thf(5349,plain,
! [SV1490: $i,SV813: $i,SV63: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(5350,plain,
! [SV1491: $i,SV814: $i,SV64: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(5351,plain,
! [SV1492: $i,SV815: $i,SV65: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4708]) ).
thf(5352,plain,
! [SV1493: $i,SV816: $i,SV66: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(5353,plain,
! [SV67: $i,SV817: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV817 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV67 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV67 @ SV817 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(5354,plain,
! [SV68: $i,SV818: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV818 @ SV818 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV818 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4711]) ).
thf(5355,plain,
! [SV69: $i,SV819: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV819 @ SV819 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4712]) ).
thf(5356,plain,
! [SV70: $i,SV820: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV820 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4713]) ).
thf(5357,plain,
! [SV71: $i,SV821: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV821 @ SV71 ) @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV821 @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4714]) ).
thf(5358,plain,
! [SV1937: $i,SV1494: $i,SV823: $i,SV76: $i] :
( ( ( ~ ( c_lessequals @ SV76 @ SV823 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1494 @ tc_nat ) @ SV1937 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV76 @ SV1494 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV823 @ SV76 @ tc_nat ) @ SV1494 @ tc_nat ) @ SV1937 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(5359,plain,
! [SV1938: $i,SV1495: $i,SV824: $i,SV77: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(5360,plain,
! [SV1939: $i,SV1496: $i,SV825: $i,SV78: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(5361,plain,
! [SV1940: $i,SV1497: $i,SV826: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV79 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(5362,plain,
! [SV1941: $i,SV1498: $i,SV827: $i,SV80: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring @ SV80 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4720]) ).
thf(5363,plain,
! [SV1499: $i,SV829: $i,SV82: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV82 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV82 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV829 @ SV829 @ SV82 ) @ ( c_HOL_Otimes__class_Otimes @ SV1499 @ SV1499 @ SV82 ) @ SV82 ) @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(5364,plain,
! [SV1942: $i,SV1500: $i,SV831: $i,SV84: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV84 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(5365,plain,
! [SV1943: $i,SV1501: $i,SV832: $i,SV85: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV85 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4725]) ).
thf(5366,plain,
! [SV1944: $i,SV1502: $i,SV833: $i,SV86: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV86 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(5367,plain,
! [SV1945: $i,SV1503: $i,SV834: $i,SV87: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV87 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4727]) ).
thf(5368,plain,
! [SV2155: $i,SV1946: $i,SV1504: $i,SV835: $i,SV88: $i] :
( ( ! [SY4848: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2155 @ SV1504 @ SV88 ) @ SY4848 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2155 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SY4848 @ SV88 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4728]) ).
thf(5369,plain,
! [SV2156: $i,SV1947: $i,SV1505: $i,SV836: $i,SV89: $i] :
( ( ! [SY4849: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 )
| ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SV2156 @ SV89 ) @ SY4849 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SV2156 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SV2156 @ SV89 ) @ SY4849 @ SV89 ) @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4729]) ).
thf(5370,plain,
! [SV2157: $i,SV1948: $i,SV1506: $i,SV837: $i,SV90: $i] :
( ( ! [SY4850: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2157 @ SV1506 @ SV90 ) @ SY4850 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SV2157 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SY4850 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4730]) ).
thf(5371,plain,
! [SV2158: $i,SV1949: $i,SV1507: $i,SV838: $i,SV91: $i] :
( ( ! [SY4851: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ SY4851 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SY4851 @ SV91 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4731]) ).
thf(5372,plain,
! [SV1950: $i,SV1508: $i,SV843: $i,SV96: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(5373,plain,
! [SV1951: $i,SV1509: $i,SV844: $i,SV97: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
| ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5374,plain,
! [SV845: $i,SV1510: $i,SV98: $i] :
( ( ( ~ ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SV1510 @ SV845 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV845 @ SV1510 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SV845 @ tc_nat ) @ SV1510 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(5375,plain,
! [SV846: $i,SV1511: $i,SV99: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SV1511 @ tc_nat ) @ SV846 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1511 @ SV846 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1511 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(5376,plain,
! [SV2159: $i,SV1952: $i,SV1512: $i,SV850: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1952 @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1952 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV103 @ SV1952 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4740]) ).
thf(5377,plain,
! [SV2160: $i,SV1953: $i,SV1513: $i,SV851: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SV1953 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1513 @ SV851 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4741]) ).
thf(5378,plain,
! [SV2161: $i,SV1954: $i,SV1514: $i,SV852: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1954 @ SV852 @ tc_nat ) @ SV2161 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SV1954 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SV2161 @ tc_nat )
| ~ ( c_lessequals @ SV1954 @ SV105 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4742]) ).
thf(5379,plain,
! [SV2162: $i,SV1955: $i,SV1515: $i,SV853: $i,SV106: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ SV2162 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SV2162 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4743]) ).
thf(5380,plain,
! [SV2163: $i,SV1956: $i,SV1516: $i,SV854: $i,SV107: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV107 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV1516 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1956 @ SV854 @ SV107 ) @ SV1516 @ SV107 ) @ SV2163 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1956 @ SV1516 @ SV107 ) @ SV2163 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4744]) ).
thf(5381,plain,
! [SV1517: $i,SV855: $i,SV108: $i] :
( ( ( class_Ring__and__Field_Olordered__ring @ SV108 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV855 @ SV1517 @ SV108 ) @ SV108 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV855 @ SV108 ) @ ( c_HOL_Oabs__class_Oabs @ SV1517 @ SV108 ) @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4745]) ).
thf(5382,plain,
! [SV1518: $i,SV856: $i,SV109: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 )
= $false )
| ( ( ( c_lessequals @ SV856 @ SV1518 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV856 @ SV109 ) @ SV1518 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4746]) ).
thf(5383,plain,
! [SV2164: $i,SV1957: $i,SV1519: $i,SV857: $i,SV110: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4747]) ).
thf(5384,plain,
! [SV1958: $i,SV1520: $i,SV858: $i,SV111: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV111 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV858 @ SV1520 @ SV111 ) @ SV1958 @ SV111 ) @ SV1520 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV858 @ SV1958 @ SV111 ) @ SV1520 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(5385,plain,
! [SV1959: $i,SV1521: $i,SV859: $i,SV112: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV112 ) )
= $true )
| ( ( ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1959 @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4749]) ).
thf(5386,plain,
! [SV1960: $i,SV1522: $i,SV860: $i,SV113: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV113 ) )
= $true )
| ( ( ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1960 @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(5387,plain,
! [SV1961: $i,SV1523: $i,SV861: $i,SV114: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV114 ) )
= $true )
| ( ( ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1961 @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(5388,plain,
! [SV1524: $i,SV862: $i,SV115: $i] :
( ( ( class_Orderings_Olinorder @ SV115 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV862 @ SV1524 @ SV115 ) @ SV1524 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4752]) ).
thf(5389,plain,
! [SV1525: $i,SV863: $i,SV116: $i] :
( ( ( class_Orderings_Olinorder @ SV116 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV863 @ SV1525 @ SV116 ) @ SV863 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4753]) ).
thf(5390,plain,
! [SV1526: $i,SV117: $i,SV864: $i] :
( ( ( c_lessequals @ SV864 @ SV117 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV117 @ SV864 @ tc_nat ) ) @ SV1526 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV117 ) @ ( c_HOL_Oplus__class_Oplus @ SV864 @ SV1526 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4754]) ).
thf(5391,plain,
! [SV1527: $i,SV865: $i,SV118: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV118 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV865 @ ( c_HOL_Otimes__class_Otimes @ SV1527 @ SV865 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4755]) ).
thf(5392,plain,
! [SV1528: $i,SV866: $i,SV119: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV119 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV866 @ ( c_HOL_Otimes__class_Otimes @ SV866 @ SV1528 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4756]) ).
thf(5393,plain,
! [SV1529: $i,SV867: $i,SV120: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV120 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV867 @ ( c_HOL_Otimes__class_Otimes @ SV867 @ SV1529 @ SV120 ) @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4757]) ).
thf(5394,plain,
! [SV1530: $i,SV868: $i,SV121: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV121 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV868 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1530 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ SV868 @ SV1530 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(5395,plain,
! [SV1531: $i,SV869: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV122 )
= $false )
| ( ( ( c_lessequals @ SV869 @ SV1531 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV869 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1531 @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(5396,plain,
! [SV1962: $i,SV1532: $i,SV871: $i,SV124: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV124 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5397,plain,
! [SV1963: $i,SV1533: $i,SV872: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV125 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(5398,plain,
! [SV1536: $i,SV875: $i,SV129: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV129 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV875 @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ SV1536 @ SV129 ) @ SV129 ) @ SV129 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV875 @ SV1536 @ SV129 ) @ SV129 ) @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(5399,plain,
! [SV1537: $i,SV876: $i,SV130: $i] :
( ( ( class_Orderings_Olinorder @ SV130 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV876 @ ( c_Orderings_Oord__class_Omin @ SV876 @ SV1537 @ SV130 ) @ SV130 )
= ( c_Orderings_Oord__class_Omin @ SV876 @ SV1537 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(5400,plain,
! [SV2165: $i,SV1964: $i,SV1538: $i,SV877: $i,SV131: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV131 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4765]) ).
thf(5401,plain,
! [SV135: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4768]) ).
thf(5402,plain,
! [SV1541: $i,SV881: $i,SV136: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV881 @ SV1541 @ SV136 )
= ( c_HOL_Otimes__class_Otimes @ SV1541 @ SV881 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4769]) ).
thf(5403,plain,
! [SV1542: $i,SV883: $i,SV139: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV139 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV883 @ SV1542 @ SV139 )
= ( c_HOL_Otimes__class_Otimes @ SV1542 @ SV883 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(5404,plain,
! [SV1965: $i,SV1543: $i,SV884: $i,SV140: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV140 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV884 @ SV1543 @ SV140 ) @ SV1965 @ SV140 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV884 @ SV1965 @ SV140 ) @ ( c_Divides_Odiv__class_Omod @ SV1543 @ SV1965 @ SV140 ) @ SV140 ) @ SV1965 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4771]) ).
thf(5405,plain,
! [SV1966: $i,SV1544: $i,SV885: $i,SV142: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV142 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV885 @ ( c_HOL_Oplus__class_Oplus @ SV1544 @ SV1966 @ SV142 ) @ SV142 )
= ( c_HOL_Oplus__class_Oplus @ SV1544 @ ( c_HOL_Oplus__class_Oplus @ SV885 @ SV1966 @ SV142 ) @ SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4772]) ).
thf(5406,plain,
! [SV1967: $i,SV1545: $i,SV886: $i,SV143: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV143 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV886 @ SV1545 @ SV143 ) @ SV1967 @ SV143 )
= ( c_HOL_Oplus__class_Oplus @ SV886 @ ( c_HOL_Oplus__class_Oplus @ SV1545 @ SV1967 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4773]) ).
thf(5407,plain,
! [SV1968: $i,SV1546: $i,SV887: $i,SV144: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SV1546 @ SV1968 @ SV144 ) @ SV144 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SV1968 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(5408,plain,
! [SV1969: $i,SV1547: $i,SV888: $i,SV145: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SV1547 @ SV1969 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SV1547 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4775]) ).
thf(5409,plain,
! [SV1970: $i,SV1548: $i,SV889: $i,SV146: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SV1548 @ SV146 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SV1970 @ SV146 ) @ SV1548 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4776]) ).
thf(5410,plain,
! [SV1971: $i,SV1549: $i,SV890: $i,SV147: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SV1549 @ SV147 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1971 @ SV890 @ SV147 ) @ SV1549 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4777]) ).
thf(5411,plain,
! [SV1972: $i,SV1550: $i,SV891: $i,SV148: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV148 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(5412,plain,
! [SV1973: $i,SV1551: $i,SV894: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SV1551 @ tc_nat ) @ tc_nat ) @ SV1973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SV1551 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1973 @ SV151 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1551 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(5413,plain,
! [SV1974: $i,SV1552: $i,SV895: $i,SV152: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__mono1 @ SV152 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
| ~ ( c_lessequals @ SV1552 @ SV1974 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(5414,plain,
! [SV1975: $i,SV1553: $i,SV896: $i,SV153: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__mono @ SV153 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
| ~ ( c_lessequals @ SV1553 @ SV1975 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4781]) ).
thf(5415,plain,
! [SV1976: $i,SV1554: $i,SV897: $i,SV154: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__mono @ SV154 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
| ~ ( c_lessequals @ SV897 @ SV1976 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4782]) ).
thf(5416,plain,
! [SV1977: $i,SV1555: $i,SV898: $i,SV155: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV155 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV1977 @ SV1555 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(5417,plain,
! [SV1978: $i,SV1556: $i,SV899: $i,SV156: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV156 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1978 @ SV899 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(5418,plain,
! [SV2166: $i,SV1979: $i,SV1557: $i,SV901: $i,SV158: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4786]) ).
thf(5419,plain,
! [SV902: $i,SV1558: $i,SV159: $i] :
( ( ( c_lessequals @ SV159 @ SV1558 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV159 @ SV902 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1558 @ SV902 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4787]) ).
thf(5420,plain,
! [SV160: $i,SV1559: $i,SV903: $i] :
( ( ( c_lessequals @ SV903 @ SV1559 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV903 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV160 @ SV1559 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4788]) ).
thf(5421,plain,
! [SV161: $i,SV1560: $i,SV904: $i] :
( ( ( c_lessequals @ SV904 @ SV1560 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV904 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV161 @ SV1560 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4789]) ).
thf(5422,plain,
! [SV905: $i,SV1561: $i,SV162: $i] :
( ( ( c_lessequals @ SV162 @ SV1561 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV162 @ SV905 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1561 @ SV905 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(5423,plain,
! [SV1562: $i,SV906: $i,SV163: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV163 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV906 @ SV1562 @ tc_nat ) @ SV163 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV906 @ SV163 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1562 @ SV163 ) @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4791]) ).
thf(5424,plain,
! [SV1980: $i,SV1563: $i,SV907: $i,SV164: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV164 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ ( c_Divides_Odiv__class_Omod @ SV1563 @ SV1980 @ SV164 ) @ SV164 ) @ SV1980 @ SV164 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ SV1563 @ SV164 ) @ SV1980 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(5425,plain,
! [SV1981: $i,SV1564: $i,SV908: $i,SV165: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV165 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV908 @ SV1564 @ SV165 ) @ SV1981 @ SV165 ) @ SV1564 @ SV165 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV908 @ SV1981 @ SV165 ) @ SV1564 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4793]) ).
thf(5426,plain,
! [SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ! [SY4852: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV166 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SY4852 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SY4852 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4794]) ).
thf(5427,plain,
! [SV2168: $i,SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ! [SY4853: $i] :
( ~ ( class_Ring__and__Field_Odvd @ SV167 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SY4853 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SY4853 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4795]) ).
thf(5428,plain,
! [SV1567: $i,SV911: $i,SV168: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV168 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4796]) ).
thf(5429,plain,
! [SV1568: $i,SV912: $i,SV169: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV169 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(5430,plain,
! [SV1569: $i,SV913: $i,SV170: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV170 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(5431,plain,
! [SV1570: $i,SV915: $i,SV172: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(5432,plain,
! [SV1571: $i,SV916: $i,SV173: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4801]) ).
thf(5433,plain,
! [SV1572: $i,SV917: $i,SV174: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(5434,plain,
! [SV1573: $i,SV918: $i,SV175: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV175 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ SV918 @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ SV1573 @ SV175 ) @ SV175 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1573 @ SV175 ) @ SV175 ) @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(5435,plain,
! [SV1984: $i,SV1574: $i,SV919: $i,SV176: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ SV176 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1574 @ SV176 ) @ SV1984 @ SV176 )
= ( c_HOL_Otimes__class_Otimes @ SV919 @ ( c_HOL_Otimes__class_Otimes @ SV1574 @ SV1984 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4804]) ).
thf(5436,plain,
! [SV1985: $i,SV1575: $i,SV920: $i,SV177: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV177 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1575 @ SV177 ) @ SV1985 @ SV177 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1985 @ SV177 ) @ SV1575 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(5437,plain,
! [SV1986: $i,SV1576: $i,SV921: $i,SV178: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV178 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1576 @ SV178 ) @ SV1986 @ SV178 )
= ( c_HOL_Otimes__class_Otimes @ SV921 @ ( c_HOL_Otimes__class_Otimes @ SV1576 @ SV1986 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4806]) ).
thf(5438,plain,
! [SV1987: $i,SV1577: $i,SV922: $i,SV179: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV179 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV922 @ ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV1987 @ SV179 ) @ SV179 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV922 @ SV1577 @ SV179 ) @ SV1987 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4807]) ).
thf(5439,plain,
! [SV1988: $i,SV1578: $i,SV923: $i,SV180: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV180 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV923 @ ( c_HOL_Otimes__class_Otimes @ SV1578 @ SV1988 @ SV180 ) @ SV180 )
= ( c_HOL_Otimes__class_Otimes @ SV1578 @ ( c_HOL_Otimes__class_Otimes @ SV923 @ SV1988 @ SV180 ) @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(5440,plain,
! [SV1989: $i,SV1580: $i,SV925: $i,SV182: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV182 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV925 @ ( c_HOL_Otimes__class_Otimes @ SV1580 @ SV1989 @ SV182 ) @ SV182 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV925 @ SV1580 @ SV182 ) @ SV1989 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4809]) ).
thf(5441,plain,
! [SV1990: $i,SV1581: $i,SV926: $i,SV183: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV926 @ SV1581 @ SV183 ) @ SV1990 @ SV183 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV926 @ SV1990 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV1581 @ SV1990 @ SV183 ) @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5442,plain,
! [SV1991: $i,SV1582: $i,SV927: $i,SV184: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV184 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV927 @ ( c_HOL_Oplus__class_Oplus @ SV1582 @ SV1991 @ SV184 ) @ SV184 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1582 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1991 @ SV184 ) @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5443,plain,
! [SV1992: $i,SV1583: $i,SV928: $i,SV185: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV185 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV928 @ ( c_HOL_Oplus__class_Oplus @ SV1583 @ SV1992 @ SV185 ) @ SV185 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1583 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1992 @ SV185 ) @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4812]) ).
thf(5444,plain,
! [SV1993: $i,SV1584: $i,SV929: $i,SV186: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV186 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV929 @ SV1584 @ SV186 ) @ SV1993 @ SV186 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SV1993 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV1584 @ SV1993 @ SV186 ) @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4813]) ).
thf(5445,plain,
! [SV1994: $i,SV1585: $i,SV930: $i,SV187: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV187 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV930 @ SV1585 @ SV187 ) @ SV1994 @ SV187 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV930 @ SV1994 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV1585 @ SV1994 @ SV187 ) @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4814]) ).
thf(5446,plain,
! [SV1995: $i,SV1588: $i,SV933: $i,SV190: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV190 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV933 @ ( c_HOL_Oplus__class_Oplus @ SV1588 @ SV1995 @ SV190 ) @ SV190 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1588 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1995 @ SV190 ) @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4815]) ).
thf(5447,plain,
! [SV1996: $i,SV1589: $i,SV934: $i,SV191: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring @ SV191 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV934 @ SV1589 @ SV191 ) @ SV1996 @ SV191 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV1996 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV1589 @ SV1996 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4816]) ).
thf(5448,plain,
! [SV937: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV937 @ SV194 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV937 @ SV194 ) @ SV194 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4819]) ).
thf(5449,plain,
! [SV938: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV938 @ SV195 ) @ SV195 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV938 @ SV195 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(5450,plain,
! [SV1590: $i,SV939: $i,SV196: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
= $false )
| ( ( ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SV1590 @ SV196 ) @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4821]) ).
thf(5451,plain,
! [SV1591: $i,SV940: $i,SV197: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
= $false )
| ( ( ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1591 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SV1591 @ SV940 @ SV197 ) @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(5452,plain,
! [SV1592: $i,SV941: $i,SV198: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
= $false )
| ( ( ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1592 @ SV198 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SV1592 @ SV198 ) @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(5453,plain,
! [SV1593: $i,SV942: $i,SV199: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
= $false )
| ( ( ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SV1593 @ SV942 @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(5454,plain,
! [SV1997: $i,SV1594: $i,SV943: $i,SV201: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV943 @ SV1594 @ SV201 ) @ ( c_HOL_Otimes__class_Otimes @ SV1997 @ SV1594 @ SV201 ) @ SV201 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV943 @ SV1997 @ SV201 ) @ SV1594 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4826]) ).
thf(5455,plain,
! [SV1998: $i,SV1595: $i,SV944: $i,SV202: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1595 @ SV1998 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV944 @ SV1998 @ tc_nat )
| ~ ( c_lessequals @ SV202 @ SV1595 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4827]) ).
thf(5456,plain,
! [SV2169: $i,SV1999: $i,SV1596: $i,SV945: $i,SV204: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV204 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4828]) ).
thf(5457,plain,
! [SV2170: $i,SV2000: $i,SV1597: $i,SV946: $i,SV205: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV205 )
| ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4829]) ).
thf(5458,plain,
! [SV207: $i,SV948: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV948 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV207 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV207 @ SV948 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(5459,plain,
! [SV208: $i,SV949: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV949 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV208 @ SV949 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV208 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(5460,plain,
! [SV209: $i,SV950: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV950 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV950 @ SV209 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV209 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4833]) ).
thf(5461,plain,
! [SV210: $i,SV951: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV951 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV210 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SV951 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(5462,plain,
! [SV212: $i,SV953: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV953 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV212 @ SV953 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV212 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(5463,plain,
! [SV213: $i,SV954: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV954 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV954 @ SV213 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV213 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(5464,plain,
! [SV214: $i,SV955: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV955 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV214 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV214 @ SV955 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4838]) ).
thf(5465,plain,
! [SV215: $i,SV956: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV956 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV215 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV215 @ SV956 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(5466,plain,
! [SV217: $i,SV958: $i] :
( ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV958 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV217 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV217 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(5467,plain,
! [SV959: $i,SV218: $i] :
( ( ( c_lessequals @ SV218 @ ( c_Suc @ SV959 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV218 @ SV959 @ tc_nat )
= $true )
| ( ( SV218
= ( c_Suc @ SV959 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4842]) ).
thf(5468,plain,
! [SV2001: $i,SV1598: $i,SV960: $i,SV219: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV219 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV2001 @ SV219 ) @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5469,plain,
! [SV2002: $i,SV1599: $i,SV961: $i,SV220: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV220 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SV2002 @ SV961 @ SV220 ) @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(5470,plain,
! [SV2003: $i,SV1600: $i,SV962: $i,SV221: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(5471,plain,
! [SV2171: $i,SV2004: $i,SV1601: $i,SV963: $i,SV223: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1601 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV2004 @ SV2171 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV2004 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV1601 @ SV2171 @ SV223 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4846]) ).
thf(5472,plain,
! [SV2005: $i,SV1602: $i,SV965: $i,SV225: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ SV965 @ SV1602 @ SV225 ) @ SV2005 @ SV225 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ SV965 @ SV2005 @ SV225 ) @ ( c_HOL_Oplus__class_Oplus @ SV1602 @ SV2005 @ SV225 ) @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4848]) ).
thf(5473,plain,
! [SV226: $i,SV966: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV966 @ SV966 @ SV226 ) @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV226 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(5474,plain,
! [SV2006: $i,SV1603: $i,SV967: $i,SV227: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV967 @ ( c_HOL_Oplus__class_Oplus @ SV1603 @ SV2006 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1603 @ SV227 ) @ SV2006 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(5475,plain,
! [SV2007: $i,SV1604: $i,SV968: $i,SV228: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV228 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV968 @ ( c_HOL_Oplus__class_Oplus @ SV1604 @ SV2007 @ SV228 ) @ SV228 )
= ( c_HOL_Oplus__class_Oplus @ SV1604 @ ( c_HOL_Oplus__class_Oplus @ SV968 @ SV2007 @ SV228 ) @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4851]) ).
thf(5476,plain,
! [SV2008: $i,SV1607: $i,SV971: $i,SV231: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV231 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV971 @ SV1607 @ SV231 ) @ SV2008 @ SV231 )
= ( c_HOL_Oplus__class_Oplus @ SV971 @ ( c_HOL_Oplus__class_Oplus @ SV1607 @ SV2008 @ SV231 ) @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4852]) ).
thf(5477,plain,
! [SV2009: $i,SV1608: $i,SV972: $i,SV232: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV232 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV972 @ ( c_HOL_Oplus__class_Oplus @ SV1608 @ SV2009 @ SV232 ) @ SV232 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV972 @ SV1608 @ SV232 ) @ SV2009 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(5478,plain,
! [SV2010: $i,SV1609: $i,SV973: $i,SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV1609 @ SV233 ) @ SV2010 @ SV233 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV2010 @ SV233 ) @ SV1609 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5479,plain,
! [SV2011: $i,SV1610: $i,SV974: $i,SV234: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV974 @ ( c_HOL_Oplus__class_Oplus @ SV1610 @ SV2011 @ SV234 ) @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV1610 @ ( c_HOL_Oplus__class_Oplus @ SV974 @ SV2011 @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(5480,plain,
! [SV2012: $i,SV1611: $i,SV975: $i,SV235: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SV1611 @ SV235 ) @ SV2012 @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV975 @ ( c_HOL_Oplus__class_Oplus @ SV1611 @ SV2012 @ SV235 ) @ SV235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4856]) ).
thf(5481,plain,
! [SV236: $i,SV976: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV976 @ SV236 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV976 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV236 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(5482,plain,
! [SV1612: $i,SV977: $i,SV238: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV238 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ SV977 @ SV1612 @ SV238 ) @ SV238 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV977 @ SV238 ) @ ( c_HOL_Oabs__class_Oabs @ SV1612 @ SV238 ) @ SV238 ) @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(5483,plain,
! [SV1613: $i,SV978: $i,SV239: $i] :
( ( ( c_lessequals @ SV239 @ SV978 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV239 @ ( c_HOL_Oplus__class_Oplus @ SV978 @ SV1613 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(5484,plain,
! [SV979: $i,SV1614: $i,SV240: $i] :
( ( ( c_lessequals @ SV240 @ SV1614 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV240 @ ( c_HOL_Oplus__class_Oplus @ SV979 @ SV1614 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(5485,plain,
! [SV980: $i,SV1615: $i,SV241: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV241 @ SV1615 @ tc_nat ) @ SV980 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV241 @ SV980 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4861]) ).
thf(5486,plain,
! [SV981: $i,SV242: $i,SV1616: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV242 @ tc_nat ) @ SV981 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV242 @ SV981 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(5487,plain,
! [SV1617: $i,SV982: $i,SV243: $i] :
( ( ( c_lessequals @ SV243 @ SV982 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV243 @ ( c_HOL_Oplus__class_Oplus @ SV982 @ SV1617 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(5488,plain,
! [SV983: $i,SV1618: $i,SV244: $i] :
( ( ( c_lessequals @ SV244 @ SV1618 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV244 @ ( c_HOL_Oplus__class_Oplus @ SV983 @ SV1618 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(5489,plain,
! [SV2013: $i,SV1619: $i,SV984: $i,SV246: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV246 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ SV1619 @ SV246 ) @ SV2013 @ SV246 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ ( c_Divides_Odiv__class_Omod @ SV1619 @ SV2013 @ SV246 ) @ SV246 ) @ SV2013 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(5490,plain,
! [SV2014: $i,SV1620: $i,SV985: $i,SV247: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV247 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV985 @ SV1620 @ SV247 ) @ SV2014 @ SV247 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV985 @ SV2014 @ SV247 ) @ SV1620 @ SV247 ) @ SV2014 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5491,plain,
! [SV2015: $i,SV1621: $i,SV986: $i,SV248: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(5492,plain,
! [SV1622: $i,SV988: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV988 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV250 @ SV1622 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV250 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4868]) ).
thf(5493,plain,
! [SV1623: $i,SV251: $i,SV989: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV989 @ SV251 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1623 @ SV251 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV251 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4869]) ).
thf(5494,plain,
! [SV2016: $i,SV1624: $i,SV990: $i,SV252: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 ) )
= $true )
| ( ( ( c_lessequals @ SV990 @ SV1624 @ SV252 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(5495,plain,
! [SV2017: $i,SV1625: $i,SV991: $i,SV253: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 ) )
= $true )
| ( ( ( c_lessequals @ SV991 @ SV1625 @ SV253 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(5496,plain,
! [SV2018: $i,SV1626: $i,SV992: $i,SV254: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV254 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
| ~ ( c_lessequals @ SV1626 @ SV2018 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4872]) ).
thf(5497,plain,
! [SV2019: $i,SV1627: $i,SV993: $i,SV255: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV255 ) )
= $true )
| ( ( ( c_lessequals @ SV993 @ SV1627 @ SV255 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5498,plain,
! [SV2020: $i,SV1628: $i,SV994: $i,SV256: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV256 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
| ~ ( c_lessequals @ SV2020 @ SV1628 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5499,plain,
! [SV2021: $i,SV1629: $i,SV995: $i,SV257: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV257 ) )
= $true )
| ( ( ( c_lessequals @ SV995 @ SV1629 @ SV257 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(5500,plain,
! [SV258: $i,SV1630: $i,SV996: $i] :
( ( ( ~ ( c_lessequals @ SV996 @ SV1630 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV996 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV1630 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(5501,plain,
! [SV997: $i,SV259: $i,SV1631: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV997 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1631 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV259 @ SV997 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4877]) ).
thf(5502,plain,
! [SV998: $i,SV260: $i,SV1632: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1632 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV998 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV260 @ SV998 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4878]) ).
thf(5503,plain,
! [SV999: $i,SV261: $i,SV1633: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1633 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SV1633 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV999 @ SV1633 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV261 @ SV999 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4879]) ).
thf(5504,plain,
! [SV2172: $i,SV2022: $i,SV1634: $i,SV1000: $i,SV263: $i] :
( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV263 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1634 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ SV2172 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SV2172 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ SV2172 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SV2172 @ SV263 ) @ SV263 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4881]) ).
thf(5505,plain,
! [SV1635: $i,SV1001: $i,SV266: $i] :
( ( ( class_Orderings_Olinorder @ SV266 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1001 @ SV1635 @ SV266 )
= ( c_Orderings_Oord__class_Omin @ SV1635 @ SV1001 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4882]) ).
thf(5506,plain,
! [SV2173: $i,SV2023: $i,SV1636: $i,SV1002: $i,SV267: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring @ SV267 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1636 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2023 @ SV1636 @ SV267 ) @ SV2173 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV1002 @ SV2023 @ SV267 ) @ SV1636 @ SV267 ) @ SV2173 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4883]) ).
thf(5507,plain,
! [SV1638: $i,SV1006: $i,SV271: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(5508,plain,
! [SV1639: $i,SV1007: $i,SV272: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV272 )
= $false )
| ( ( ( SV1007
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1639 @ SV1639 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SV1007 @ SV1007 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4888]) ).
thf(5509,plain,
! [SV1640: $i,SV1008: $i,SV273: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV273 )
= $false )
| ( ( ( SV1008
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1008 @ SV1008 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1640 @ SV1640 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(5510,plain,
! [SV1009: $i,SV275: $i,SV1641: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1641 ) @ SV275 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1641 ) @ SV1009 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV275 @ SV1009 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4890]) ).
thf(5511,plain,
! [SV276: $i,SV1642: $i,SV1010: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1010 @ SV1642 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1010 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV276 ) @ SV1642 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5512,plain,
! [SV278: $i,SV1012: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV1012 ) @ SV278 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV278 @ SV1012 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5513,plain,
! [SV281: $i,SV1014: $i,SV1643: $i] :
( ( ( c_lessequals @ SV1643 @ SV1014 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV281 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1014 @ SV281 @ tc_nat ) @ SV1643 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(5514,plain,
! [SV282: $i,SV1015: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1015 @ SV282 )
= SV1015 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV1015 @ SV282 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4894]) ).
thf(5515,plain,
! [SV2025: $i,SV1644: $i,SV1016: $i,SV283: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV283 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ SV1644 @ SV283 ) @ SV2025 @ SV283 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ ( c_Divides_Odiv__class_Omod @ SV1644 @ SV2025 @ SV283 ) @ SV283 ) @ SV2025 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4895]) ).
thf(5516,plain,
! [SV2026: $i,SV1645: $i,SV1017: $i,SV284: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV284 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1017 @ SV1645 @ SV284 ) @ SV2026 @ SV284 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1017 @ SV2026 @ SV284 ) @ SV1645 @ SV284 ) @ SV2026 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4896]) ).
thf(5517,plain,
! [SV1018: $i,SV285: $i,SV1646: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1646 ) @ SV285 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV1646 ) @ SV1018 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV285 @ SV1018 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4897]) ).
thf(5518,plain,
! [SV286: $i,SV1647: $i,SV1019: $i] :
( ( ( c_lessequals @ SV1019 @ SV1647 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1019 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV286 ) @ SV1647 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(5519,plain,
! [SV1648: $i,SV1020: $i,SV287: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV287 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV287 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1020 @ SV1020 @ SV287 ) @ ( c_HOL_Otimes__class_Otimes @ SV1648 @ SV1648 @ SV287 ) @ SV287 ) @ SV287 )
| ( SV1648
= ( c_HOL_Ozero__class_Ozero @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(5520,plain,
! [SV1649: $i,SV1021: $i,SV288: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV288 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV288 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1021 @ SV1021 @ SV288 ) @ ( c_HOL_Otimes__class_Otimes @ SV1649 @ SV1649 @ SV288 ) @ SV288 ) @ SV288 )
| ( SV1021
= ( c_HOL_Ozero__class_Ozero @ SV288 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(5521,plain,
! [SV289: $i,SV1022: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1022 @ SV289 ) @ ( c_HOL_Ozero__class_Ozero @ SV289 ) @ SV289 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV289 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4901]) ).
thf(5522,plain,
! [SV2027: $i,SV1652: $i,SV1026: $i,SV298: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5523,plain,
! [SV2028: $i,SV1653: $i,SV1027: $i,SV299: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV299 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(5524,plain,
! [SV2029: $i,SV1654: $i,SV1028: $i,SV300: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV300 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4905]) ).
thf(5525,plain,
! [SV2030: $i,SV1655: $i,SV1029: $i,SV301: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4906]) ).
thf(5526,plain,
! [SV2031: $i,SV1656: $i,SV1030: $i,SV302: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV302 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(5527,plain,
! [SV2032: $i,SV1657: $i,SV1031: $i,SV303: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV303 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4908]) ).
thf(5528,plain,
! [SV2033: $i,SV1658: $i,SV1032: $i,SV304: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV304 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4909]) ).
thf(5529,plain,
! [SV2034: $i,SV1659: $i,SV1033: $i,SV305: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4910]) ).
thf(5530,plain,
! [SV2035: $i,SV1660: $i,SV1034: $i,SV306: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV306 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4911]) ).
thf(5531,plain,
! [SV2036: $i,SV1661: $i,SV1035: $i,SV307: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV307 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4912]) ).
thf(5532,plain,
! [SV2037: $i,SV1662: $i,SV1036: $i,SV308: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV308 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(5533,plain,
! [SV2038: $i,SV1663: $i,SV1037: $i,SV309: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV309 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5534,plain,
! [SV2039: $i,SV1664: $i,SV1038: $i,SV310: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV310 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(5535,plain,
! [SV311: $i,SV1665: $i,SV1039: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV1665 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1039 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1665 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4916]) ).
thf(5536,plain,
! [SV1040: $i,SV312: $i,SV1666: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV1040 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1666 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV312 @ SV1040 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4917]) ).
thf(5537,plain,
! [SV1667: $i,SV313: $i,SV1041: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1041 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1667 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SV1041 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1667 @ SV1041 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4918]) ).
thf(5538,plain,
! [SV1668: $i,SV1042: $i,SV314: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1668 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1042 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1668 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4919]) ).
thf(5539,plain,
! [SV315: $i,SV1669: $i,SV1043: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1043 @ SV1669 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1043 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5540,plain,
! [SV1044: $i,SV1670: $i,SV316: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV316 @ SV1670 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1044 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SV1044 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1670 @ SV1044 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5541,plain,
! [SV2040: $i,SV1671: $i,SV1045: $i,SV317: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV317 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1045 @ ( c_HOL_Otimes__class_Otimes @ SV1671 @ SV2040 @ SV317 ) @ SV317 ) @ SV1671 @ SV317 )
= ( c_Divides_Odiv__class_Omod @ SV1045 @ SV1671 @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5542,plain,
! [SV2041: $i,SV1672: $i,SV1046: $i,SV318: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV318 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1046 @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2041 @ SV318 ) @ SV318 ) @ SV2041 @ SV318 )
= ( c_Divides_Odiv__class_Omod @ SV1046 @ SV2041 @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(5543,plain,
! [SV2042: $i,SV1674: $i,SV1048: $i,SV320: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV320 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
| ( SV2042
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SV2042 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SV2042 @ SV320 ) @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4924]) ).
thf(5544,plain,
! [SV2043: $i,SV1675: $i,SV1049: $i,SV321: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV321 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
| ( SV2043
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1675 @ SV321 ) @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4925]) ).
thf(5545,plain,
! [SV1050: $i,SV322: $i,SV1676: $i] :
( ( ( SV1676
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV322 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV1050 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV322 @ SV1050 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(5546,plain,
! [SV1677: $i,SV1051: $i,SV323: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(5547,plain,
! [SV1678: $i,SV1052: $i,SV324: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 )
| ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4928]) ).
thf(5548,plain,
! [SV1679: $i,SV1053: $i,SV325: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4929]) ).
thf(5549,plain,
! [SV1680: $i,SV1054: $i,SV326: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 )
| ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4930]) ).
thf(5550,plain,
! [SV1681: $i,SV1055: $i,SV327: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(5551,plain,
! [SV1682: $i,SV1056: $i,SV328: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 )
| ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4932]) ).
thf(5552,plain,
! [SV1683: $i,SV1057: $i,SV329: $i] :
( ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4933]) ).
thf(5553,plain,
! [SV1684: $i,SV1058: $i,SV331: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5554,plain,
! [SV1685: $i,SV1059: $i,SV332: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4935]) ).
thf(5555,plain,
! [SV1686: $i,SV1060: $i,SV333: $i] :
( ( ( class_Divides_Osemiring__div @ SV333 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1060 @ SV1686 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1686 @ SV1060 @ SV333 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4936]) ).
thf(5556,plain,
! [SV334: $i,SV1061: $i] :
( ( ( SV1061
= ( c_HOL_Ozero__class_Ozero @ SV334 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV334 ) @ SV1061 @ SV334 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4937]) ).
thf(5557,plain,
! [SV1062: $i,SV336: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV336 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1062 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV1062 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(5558,plain,
! [SV2044: $i,SV1687: $i,SV1064: $i,SV338: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV338 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1064 @ SV1687 @ SV338 ) @ SV2044 @ SV338 )
= ( c_Orderings_Oord__class_Omin @ SV1064 @ ( c_Orderings_Oord__class_Omin @ SV1687 @ SV2044 @ SV338 ) @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4939]) ).
thf(5559,plain,
! [SV2045: $i,SV1688: $i,SV1065: $i,SV339: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV339 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1065 @ ( c_Orderings_Oord__class_Omin @ SV1688 @ SV2045 @ SV339 ) @ SV339 )
= ( c_Orderings_Oord__class_Omin @ SV1688 @ ( c_Orderings_Oord__class_Omin @ SV1065 @ SV2045 @ SV339 ) @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4940]) ).
thf(5560,plain,
! [SV1689: $i,SV1066: $i,SV340: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4941]) ).
thf(5561,plain,
! [SV1690: $i,SV1068: $i,SV342: $i] :
( ( ( class_Orderings_Olinorder @ SV342 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1068 @ SV1690 @ SV342 )
= SV1068 )
| ~ ( c_lessequals @ SV1068 @ SV1690 @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5562,plain,
! [SV1691: $i,SV1069: $i,SV343: $i] :
( ( ( class_Orderings_Olinorder @ SV343 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1069 @ SV1691 @ SV343 )
= SV1691 )
| ~ ( c_lessequals @ SV1691 @ SV1069 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5563,plain,
! [SV1692: $i,SV1072: $i,SV346: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4947]) ).
thf(5564,plain,
! [SV2046: $i,SV1693: $i,SV1075: $i,SV350: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1693 @ SV2046 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1075 @ SV2046 @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SV1693 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4950]) ).
thf(5565,plain,
! [SV2174: $i,SV2047: $i,SV1694: $i,SV1076: $i,SV351: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SV1694 @ SV2174 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4951]) ).
thf(5566,plain,
! [SV2175: $i,SV2048: $i,SV1695: $i,SV1077: $i,SV352: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2048 @ SV1077 @ tc_nat ) @ SV2175 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SV2048 @ tc_nat ) @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ SV2175 @ tc_nat ) )
| ~ ( c_lessequals @ SV2048 @ SV352 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4952]) ).
thf(5567,plain,
! [SV2176: $i,SV2049: $i,SV1696: $i,SV1078: $i,SV353: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV1078 @ tc_nat ) @ SV1696 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2049 @ SV1078 @ tc_nat ) @ SV2176 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1696 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2049 @ SV353 @ tc_nat ) @ SV1078 @ tc_nat ) @ SV2176 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV353 @ SV2049 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4953]) ).
thf(5568,plain,
! [SV1079: $i,SV354: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV1079 @ SV354 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ ( c_HOL_Oplus__class_Oplus @ SV1079 @ SV1079 @ SV354 ) @ SV354 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(5569,plain,
! [SV1080: $i,SV355: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ ( c_HOL_Oplus__class_Oplus @ SV1080 @ SV1080 @ SV355 ) @ SV355 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ SV1080 @ SV355 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5570,plain,
! [SV1697: $i,SV1081: $i,SV356: $i] :
( ( ( class_Divides_Osemiring__div @ SV356 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1081 @ SV1697 @ SV356 ) @ SV1697 @ SV356 )
= ( c_Divides_Odiv__class_Omod @ SV1081 @ SV1697 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(5571,plain,
! [SV2177: $i,SV2050: $i,SV1698: $i,SV1082: $i,SV357: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 )
| ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1082 @ SV1698 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SV2050 @ SV2177 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1082 @ SV2050 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1698 @ SV2177 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4957]) ).
thf(5572,plain,
! [SV2051: $i,SV1699: $i,SV1083: $i,SV358: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4958]) ).
thf(5573,plain,
! [SV360: $i,SV1700: $i,SV1085: $i] :
( ( ( ~ ( c_lessequals @ SV1085 @ SV1700 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(5574,plain,
! [SV361: $i,SV1086: $i,SV1701: $i] :
( ( ( ~ ( c_lessequals @ SV1701 @ SV1086 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5575,plain,
! [SV2178: $i,SV2052: $i,SV1702: $i,SV1087: $i,SV362: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV362 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1702 @ SV362 ) @ SV2052 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2178 @ SV1702 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV2178 @ SV362 ) @ SV1702 @ SV362 ) @ SV2052 @ SV362 ) @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4962]) ).
thf(5576,plain,
! [SV363: $i,SV1703: $i,SV1088: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1088 @ SV1703 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1088 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV363 @ SV1703 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4963]) ).
thf(5577,plain,
! [SV2053: $i,SV1704: $i,SV1089: $i,SV364: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV364 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV1704 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV2053 @ SV364 ) @ SV364 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1704 @ SV2053 @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(5578,plain,
! [SV2054: $i,SV1705: $i,SV1090: $i,SV365: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV365 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SV1705 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SV2054 @ SV1705 @ SV365 ) @ SV365 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SV2054 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4965]) ).
thf(5579,plain,
! [SV1094: $i,SV369: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV369 ) @ ( c_HOL_Oabs__class_Oabs @ SV1094 @ SV369 ) @ SV369 )
= $true )
| ( ( SV1094
= ( c_HOL_Ozero__class_Ozero @ SV369 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV369 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4967]) ).
thf(5580,plain,
! [SV1706: $i,SV1099: $i,SV374: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV374 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1099 @ SV1706 @ SV374 )
= ( c_HOL_Oplus__class_Oplus @ SV1706 @ SV1099 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4972]) ).
thf(5581,plain,
! [SV1707: $i,SV1101: $i,SV376: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV376 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1101 @ SV1707 @ SV376 )
= ( c_HOL_Oplus__class_Oplus @ SV1707 @ SV1101 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4973]) ).
thf(5582,plain,
! [SV1708: $i,SV1102: $i,SV377: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV377 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1102 @ SV1708 @ SV377 )
= ( c_HOL_Oplus__class_Oplus @ SV1708 @ SV1102 @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4974]) ).
thf(5583,plain,
! [SV2055: $i,SV1709: $i,SV1103: $i,SV378: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV378 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1103 @ SV1709 @ SV378 ) @ SV2055 @ SV378 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1103 @ SV2055 @ SV378 ) @ ( c_Divides_Odiv__class_Omod @ SV1709 @ SV2055 @ SV378 ) @ SV378 ) @ SV2055 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5584,plain,
! [SV2056: $i,SV1710: $i,SV1104: $i,SV379: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV379 ) )
= $true )
| ( ( ( c_lessequals @ SV1104 @ SV1710 @ SV379 )
| ~ ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SV1710 @ SV2056 @ SV379 ) @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4976]) ).
thf(5585,plain,
! [SV2057: $i,SV1711: $i,SV1105: $i,SV380: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV380 ) )
= $true )
| ( ( ( c_lessequals @ SV1105 @ SV1711 @ SV380 )
| ~ ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SV2057 @ SV1711 @ SV380 ) @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(5586,plain,
! [SV2058: $i,SV1712: $i,SV1106: $i,SV381: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV381 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SV1712 @ SV381 ) @ SV2058 @ SV381 )
| ~ ( c_lessequals @ SV1106 @ SV2058 @ SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(5587,plain,
! [SV2059: $i,SV1713: $i,SV1107: $i,SV382: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV382 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SV1713 @ SV382 ) @ SV2059 @ SV382 )
| ~ ( c_lessequals @ SV1713 @ SV2059 @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(5588,plain,
! [SV2060: $i,SV1714: $i,SV1108: $i,SV383: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV383 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SV1714 @ SV383 ) @ SV2060 @ SV383 )
| ~ ( c_lessequals @ SV1108 @ SV2060 @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4980]) ).
thf(5589,plain,
! [SV2061: $i,SV1715: $i,SV1109: $i,SV384: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV384 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SV1715 @ SV384 ) @ SV2061 @ SV384 )
| ~ ( c_lessequals @ SV1715 @ SV2061 @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4981]) ).
thf(5590,plain,
! [SV2062: $i,SV1716: $i,SV1110: $i,SV385: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV385 ) )
= $true )
| ( ( ( c_lessequals @ SV1110 @ SV1716 @ SV385 )
| ~ ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SV1716 @ SV2062 @ SV385 ) @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(5591,plain,
! [SV2063: $i,SV1717: $i,SV1111: $i,SV386: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV386 ) )
= $true )
| ( ( ( c_lessequals @ SV1111 @ SV1717 @ SV386 )
| ~ ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SV2063 @ SV1717 @ SV386 ) @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4983]) ).
thf(5592,plain,
! [SV2064: $i,SV1718: $i,SV1113: $i,SV388: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV388 ) )
= $true )
| ( ( ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
| ( c_lessequals @ SV2064 @ SV1718 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2064 @ SV1113 @ SV388 ) @ SV1718 @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5593,plain,
! [SV2065: $i,SV1719: $i,SV1114: $i,SV389: $i] :
( ( ( ~ ( c_lessequals @ SV389 @ SV1114 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV389 @ SV1719 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1114 @ SV389 @ tc_nat ) @ SV1719 @ tc_nat ) @ SV2065 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1114 @ SV1719 @ tc_nat ) @ SV2065 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5594,plain,
! [SV1115: $i,SV1720: $i,SV390: $i] :
( ( ( c_lessequals @ SV390 @ ( c_HOL_Oplus__class_Oplus @ SV1720 @ SV1115 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV390 @ SV1115 @ tc_nat ) @ SV1720 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5595,plain,
! [SV1116: $i,SV1721: $i,SV391: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV391 @ SV1721 @ tc_nat ) @ SV1116 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV391 @ ( c_HOL_Oplus__class_Oplus @ SV1116 @ SV1721 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5596,plain,
! [SV2179: $i,SV2066: $i,SV1722: $i,SV1117: $i,SV392: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ SV2179 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SV2179 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4989]) ).
thf(5597,plain,
! [SV2180: $i,SV2067: $i,SV1723: $i,SV1118: $i,SV393: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2067 @ SV1118 @ tc_nat ) @ SV2180 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SV2067 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SV2180 @ tc_nat )
| ~ ( c_lessequals @ SV2067 @ SV393 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4990]) ).
thf(5598,plain,
! [SV2181: $i,SV2068: $i,SV1724: $i,SV1119: $i,SV394: $i] :
( ( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SV2068 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1724 @ SV1119 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4991]) ).
thf(5599,plain,
! [SV2182: $i,SV2069: $i,SV1725: $i,SV1120: $i,SV395: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2069 @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2069 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV395 @ SV2069 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4992]) ).
thf(5600,plain,
! [SV1726: $i,SV1121: $i,SV396: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV396 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Otimes__class_Otimes @ SV1121 @ SV1726 @ tc_nat ) @ SV396 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1121 @ SV396 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1726 @ SV396 ) @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5601,plain,
! [SV1129: $i,SV404: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV404 ) )
= $true )
| ( ( SV1129
= ( c_HOL_Oplus__class_Oplus @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5000]) ).
thf(5602,plain,
! [SV2183: $i,SV2070: $i,SV1728: $i,SV1134: $i,SV412: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SV1728 @ SV2183 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5005]) ).
thf(5603,plain,
! [SV2184: $i,SV2071: $i,SV1729: $i,SV1135: $i,SV413: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5006]) ).
thf(5604,plain,
! [SV1730: $i,SV1136: $i,SV414: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5605,plain,
! [SV1731: $i,SV1137: $i,SV415: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5606,plain,
! [SV2072: $i,SV1732: $i,SV1138: $i,SV416: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV416 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
| ~ ( c_lessequals @ SV1138 @ SV2072 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5009]) ).
thf(5607,plain,
! [SV2073: $i,SV1733: $i,SV1139: $i,SV417: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV417 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 )
| ~ ( c_lessequals @ SV2073 @ SV1733 @ SV417 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5010]) ).
thf(5608,plain,
! [SV2074: $i,SV1734: $i,SV1140: $i,SV418: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV418 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
| ~ ( c_lessequals @ SV2074 @ SV1734 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5609,plain,
! [SV2075: $i,SV1735: $i,SV1141: $i,SV419: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV419 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 )
| ~ ( c_lessequals @ SV1141 @ SV2075 @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5012]) ).
thf(5610,plain,
! [SV2076: $i,SV1736: $i,SV1142: $i,SV420: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SV1736 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SV2076 @ SV1736 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SV1142 @ SV2076 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5013]) ).
thf(5611,plain,
! [SV2077: $i,SV1737: $i,SV1143: $i,SV421: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SV1737 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SV2077 @ SV1737 @ SV421 ) @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SV1143 @ SV2077 @ SV421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5612,plain,
! [SV2078: $i,SV1738: $i,SV1144: $i,SV422: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1738 @ SV422 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SV2078 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SV1738 @ SV2078 @ SV422 ) @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5613,plain,
! [SV2079: $i,SV1739: $i,SV1145: $i,SV423: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV1739 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV2079 @ SV423 ) @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SV2079 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5016]) ).
thf(5614,plain,
! [SV2080: $i,SV1740: $i,SV1146: $i,SV424: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV1740 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV2080 @ SV424 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SV2080 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(5615,plain,
! [SV2081: $i,SV1741: $i,SV1147: $i,SV425: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1147 @ SV1741 @ SV425 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1741 @ SV425 ) @ SV425 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5018]) ).
thf(5616,plain,
! [SV1742: $i,SV1148: $i,SV426: $i] :
( ( ( class_Orderings_Opreorder @ SV426 )
= $false )
| ( ( ( c_lessequals @ SV1148 @ SV1742 @ SV426 )
| ~ ( c_HOL_Oord__class_Oless @ SV1148 @ SV1742 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5019]) ).
thf(5617,plain,
! [SV1743: $i,SV1149: $i,SV427: $i] :
( ( ( class_Orderings_Oorder @ SV427 )
= $false )
| ( ( ( c_lessequals @ SV1149 @ SV1743 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1149 @ SV1743 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5020]) ).
thf(5618,plain,
! [SV2185: $i,SV2082: $i,SV1744: $i,SV1150: $i,SV428: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5021]) ).
thf(5619,plain,
! [SV1745: $i,SV1151: $i,SV429: $i] :
( ( ( class_Orderings_Opreorder @ SV429 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1745 @ SV429 )
| ( c_lessequals @ SV1745 @ SV1151 @ SV429 )
| ~ ( c_lessequals @ SV1151 @ SV1745 @ SV429 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5620,plain,
! [SV2083: $i,SV1746: $i,SV1152: $i,SV430: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV430 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV2083 @ SV1746 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2083 @ SV1152 @ SV430 ) @ SV1746 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(5621,plain,
! [SV1747: $i,SV1153: $i,SV431: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV431 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1153 @ SV1747 @ SV431 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1153 @ SV431 ) @ SV1747 @ SV431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5024]) ).
thf(5622,plain,
! [SV2084: $i,SV1748: $i,SV1154: $i,SV432: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV432 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SV2084 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SV2084 @ SV432 ) @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5623,plain,
! [SV2085: $i,SV1749: $i,SV1155: $i,SV433: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV433 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1155 @ SV433 ) @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5624,plain,
! [SV1750: $i,SV1156: $i,SV434: $i] :
( ( ( class_Orderings_Oorder @ SV434 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1750 @ SV434 )
| ( SV1750 = SV1156 )
| ~ ( c_lessequals @ SV1156 @ SV1750 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5027]) ).
thf(5625,plain,
! [SV1751: $i,SV1157: $i,SV435: $i] :
( ( ( class_Orderings_Oorder @ SV435 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1751 @ SV435 )
| ~ ( c_lessequals @ SV1157 @ SV1751 @ SV435 )
| ( SV1751 = SV1157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5626,plain,
! [SV1752: $i,SV1158: $i,SV436: $i] :
( ( ( class_Orderings_Olinorder @ SV436 )
= $false )
| ( ( ( SV1158 = SV1752 )
| ( c_HOL_Oord__class_Oless @ SV1158 @ SV1752 @ SV436 )
| ~ ( c_lessequals @ SV1158 @ SV1752 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5627,plain,
! [SV1753: $i,SV1159: $i,SV437: $i] :
( ( ( class_Orderings_Olinorder @ SV437 )
= $false )
| ( ( ( SV1159 = SV1753 )
| ~ ( c_lessequals @ SV1159 @ SV1753 @ SV437 )
| ( c_HOL_Oord__class_Oless @ SV1159 @ SV1753 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5628,plain,
! [SV1754: $i,SV1160: $i,SV438: $i] :
( ( ( class_Orderings_Oorder @ SV438 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV1754 @ SV438 )
| ~ ( c_lessequals @ SV1160 @ SV1754 @ SV438 )
| ( SV1160 = SV1754 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5629,plain,
! [SV1755: $i,SV1161: $i,SV439: $i] :
( ( ( class_Orderings_Oorder @ SV439 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1755 @ SV439 )
| ( SV1161 = SV1755 )
| ~ ( c_lessequals @ SV1161 @ SV1755 @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5630,plain,
! [SV1756: $i,SV1162: $i,SV440: $i] :
( ( ( class_Orderings_Oorder @ SV440 )
= $false )
| ( ( ( SV1162 = SV1756 )
| ( c_HOL_Oord__class_Oless @ SV1162 @ SV1756 @ SV440 )
| ~ ( c_lessequals @ SV1162 @ SV1756 @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5631,plain,
! [SV1757: $i,SV1163: $i,SV441: $i] :
( ( ( class_Orderings_Oorder @ SV441 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV1757 @ SV441 )
| ( SV1163 = SV1757 )
| ~ ( c_lessequals @ SV1163 @ SV1757 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5034]) ).
thf(5632,plain,
! [SV2086: $i,SV1758: $i,SV1164: $i,SV442: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV442 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5035]) ).
thf(5633,plain,
! [SV1759: $i,SV1165: $i,SV443: $i] :
( ( ( class_Orderings_Opreorder @ SV443 )
= $false )
| ( ( ~ ( c_lessequals @ SV1165 @ SV1759 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ SV1759 @ SV1165 @ SV443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5634,plain,
! [SV1760: $i,SV1166: $i,SV444: $i] :
( ( ( class_Orderings_Olinorder @ SV444 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1166 @ SV1760 @ SV444 )
| ( c_lessequals @ SV1760 @ SV1166 @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5635,plain,
! [SV445: $i,SV1167: $i] :
( ( ( ~ ( c_lessequals @ SV1167 @ SV1167 @ SV445 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1167 @ SV1167 @ SV445 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5038]) ).
thf(5636,plain,
! [SV446: $i,SV1168: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1168 @ SV1168 @ SV446 )
= $true )
| ( ( c_lessequals @ SV1168 @ SV1168 @ SV446 )
= $true )
| ( ( class_Orderings_Olinorder @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5039]) ).
thf(5637,plain,
! [SV1761: $i,SV1169: $i,SV447: $i] :
( ( ( class_Orderings_Olinorder @ SV447 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1169 @ SV1761 @ SV447 )
| ~ ( c_lessequals @ SV1761 @ SV1169 @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5638,plain,
! [SV1762: $i,SV1170: $i,SV448: $i] :
( ( ( class_Orderings_Olinorder @ SV448 )
= $false )
| ( ( ( c_lessequals @ SV1170 @ SV1762 @ SV448 )
| ( c_HOL_Oord__class_Oless @ SV1762 @ SV1170 @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5041]) ).
thf(5639,plain,
! [SV1763: $i,SV1171: $i,SV449: $i] :
( ( ( class_Orderings_Olinorder @ SV449 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1171 @ SV1763 @ SV449 )
| ( c_lessequals @ SV1763 @ SV1171 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5042]) ).
thf(5640,plain,
! [SV1764: $i,SV1172: $i,SV450: $i] :
( ( ( class_Orderings_Olinorder @ SV450 )
= $false )
| ( ( ~ ( c_lessequals @ SV1172 @ SV1764 @ SV450 )
| ~ ( c_HOL_Oord__class_Oless @ SV1764 @ SV1172 @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5641,plain,
! [SV2087: $i,SV1765: $i,SV1173: $i,SV451: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV451 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SV1765 @ SV451 ) @ SV2087 @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2087 @ SV451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5044]) ).
thf(5642,plain,
! [SV2088: $i,SV1766: $i,SV1174: $i,SV452: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV452 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SV1766 @ SV452 ) @ SV2088 @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2088 @ SV452 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5643,plain,
! [SV2089: $i,SV1767: $i,SV1175: $i,SV453: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV453 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV1767 @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SV2089 @ SV1767 @ SV453 ) @ SV453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5046]) ).
thf(5644,plain,
! [SV2090: $i,SV1768: $i,SV1176: $i,SV454: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV454 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1176 @ SV1768 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2090 @ SV454 ) @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5645,plain,
! [SV2091: $i,SV1769: $i,SV1177: $i,SV455: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV455 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SV1769 @ SV455 ) @ SV2091 @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1769 @ SV2091 @ SV455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(5646,plain,
! [SV2092: $i,SV1770: $i,SV1178: $i,SV456: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV456 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SV1770 @ SV456 ) @ SV2092 @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV2092 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5049]) ).
thf(5647,plain,
! [SV2093: $i,SV1771: $i,SV1179: $i,SV457: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV457 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SV1771 @ SV2093 @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1771 @ SV457 ) @ SV457 ) @ SV2093 @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5050]) ).
thf(5648,plain,
! [SV2186: $i,SV2094: $i,SV1772: $i,SV1180: $i,SV458: $i] :
( ( ! [SY4854: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2186 @ SV1772 @ SV458 ) @ SY4854 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2186 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SY4854 @ SV458 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5051]) ).
thf(5649,plain,
! [SV2187: $i,SV2095: $i,SV1773: $i,SV1181: $i,SV459: $i] :
( ( ! [SY4855: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SV2187 @ SV459 ) @ SY4855 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SV2187 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SV2187 @ SV459 ) @ SY4855 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5052]) ).
thf(5650,plain,
! [SV2188: $i,SV2096: $i,SV1774: $i,SV1182: $i,SV460: $i] :
( ( ! [SY4856: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2188 @ SV1774 @ SV460 ) @ SY4856 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV2188 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SY4856 @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5053]) ).
thf(5651,plain,
! [SV2189: $i,SV2097: $i,SV1775: $i,SV1183: $i,SV461: $i] :
( ( ! [SY4857: $i] :
( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ SY4857 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SY4857 @ SV461 ) @ SV461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5054]) ).
thf(5652,plain,
! [SV2098: $i,SV1776: $i,SV1184: $i,SV462: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV462 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5055]) ).
thf(5653,plain,
! [SV2099: $i,SV1777: $i,SV1185: $i,SV463: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV463 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV1185 @ SV1777 @ SV463 ) @ SV2099 @ SV463 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV1185 @ SV2099 @ SV463 ) @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2099 @ SV463 ) @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(5654,plain,
! [SV2100: $i,SV1778: $i,SV1186: $i,SV464: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV464 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ SV1778 @ SV464 ) @ SV2100 @ SV464 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ ( c_Divides_Odiv__class_Omod @ SV1778 @ SV2100 @ SV464 ) @ SV464 ) @ SV2100 @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5057]) ).
thf(5655,plain,
! [SV2101: $i,SV1779: $i,SV1187: $i,SV465: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV465 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1187 @ SV1779 @ SV465 ) @ SV2101 @ SV465 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1187 @ SV2101 @ SV465 ) @ SV1779 @ SV465 ) @ SV2101 @ SV465 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5656,plain,
! [SV2102: $i,SV1780: $i,SV1188: $i,SV466: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV466 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1188 @ SV1780 @ SV466 ) @ SV2102 @ SV466 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1188 @ SV2102 @ SV466 ) @ ( c_Divides_Odiv__class_Omod @ SV1780 @ SV2102 @ SV466 ) @ SV466 ) @ SV2102 @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(5657,plain,
! [SV1781: $i,SV1189: $i,SV467: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV467 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1189 @ SV1781 @ SV467 ) @ SV467 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1781 @ SV1189 @ SV467 ) @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5060]) ).
thf(5658,plain,
! [SV2103: $i,SV1782: $i,SV1190: $i,SV468: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5061]) ).
thf(5659,plain,
! [SV1195: $i,SV473: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV473 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1195 @ SV1195 @ SV473 )
= ( c_HOL_Ozero__class_Ozero @ SV473 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(5660,plain,
! [SV1783: $i,SV1196: $i,SV474: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV474 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1783 @ SV474 ) @ SV1783 @ SV474 )
= SV1196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5067]) ).
thf(5661,plain,
! [SV2104: $i,SV1784: $i,SV1197: $i,SV475: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV475 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1197 @ ( c_HOL_Ominus__class_Ominus @ SV1784 @ SV2104 @ SV475 ) @ SV475 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV1784 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV2104 @ SV475 ) @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(5662,plain,
! [SV2105: $i,SV1785: $i,SV1198: $i,SV476: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV476 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1198 @ ( c_HOL_Ominus__class_Ominus @ SV1785 @ SV2105 @ SV476 ) @ SV476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV1785 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV2105 @ SV476 ) @ SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(5663,plain,
! [SV2106: $i,SV1786: $i,SV1199: $i,SV477: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV477 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1199 @ SV1786 @ SV477 ) @ SV2106 @ SV477 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1199 @ SV2106 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1786 @ SV2106 @ SV477 ) @ SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5070]) ).
thf(5664,plain,
! [SV2107: $i,SV1787: $i,SV1200: $i,SV478: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV478 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1200 @ SV1787 @ SV478 ) @ SV2107 @ SV478 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1200 @ SV2107 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1787 @ SV2107 @ SV478 ) @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5071]) ).
thf(5665,plain,
! [SV2190: $i,SV2108: $i,SV1788: $i,SV1201: $i,SV479: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV479 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1201 @ SV1788 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SV2108 @ SV2190 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ SV2108 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SV1788 @ SV2190 @ SV479 ) @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5072]) ).
thf(5666,plain,
! [SV1789: $i,SV1202: $i,SV480: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV480 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1789 @ SV480 ) @ SV1789 @ SV480 )
= SV1202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5073]) ).
thf(5667,plain,
! [SV481: $i,SV1790: $i,SV1203: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1203 @ SV1790 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1203 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV481 @ SV1790 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5074]) ).
thf(5668,plain,
! [SV1204: $i,SV482: $i,SV1791: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1791 @ SV482 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1791 @ SV1204 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV482 @ SV1204 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5075]) ).
thf(5669,plain,
! [SV1205: $i,SV1792: $i,SV483: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV483 @ SV1792 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV483 @ SV1205 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1792 @ SV1205 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5076]) ).
thf(5670,plain,
! [SV2109: $i,SV1793: $i,SV1210: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1793 @ SV2109 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1210 @ SV2109 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1793 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(5671,plain,
! [SV1211: $i,SV490: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV490 @ ( c_Suc @ SV1211 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV490 @ SV1211 @ tc_nat )
= $true )
| ( ( SV490 = SV1211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5080]) ).
thf(5672,plain,
! [SV491: $i,SV1212: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1212 @ ( c_Suc @ SV491 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1212 @ SV491 @ tc_nat )
= $true )
| ( ( SV491 = SV1212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5673,plain,
! [SV507: $i,SV1225: $i,SV1794: $i] :
( ( ( c_lessequals @ SV1794 @ SV1225 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV507 @ ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1794 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV507 @ SV1794 @ tc_nat ) @ SV1225 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5094]) ).
thf(5674,plain,
! [SV1795: $i,SV1226: $i,SV509: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV509 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1226 @ SV509 ) @ SV1795 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV1226 @ SV1795 @ SV509 ) @ SV509 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SV1795 @ SV509 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5095]) ).
thf(5675,plain,
! [SV1796: $i,SV1229: $i,SV512: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV512 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1229 @ SV1796 @ SV512 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1229 @ SV512 ) @ SV1796 @ SV512 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5098]) ).
thf(5676,plain,
! [SV1797: $i,SV1230: $i,SV513: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV513 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1230 @ SV513 ) @ SV1797 @ SV513 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1230 @ SV1797 @ SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5677,plain,
! [SV1798: $i,SV1231: $i,SV514: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV514 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ SV1798 @ SV514 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ ( c_HOL_Oabs__class_Oabs @ SV1798 @ SV514 ) @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5100]) ).
thf(5678,plain,
! [SV1799: $i,SV1232: $i,SV515: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV515 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ ( c_HOL_Oabs__class_Oabs @ SV1799 @ SV515 ) @ SV515 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ SV1799 @ SV515 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5101]) ).
thf(5679,plain,
! [SV1800: $i,SV1234: $i,SV517: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5680,plain,
! [SV522: $i,SV1239: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV522 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1239 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SV1239 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(5681,plain,
! [SV1801: $i,SV1240: $i,SV523: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV523 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1240 @ SV1801 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1240 @ SV1801 @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5105]) ).
thf(5682,plain,
! [SV1802: $i,SV1241: $i,SV524: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV524 )
= $false )
| ( ( ( c_lessequals @ SV1241 @ SV1802 @ SV524 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1241 @ SV1802 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5106]) ).
thf(5683,plain,
! [SV525: $i,SV1242: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1242 @ SV525 ) @ ( c_HOL_Ozero__class_Ozero @ SV525 ) @ SV525 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5684,plain,
! [SV1246: $i,SV529: $i,SV1803: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1803 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV1246 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SV1246 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(5685,plain,
! [SV1247: $i,SV530: $i,SV1804: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV1247 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1804 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SV1247 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5112]) ).
thf(5686,plain,
! [SV531: $i,SV1805: $i,SV1248: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1248 @ SV1805 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1248 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1805 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5113]) ).
thf(5687,plain,
! [SV1806: $i,SV532: $i,SV1249: $i] :
( ( ( c_lessequals @ SV1249 @ SV532 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV532 @ SV1249 @ tc_nat ) @ SV1806 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV532 @ SV1806 @ tc_nat ) @ SV1249 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5688,plain,
! [SV533: $i,SV1250: $i,SV1807: $i] :
( ( ( c_lessequals @ SV1807 @ SV1250 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV533 @ ( c_HOL_Ominus__class_Ominus @ SV1250 @ SV1807 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV533 @ SV1250 @ tc_nat ) @ SV1807 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5689,plain,
! [SV534: $i,SV1251: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1251 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV534 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1251 @ SV534 ) @ SV534 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV534 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(5690,plain,
! [SV1252: $i,SV535: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1252 @ SV535 ) @ SV535 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1252 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV535 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5691,plain,
! [SV2191: $i,SV2110: $i,SV1808: $i,SV1253: $i,SV536: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5118]) ).
thf(5692,plain,
! [SV2192: $i,SV2111: $i,SV1809: $i,SV1254: $i,SV537: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5119]) ).
thf(5693,plain,
! [SV1810: $i,SV1255: $i,SV538: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV538 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SV1810 @ SV538 ) @ SV538 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1255 @ SV538 ) @ ( c_HOL_Oabs__class_Oabs @ SV1810 @ SV538 ) @ SV538 ) @ SV538 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5694,plain,
! [SV541: $i,SV1258: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1258 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV541 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV541 @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1258 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5123]) ).
thf(5695,plain,
! [SV542: $i,SV1259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1259 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV542 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV542 @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV542 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5124]) ).
thf(5696,plain,
! [SV2112: $i,SV1811: $i,SV1260: $i,SV544: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV544 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SV1811 @ SV544 ) @ SV2112 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SV2112 @ SV544 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV2112 @ SV1811 @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5697,plain,
! [SV545: $i,SV1261: $i] :
( ( ( c_lessequals @ SV1261 @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1261 @ SV1261 @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5698,plain,
! [SV546: $i,SV1262: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1262 @ SV1262 @ SV546 ) @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
= $true )
| ( ( ~ ( c_lessequals @ SV1262 @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV546 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5699,plain,
! [SV1263: $i,SV547: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 ) )
= $true )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1263 @ SV547 )
= SV1263 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV547 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5700,plain,
! [SV548: $i,SV1264: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1264 @ SV548 )
= SV1264 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1264 @ ( c_HOL_Ozero__class_Ozero @ SV548 ) @ SV548 )
= $true )
| ( ( class_Ring__and__Field_Oabs__if @ SV548 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5701,plain,
! [SV2193: $i,SV2113: $i,SV1812: $i,SV1265: $i,SV549: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5130]) ).
thf(5702,plain,
! [SV1813: $i,SV1266: $i,SV550: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV550 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SV1813 @ SV550 ) @ SV550 ) @ SV550 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ SV1266 @ SV550 ) @ ( c_HOL_Oabs__class_Oabs @ SV1813 @ SV550 ) @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5131]) ).
thf(5703,plain,
! [SV553: $i,SV1268: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1268 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV553 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV553 @ SV1268 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5133]) ).
thf(5704,plain,
! [SV557: $i,SV1271: $i,SV1814: $i] :
( ( ( ~ ( c_lessequals @ SV1814 @ SV1271 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV557 @ SV1814 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV557 @ SV1271 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5705,plain,
! [SV2194: $i,SV2114: $i,SV1815: $i,SV1272: $i,SV559: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
| ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SV2194 @ SV2114 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5137]) ).
thf(5706,plain,
! [SV2115: $i,SV1816: $i,SV1273: $i,SV560: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV560 ) )
= $true )
| ( ( ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV2115 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV1273 @ SV2115 @ SV560 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5138]) ).
thf(5707,plain,
! [SV1817: $i,SV1274: $i,SV561: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5139]) ).
thf(5708,plain,
! [SV2116: $i,SV1818: $i,SV1275: $i,SV562: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV562 ) )
= $true )
| ( ( ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
| ~ ( c_lessequals @ SV1275 @ SV2116 @ SV562 )
| ~ ( c_lessequals @ SV2116 @ SV1818 @ SV562 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5709,plain,
! [SV563: $i,SV1276: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Otimes__class_Otimes @ SV1276 @ SV563 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV1276 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV563 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5141]) ).
thf(5710,plain,
! [SV1819: $i,SV1278: $i,SV565: $i] :
( ( ( class_Divides_Osemiring__div @ SV565 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1278 @ SV1819 @ SV565 ) @ SV1278 @ SV565 )
= ( c_HOL_Ozero__class_Ozero @ SV565 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5142]) ).
thf(5711,plain,
! [SV1820: $i,SV1279: $i,SV566: $i] :
( ( ( class_Divides_Osemiring__div @ SV566 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1279 @ SV1820 @ SV566 ) @ SV1820 @ SV566 )
= ( c_HOL_Ozero__class_Ozero @ SV566 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5143]) ).
thf(5712,plain,
! [SV1280: $i,SV567: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV567 @ ( c_Suc @ SV1280 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1280 @ SV567 @ tc_nat ) )
= $true )
| ( ( SV567 = SV1280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5713,plain,
! [SV2117: $i,SV1821: $i,SV1281: $i,SV569: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV569 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV2117 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1281 @ SV569 ) @ SV569 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5145]) ).
thf(5714,plain,
! [SV2118: $i,SV1822: $i,SV1282: $i,SV570: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV570 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1822 @ SV2118 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV2118 @ SV570 ) @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5146]) ).
thf(5715,plain,
! [SV2119: $i,SV1823: $i,SV1283: $i,SV571: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV571 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SV2119 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV2119 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SV2119 @ SV571 ) @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5147]) ).
thf(5716,plain,
! [SV2120: $i,SV1824: $i,SV1284: $i,SV572: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ SV572 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1824 @ SV2120 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SV2120 @ SV1284 @ SV572 ) @ SV572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(5717,plain,
! [SV2121: $i,SV1825: $i,SV1285: $i,SV573: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV573 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV1825 @ SV573 ) @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV2121 @ SV573 ) @ SV573 )
= ( c_HOL_Otimes__class_Otimes @ SV1285 @ ( c_Divides_Odiv__class_Omod @ SV1825 @ SV2121 @ SV573 ) @ SV573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(5718,plain,
! [SV2122: $i,SV1826: $i,SV1286: $i,SV574: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV574 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV1826 @ SV574 ) @ ( c_HOL_Otimes__class_Otimes @ SV2122 @ SV1826 @ SV574 ) @ SV574 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1286 @ SV2122 @ SV574 ) @ SV1826 @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5719,plain,
! [SV575: $i,SV1287: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1287 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV575 @ SV1287 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV575 @ SV1287 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5720,plain,
! [SV1827: $i,SV1291: $i,SV579: $i] :
( ( ( class_Orderings_Olinorder @ SV579 )
= $false )
| ( ( ( c_lessequals @ SV1291 @ SV1827 @ SV579 )
| ( c_lessequals @ SV1827 @ SV1291 @ SV579 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5721,plain,
! [SV580: $i,SV1292: $i,SV1828: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV1292 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV580 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1828 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5156]) ).
thf(5722,plain,
! [SV581: $i,SV1829: $i,SV1293: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SV1829 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1829 @ SV1293 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1829 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5157]) ).
thf(5723,plain,
! [SV1295: $i,SV583: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV583 @ ( c_Suc @ SV1295 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV583 @ SV1295 @ tc_nat )
= $true )
| ( ( SV583 = SV1295 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5158]) ).
thf(5724,plain,
! [SV587: $i,SV1297: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1297 @ ( c_Suc @ SV587 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV587 @ SV1297 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5159]) ).
thf(5725,plain,
! [SV1298: $i,SV589: $i] :
( ( ( c_lessequals @ SV589 @ SV1298 @ tc_nat )
= $false )
| ( ( SV589 = SV1298 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV589 @ SV1298 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5160]) ).
thf(5726,plain,
! [SV1299: $i,SV590: $i] :
( ( ( c_lessequals @ SV590 @ SV1299 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV590 @ SV1299 @ tc_nat )
= $true )
| ( ( SV590 = SV1299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5161]) ).
thf(5727,plain,
! [SV1300: $i,SV591: $i] :
( ( ( c_lessequals @ SV591 @ SV1300 @ tc_nat )
= $false )
| ( ( SV591 = SV1300 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV591 @ SV1300 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5162]) ).
thf(5728,plain,
! [SV1303: $i,SV594: $i,SV1830: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1830 @ SV594 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1830 @ SV1303 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV594 @ SV1303 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5729,plain,
! [SV1304: $i,SV1831: $i,SV595: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV595 @ SV1831 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1304 @ SV1831 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV595 @ SV1304 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5730,plain,
! [SV598: $i,SV1305: $i,SV1832: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1832 @ SV1305 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV598 @ SV1832 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SV1305 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5167]) ).
thf(5731,plain,
! [SV1833: $i,SV1307: $i,SV600: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV600 @ SV1307 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV600 @ ( c_HOL_Oplus__class_Oplus @ SV1307 @ SV1833 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5169]) ).
thf(5732,plain,
! [SV1308: $i,SV1834: $i,SV601: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV601 @ SV1834 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV601 @ ( c_HOL_Oplus__class_Oplus @ SV1308 @ SV1834 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5733,plain,
! [SV1309: $i,SV1835: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV602 @ SV1835 @ tc_nat ) @ SV1309 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV602 @ SV1309 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5734,plain,
! [SV1836: $i,SV1310: $i,SV603: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV603 @ SV1310 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV603 @ ( c_HOL_Oplus__class_Oplus @ SV1310 @ SV1836 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5172]) ).
thf(5735,plain,
! [SV1311: $i,SV1837: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ SV1837 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Oplus__class_Oplus @ SV1311 @ SV1837 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5173]) ).
thf(5736,plain,
! [SV1312: $i,SV605: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV605 @ SV1312 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV605 )
= SV1312 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV605 ) @ SV1312 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5174]) ).
thf(5737,plain,
! [SV1838: $i,SV1316: $i,SV609: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV609 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1316 @ SV1838 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1316 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1838 @ SV609 ) @ SV609 ) )
| ~ ( c_lessequals @ SV1838 @ SV1316 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5178]) ).
thf(5738,plain,
! [SV1324: $i,SV1843: $i,SV618: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1843 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1324 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SV1324 @ SV1843 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(5739,plain,
! [SV1325: $i,SV1844: $i,SV621: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1844 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ SV1844 @ SV621 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5740,plain,
! [SV1326: $i,SV1845: $i,SV622: $i] :
( ( ( ~ ( c_lessequals @ SV622 @ SV1845 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1326 @ SV1845 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5741,plain,
! [SV1327: $i,SV1846: $i,SV623: $i] :
( ( ( c_lessequals @ SV623 @ SV1846 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV623 @ SV1327 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1846 @ SV1327 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5742,plain,
! [SV624: $i,SV1328: $i,SV1847: $i] :
( ( ( c_lessequals @ SV1847 @ SV1328 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1328 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV624 @ SV1847 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5743,plain,
! [SV628: $i,SV1331: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1331 @ tc_nat )
= $false )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ SV628 @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV628 @ SV1331 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5187]) ).
thf(5744,plain,
! [SV632: $i,SV1851: $i,SV1335: $i] :
( ( ( ~ ( c_lessequals @ SV1335 @ SV1851 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1335 @ SV632 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1335 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1851 @ SV1335 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1851 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5188]) ).
thf(5745,plain,
! [SV1852: $i,SV1338: $i,SV635: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV635 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1338 @ SV1852 @ SV635 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1338 @ SV1852 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5189]) ).
thf(5746,plain,
! [SV1853: $i,SV1339: $i,SV636: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV636 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1339 @ SV1853 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
| ~ ( c_HOL_Oord__class_Oless @ SV1339 @ SV1853 @ SV636 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5190]) ).
thf(5747,plain,
! [SV2123: $i,SV1854: $i,SV1340: $i,SV637: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV637 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SV1854 @ SV637 ) @ SV2123 @ SV637 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV2123 @ SV1340 @ SV637 ) @ SV637 ) @ SV1854 @ SV637 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5748,plain,
! [SV1855: $i,SV1341: $i,SV638: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV638 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1341 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1855 @ SV638 ) @ SV638 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV1855 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5749,plain,
! [SV1856: $i,SV1342: $i,SV639: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1342 @ SV1856 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1342 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1856 @ SV639 ) @ SV639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5193]) ).
thf(5750,plain,
! [SV1344: $i,SV641: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV641 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1344 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV1344 @ tc_nat ) @ SV641 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5751,plain,
! [SV642: $i,SV1345: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1345 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV642 @ SV1345 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SV1345 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5752,plain,
! [SV643: $i,SV1346: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV1346 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1346 @ SV643 @ tc_nat )
| ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV1346 @ SV643 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5196]) ).
thf(5753,plain,
! [SV1347: $i,SV1857: $i,SV644: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV644 @ ( c_HOL_Ominus__class_Ominus @ SV1857 @ SV1347 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV644 @ SV1347 @ tc_nat ) @ SV1857 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5197]) ).
thf(5754,plain,
! [SV1348: $i,SV1858: $i,SV645: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV645 @ SV1858 @ tc_nat ) @ SV1348 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV645 @ ( c_HOL_Ominus__class_Ominus @ SV1348 @ SV1858 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5198]) ).
thf(5755,plain,
! [SV1349: $i,SV1859: $i,SV646: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1859 @ SV1349 @ tc_nat )
| ~ ( c_lessequals @ SV1859 @ SV646 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5199]) ).
thf(5756,plain,
! [SV1350: $i,SV1860: $i,SV647: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1350 @ SV1860 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(5757,plain,
! [SV1861: $i,SV652: $i,SV1355: $i] :
( ( ( ~ ( c_lessequals @ SV1355 @ SV652 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV652 @ SV1861 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SV1355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1861 @ SV1355 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5203]) ).
thf(5758,plain,
! [SV1862: $i,SV1357: $i,SV654: $i] :
( ( ( class_Orderings_Oorder @ SV654 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV1862 @ SV654 )
| ~ ( c_HOL_Oord__class_Oless @ SV1862 @ SV1357 @ SV654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5759,plain,
! [SV1863: $i,SV1358: $i,SV655: $i] :
( ( ( class_Orderings_Olinorder @ SV655 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1358 @ SV1863 @ SV655 )
| ~ ( c_HOL_Oord__class_Oless @ SV1863 @ SV1358 @ SV655 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5206]) ).
thf(5760,plain,
! [SV1864: $i,SV1359: $i,SV656: $i] :
( ( ( class_Orderings_Opreorder @ SV656 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1359 @ SV1864 @ SV656 )
| ~ ( c_HOL_Oord__class_Oless @ SV1864 @ SV1359 @ SV656 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5207]) ).
thf(5761,plain,
! [SV1865: $i,SV1360: $i,SV657: $i] :
( ( ( class_Orderings_Opreorder @ SV657 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1360 @ SV1865 @ SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SV1865 @ SV1360 @ SV657 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5208]) ).
thf(5762,plain,
! [SV658: $i,SV1361: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1361 @ SV1361 @ SV658 )
= $false )
| ( ( class_Orderings_Opreorder @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5209]) ).
thf(5763,plain,
! [SV659: $i,SV1362: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1362 @ SV1362 @ SV659 )
= $false )
| ( ( class_Orderings_Olinorder @ SV659 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5210]) ).
thf(5764,plain,
! [SV662: $i,SV1363: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1363 @ SV1363 @ SV662 )
= $false )
| ( ( class_Orderings_Oorder @ SV662 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5211]) ).
thf(5765,plain,
! [SV1364: $i,SV1866: $i,SV663: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV663 @ SV1866 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV663 @ SV1364 @ tc_nat ) @ SV1866 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5212]) ).
thf(5766,plain,
! [SV1365: $i,SV664: $i,SV1867: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV664 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV1365 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1867 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5213]) ).
thf(5767,plain,
! [SV1868: $i,SV1366: $i,SV665: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV665 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1366 @ SV1868 @ SV665 )
| ( c_HOL_Oord__class_Oless @ SV1868 @ SV1366 @ SV665 )
| ( SV1868 = SV1366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5214]) ).
thf(5768,plain,
! [SV1869: $i,SV1367: $i,SV666: $i] :
( ( ( class_Orderings_Olinorder @ SV666 )
= $false )
| ( ( ( SV1367 = SV1869 )
| ( c_HOL_Oord__class_Oless @ SV1869 @ SV1367 @ SV666 )
| ( c_HOL_Oord__class_Oless @ SV1367 @ SV1869 @ SV666 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5215]) ).
thf(5769,plain,
! [SV1870: $i,SV1368: $i,SV667: $i] :
( ( ( class_Orderings_Olinorder @ SV667 )
= $false )
| ( ( ( SV1368 = SV1870 )
| ( c_HOL_Oord__class_Oless @ SV1368 @ SV1870 @ SV667 )
| ( c_HOL_Oord__class_Oless @ SV1870 @ SV1368 @ SV667 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5216]) ).
thf(5770,plain,
! [SV1871: $i,SV1369: $i,SV668: $i] :
( ( ( class_Orderings_Olinorder @ SV668 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1369 @ SV1871 @ SV668 )
| ( SV1871 = SV1369 )
| ( c_HOL_Oord__class_Oless @ SV1871 @ SV1369 @ SV668 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5771,plain,
! [SV1872: $i,SV1372: $i,SV671: $i] :
( ( ( class_Orderings_Olinorder @ SV671 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1372 @ SV1872 @ SV671 )
| ( c_HOL_Oord__class_Oless @ SV1872 @ SV1372 @ SV671 )
| ( SV1872 = SV1372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5220]) ).
thf(5772,plain,
! [SV2124: $i,SV1873: $i,SV1373: $i,SV672: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV672 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(5773,plain,
! [SV2125: $i,SV1874: $i,SV1374: $i,SV673: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV673 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5222]) ).
thf(5774,plain,
! [SV1876: $i,SV1376: $i,SV675: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1376 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV675 @ SV1876 @ tc_nat ) )
= $false )
| ( ( SV1376 = SV1876 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5775,plain,
! [SV1377: $i,SV677: $i] :
( ( ( SV677
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV677
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV677 @ SV1377 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5224]) ).
thf(5776,plain,
! [SV679: $i,SV1378: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1378 @ SV679 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1378 = SV679 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV679 @ SV1378 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5226]) ).
thf(5777,plain,
! [SV1877: $i,SV1379: $i,SV680: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1379 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ ( c_Suc @ SV680 ) @ SV1877 @ tc_nat ) )
= $false )
| ( ( SV1379 = SV1877 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5227]) ).
thf(5778,plain,
! [SV1878: $i,SV1380: $i,SV681: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV681 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1380 @ SV1380 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SV1878 @ SV1878 @ SV681 ) @ SV681 )
!= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
| ( SV1380
= ( c_HOL_Ozero__class_Ozero @ SV681 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5228]) ).
thf(5779,plain,
! [SV2126: $i,SV1879: $i,SV1381: $i,SV682: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV682 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV682 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
| ( SV1879 = SV2126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5229]) ).
thf(5780,plain,
! [SV2195: $i,SV2127: $i,SV1880: $i,SV1382: $i,SV683: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV1880 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV2127 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2195 @ tc_nat ) @ tc_nat ) )
| ( ( c_Divides_Odiv__class_Omod @ SV683 @ SV1382 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SV2127 @ SV1382 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5230]) ).
thf(5781,plain,
! [SV1881: $i,SV1383: $i,SV684: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV684 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1383 @ SV684 )
!= ( c_HOL_Oabs__class_Oabs @ SV1881 @ SV684 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1383 @ SV1881 @ SV684 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5231]) ).
thf(5782,plain,
! [SV2128: $i,SV1882: $i,SV1384: $i,SV685: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV1882 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV2128 @ SV685 ) )
| ( SV1882 = SV2128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5232]) ).
thf(5783,plain,
! [SV1883: $i,SV1385: $i,SV686: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
!= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5233]) ).
thf(5784,plain,
! [SV1386: $i,SV687: $i] :
( ( ( SV687
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV687
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV687 @ SV1386 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5785,plain,
! [SV2196: $i,SV2129: $i,SV1884: $i,SV1387: $i,SV688: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
| ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SV2196 @ SV2129 @ SV688 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5235]) ).
thf(5786,plain,
! [SV1885: $i,SV1388: $i,SV689: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SV1885 @ SV689 )
!= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1885
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5236]) ).
thf(5787,plain,
! [SV2197: $i,SV2130: $i,SV1886: $i,SV1389: $i,SV690: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
| ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5788,plain,
! [SV1887: $i,SV1390: $i,SV691: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV691 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1390 @ SV1887 @ SV691 )
!= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
| ( SV1390 = SV1887 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5238]) ).
thf(5789,plain,
! [SV1888: $i,SV1391: $i,SV693: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SV1888 @ SV693 )
!= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1888
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5239]) ).
thf(5790,plain,
! [SV695: $i,SV1392: $i] :
( ( ( SV1392
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1392
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1392 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5240]) ).
thf(5791,plain,
! [SV2131: $i,SV1889: $i,SV1393: $i,SV696: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV696 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SV1889 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SV2131 @ SV2131 @ SV696 ) )
| ( SV1393 = SV1889 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5241]) ).
thf(5792,plain,
! [SV697: $i,SV1394: $i] :
( ( ( SV1394
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV697
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1394 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5242]) ).
thf(5793,plain,
! [SV1890: $i,SV1395: $i,SV698: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV698 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV698 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SV1395 = SV1890 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5243]) ).
thf(5794,plain,
! [SV2198: $i,SV2132: $i,SV1891: $i,SV1397: $i,SV702: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV702 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2132 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2198 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SV2132 @ SV702 )
= SV2198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5245]) ).
thf(5795,plain,
! [SV1398: $i,SV703: $i] :
( ( ( SV703
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1398
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV703 @ SV1398 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5246]) ).
thf(5796,plain,
! [SV1892: $i,SV1399: $i,SV704: $i] :
( ( ( class_Divides_Osemiring__div @ SV704 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1399 @ SV1892 @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1892 @ SV1399 @ SV704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5797,plain,
! [SV1893: $i,SV1400: $i,SV705: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
!= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5248]) ).
thf(5798,plain,
! [SV706: $i,SV1401: $i] :
( ( ( SV1401
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV706
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV706 @ SV1401 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(5799,plain,
! [SV2133: $i,SV1894: $i,SV1402: $i,SV708: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV708 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SV1894 @ SV2133 @ SV708 ) )
| ( SV1894 = SV2133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5800,plain,
! [SV2199: $i,SV2134: $i,SV1895: $i,SV1403: $i,SV709: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV709 )
| ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5251]) ).
thf(5801,plain,
! [SV2200: $i,SV2135: $i,SV1896: $i,SV1404: $i,SV710: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5252]) ).
thf(5802,plain,
! [SV711: $i,SV1405: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1405 @ SV1405 @ SV711 )
!= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
= $true )
| ( ( SV1405
= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV711 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5253]) ).
thf(5803,plain,
! [SV2136: $i,SV1897: $i,SV1406: $i,SV712: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1897 @ SV2136 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1897 @ SV1406 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV712 @ SV2136 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(5804,plain,
! [SV2201: $i,SV2137: $i,SV1898: $i,SV1407: $i,SV713: $i] :
( ( ! [SY4858: $i] :
( ~ ( class_Divides_Oring__div @ SV713 )
| ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SY4858 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY4858 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5255]) ).
thf(5805,plain,
! [SV714: $i,SV1408: $i] :
( ( ( SV1408
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV714
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV714 @ SV1408 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5256]) ).
thf(5806,plain,
! [SV1899: $i,SV1409: $i,SV715: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV715 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1409 @ SV715 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1899 @ SV715 ) )
| ( SV1409 = SV1899 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5807,plain,
! [SV1900: $i,SV1414: $i,SV720: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV720 @ SV1414 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV1900 @ SV1414 @ tc_nat ) )
= $false )
| ( ( ( SV1414
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV720 = SV1900 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5808,plain,
! [SV1901: $i,SV1415: $i,SV721: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1415 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV721 @ SV1901 @ tc_nat ) )
= $false )
| ( ( SV1415 = SV1901 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5263]) ).
thf(5809,plain,
! [SV1902: $i,SV1416: $i,SV722: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV722 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV722 )
| ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
| ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5264]) ).
thf(5810,plain,
! [SV723: $i,SV1417: $i] :
( ( ( SV1417
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1417
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV723 @ SV1417 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5265]) ).
thf(5811,plain,
! [SV1903: $i,SV1418: $i,SV724: $i] :
( ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
= $false )
| ( ( ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SV1903 @ SV724 )
!= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1903
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5266]) ).
thf(5812,plain,
! [SV2138: $i,SV1904: $i,SV1419: $i,SV725: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SV1904 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SV2138 @ SV1904 @ SV725 ) )
| ( SV1419 = SV2138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(5813,plain,
! [SV1905: $i,SV1421: $i,SV727: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1421 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1905 @ tc_nat ) )
= $false )
| ( ( ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1421 = SV1905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5269]) ).
thf(5814,plain,
! [SV1906: $i,SV1422: $i,SV728: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV728 @ SV1422 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1906 @ SV1422 @ tc_nat ) )
= $false )
| ( ( SV728 = SV1906 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5270]) ).
thf(5815,plain,
! [SV2202: $i,SV2139: $i,SV1907: $i,SV1423: $i,SV729: $i] :
( ( ! [SY4859: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV729 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2202 @ SV1907 @ SV729 ) @ SY4859 @ SV729 ) )
| ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2202 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SY4859 @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5271]) ).
thf(5816,plain,
! [SV730: $i,SV1424: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1424 @ SV730 )
!= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $true )
| ( ( SV1424
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV730 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5272]) ).
thf(5817,plain,
! [SV1908: $i,SV1426: $i,SV732: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV732 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1426 @ SV1908 @ SV732 )
!= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
| ( SV1426 = SV1908 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5818,plain,
! [SV1427: $i,SV733: $i] :
( ( ( SV733
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1427
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV733 @ SV1427 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5275]) ).
thf(5819,plain,
! [SV1909: $i,SV1428: $i,SV734: $i] :
( ( ( class_Orderings_Olinorder @ SV734 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omin @ SV1428 @ SV1909 @ SV734 )
!= SV1428 )
| ( c_lessequals @ SV1428 @ SV1909 @ SV734 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5820,plain,
! [SV1910: $i,SV1429: $i,SV735: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1429 @ SV1910 @ tc_nat )
| ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
| ( SV735 = SV1910 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5277]) ).
thf(5821,plain,
! [SV2203: $i,SV2140: $i,SV1911: $i,SV1432: $i,SV738: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2140 @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
| ~ ( c_lessequals @ SV738 @ SV2140 @ tc_nat )
| ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2140 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5280]) ).
thf(5822,plain,
! [SV2204: $i,SV2141: $i,SV1912: $i,SV1434: $i,SV741: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5282]) ).
thf(5823,plain,
! [SV2205: $i,SV2142: $i,SV1913: $i,SV1435: $i,SV742: $i] :
( ( ! [SY4860: $i] :
( ~ ( class_Divides_Osemiring__div @ SV742 )
| ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SY4860 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY4860 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5283]) ).
thf(5824,plain,
! [SV2206: $i,SV2143: $i,SV1914: $i,SV1436: $i,SV743: $i] :
( ( ! [SY4861: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV743 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2206 @ SV1914 @ SV743 ) @ SY4861 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SV2206 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SY4861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5284]) ).
thf(5825,plain,
! [SV1915: $i,SV1437: $i,SV744: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1437 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1915 @ tc_nat ) )
= $false )
| ( ( ( SV1437 = SV1915 )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5285]) ).
thf(5826,plain,
! [SV1916: $i,SV1438: $i,SV745: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1438 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1916 @ tc_nat ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat )
| ( SV1438 = SV1916 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5827,plain,
! [SV2144: $i,SV1917: $i,SV1439: $i,SV746: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV1439 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV2144 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV2144 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV1439 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( SV1439 = SV2144 )
| ( SV746 = SV1917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5287]) ).
thf(5828,plain,
! [SV1918: $i,SV1440: $i,SV747: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1440 @ SV1440 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SV1918 @ SV1918 @ SV747 ) @ SV747 )
!= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
| ( SV1918
= ( c_HOL_Ozero__class_Ozero @ SV747 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5829,plain,
! [SV2207: $i,SV2145: $i,SV1919: $i,SV1441: $i,SV748: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV748 )
| ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5289]) ).
thf(5830,plain,
! [SV2208: $i,SV2146: $i,SV1920: $i,SV1442: $i,SV749: $i] :
( ( ! [SY4862: $i] :
( ~ ( class_Divides_Osemiring__div @ SV749 )
| ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SY4862 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SY4862 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5290]) ).
thf(5831,plain,
! [SV2147: $i,SV1921: $i,SV1443: $i,SV750: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV1921 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV2147 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( SV1921 = SV2147 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5291]) ).
thf(5832,plain,
! [SV2148: $i,SV1922: $i,SV1444: $i,SV751: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV1922 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV2148 @ SV751 ) )
| ( SV1922 = SV2148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5292]) ).
thf(5833,plain,
! [SV2149: $i,SV1923: $i,SV1445: $i,SV752: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV1445 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV2149 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV2149 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV1445 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( SV1445 = SV2149 )
| ( SV752 = SV1923 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(5834,plain,
! [SV2209: $i,SV2150: $i,SV1924: $i,SV1446: $i,SV753: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2150 @ SV1446 @ tc_nat ) @ SV2209 @ tc_nat ) )
| ~ ( c_lessequals @ SV2150 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV2150 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SV2209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5294]) ).
thf(5835,plain,
! [SV2210: $i,SV2151: $i,SV1925: $i,SV1447: $i,SV754: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV754 )
| ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
| ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5295]) ).
thf(5836,plain,
! [SV1448: $i,SV755: $i,SV1: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(5837,plain,
! [SV1449: $i,SV756: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5297]) ).
thf(5838,plain,
! [SV1450: $i,SV5: $i,SV759: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV759 @ SV759 @ SV5 ) @ ( c_HOL_Otimes__class_Otimes @ SV1450 @ SV1450 @ SV5 ) @ SV5 ) @ ( c_HOL_Ozero__class_Ozero @ SV5 ) @ SV5 )
= $false )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5839,plain,
! [SV6: $i,SV1451: $i,SV760: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(5840,plain,
! [SV7: $i,SV1452: $i,SV761: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(5841,plain,
! [SV2152: $i,SV1926: $i,SV1455: $i,SV764: $i,SV11: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1455 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1926 @ SV2152 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1926 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1455 @ SV2152 @ SV11 ) @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5303]) ).
thf(5842,plain,
! [SV2153: $i,SV1927: $i,SV1456: $i,SV765: $i,SV12: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV765 @ SV1456 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SV2153 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SV765 @ ( c_HOL_Otimes__class_Otimes @ SV1456 @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SV2153 @ SV12 ) @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5304]) ).
thf(5843,plain,
! [SV2154: $i,SV1928: $i,SV1457: $i,SV766: $i,SV13: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV1928 @ SV2154 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SV1928 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ SV2154 @ SV13 ) @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5305]) ).
thf(5844,plain,
! [SV14: $i,SV767: $i] :
( ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV767 @ SV14 ) @ ( c_HOL_Ozero__class_Ozero @ SV14 ) @ SV14 )
= $false )
| ( ( SV767
= ( c_HOL_Ozero__class_Ozero @ SV14 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5845,plain,
! [SV1929: $i,SV1458: $i,SV769: $i,SV16: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
= $false )
| ( ( ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SV1458 @ ( c_HOL_Oabs__class_Oabs @ SV1929 @ SV16 ) @ SV16 ) @ SV16 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SV1929 @ SV16 ) @ SV1458 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5846,plain,
! [SV18: $i,SV1459: $i,SV770: $i] :
( ( ( SV770 = SV1459 )
= $true )
| ( ( ~ ( c_lessequals @ SV1459 @ SV770 @ SV18 )
| ~ ( c_lessequals @ SV770 @ SV1459 @ SV18 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(5847,plain,
! [SV19: $i,SV1460: $i,SV771: $i] :
( ( ( SV771 = SV1460 )
= $true )
| ( ( ~ ( c_lessequals @ SV1460 @ SV771 @ SV19 )
| ~ ( c_lessequals @ SV771 @ SV1460 @ SV19 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5309]) ).
thf(5848,plain,
! [SV20: $i,SV772: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV772 @ SV20 @ tc_nat )
= $false )
| ( ( SV772 = SV20 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV20 @ SV772 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5310]) ).
thf(5849,plain,
! [SV21: $i,SV773: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV773 @ SV21 @ tc_nat )
= $false )
| ( ( SV773 = SV21 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV21 @ SV773 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5311]) ).
thf(5850,plain,
! [SV22: $i,SV774: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV774 @ SV22 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV22 @ SV774 @ tc_nat )
= $false )
| ( ( SV22 = SV774 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5851,plain,
! [SV775: $i,SV23: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV23 @ SV775 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV775 @ SV23 @ tc_nat )
= $false )
| ( ( SV23 = SV775 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5313]) ).
thf(5852,plain,
! [SV24: $i,SV776: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV776 @ SV24 @ tc_nat )
= $false )
| ( ( SV776 = SV24 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV24 @ SV776 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5853,plain,
! [SV777: $i,SV25: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV25 @ SV777 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV777 @ SV25 @ tc_nat )
= $false )
| ( ( SV25 = SV777 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5854,plain,
! [SV778: $i,SV26: $i] :
( ( ( c_lessequals @ SV26 @ SV778 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV778 @ SV26 @ tc_nat )
= $false )
| ( ( SV26 = SV778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5316]) ).
thf(5855,plain,
! [SV779: $i,SV27: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV27 @ SV779 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV779 @ SV27 @ tc_nat )
= $false )
| ( ( SV27 = SV779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5856,plain,
! [SV28: $i,SV1461: $i,SV780: $i] :
( ( ( SV780 = SV1461 )
= $true )
| ( ( ~ ( c_lessequals @ SV780 @ SV1461 @ SV28 )
| ~ ( c_lessequals @ SV1461 @ SV780 @ SV28 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5318]) ).
thf(5857,plain,
! [SV781: $i,SV29: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV29 ) @ SV781 @ SV29 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ SV781 @ SV29 )
= SV781 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5319]) ).
thf(5858,plain,
! [SV30: $i,SV782: $i,SV1462: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1462 @ SV782 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV1462 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV782 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5320]) ).
thf(5859,plain,
! [SV31: $i,SV783: $i,SV1463: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5321]) ).
thf(5860,plain,
! [SV32: $i,SV784: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV784 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV32 @ SV784 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV32 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5322]) ).
thf(5861,plain,
! [SV1930: $i,SV1464: $i,SV786: $i,SV35: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5323]) ).
thf(5862,plain,
! [SV1931: $i,SV1471: $i,SV794: $i,SV43: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1471 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1931 @ SV43 ) @ SV43 )
| ~ ( c_lessequals @ SV1471 @ SV1931 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5330]) ).
thf(5863,plain,
! [SV1932: $i,SV1472: $i,SV795: $i,SV44: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SV1472 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SV1932 @ SV1472 @ SV44 ) @ SV44 )
| ~ ( c_lessequals @ SV795 @ SV1932 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5864,plain,
! [SV1933: $i,SV1473: $i,SV796: $i,SV45: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
= $false )
| ( ( ( c_lessequals @ SV796 @ SV1473 @ SV45 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV1473 @ SV45 ) @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5332]) ).
thf(5865,plain,
! [SV1934: $i,SV1474: $i,SV797: $i,SV46: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1474 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1934 @ SV46 ) @ SV46 )
| ~ ( c_lessequals @ SV1474 @ SV1934 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5333]) ).
thf(5866,plain,
! [SV1935: $i,SV1475: $i,SV798: $i,SV47: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
= $false )
| ( ( ( c_lessequals @ SV798 @ SV1475 @ SV47 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SV1935 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SV1475 @ SV1935 @ SV47 ) @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5334]) ).
thf(5867,plain,
! [SV1936: $i,SV1476: $i,SV799: $i,SV48: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SV1476 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SV1936 @ SV1476 @ SV48 ) @ SV48 )
| ~ ( c_lessequals @ SV799 @ SV1936 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5335]) ).
thf(5868,plain,
! [SV50: $i,SV1478: $i,SV801: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5337]) ).
thf(5869,plain,
! [SV51: $i,SV1479: $i,SV802: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5338]) ).
thf(5870,plain,
! [SV52: $i,SV1480: $i,SV803: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 )
| ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5339]) ).
thf(5871,plain,
! [SV53: $i,SV1481: $i,SV804: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
| ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5340]) ).
thf(5872,plain,
! [SV1485: $i,SV58: $i,SV808: $i] :
( ( ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SV1485 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5344]) ).
thf(5873,plain,
! [SV1486: $i,SV809: $i,SV59: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV1486 @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5345]) ).
thf(5874,plain,
! [SV1487: $i,SV60: $i,SV810: $i] :
( ( ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
= $true )
| ( ( ( c_lessequals @ SV1487 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV1487 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5346]) ).
thf(5875,plain,
! [SV1488: $i,SV811: $i,SV61: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
= $true )
| ( ( ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1488 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5347]) ).
thf(5876,plain,
! [SV62: $i,SV1489: $i,SV812: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 )
| ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5348]) ).
thf(5877,plain,
! [SV63: $i,SV1490: $i,SV813: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5349]) ).
thf(5878,plain,
! [SV64: $i,SV1491: $i,SV814: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5350]) ).
thf(5879,plain,
! [SV1492: $i,SV815: $i,SV65: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(5880,plain,
! [SV1493: $i,SV816: $i,SV66: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
| ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5352]) ).
thf(5881,plain,
! [SV817: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV67 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV817 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV67 @ SV817 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(5882,plain,
! [SV68: $i,SV818: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV818 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV818 @ SV818 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5883,plain,
! [SV69: $i,SV819: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV819 @ SV819 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5355]) ).
thf(5884,plain,
! [SV70: $i,SV820: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV820 @ SV820 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5356]) ).
thf(5885,plain,
! [SV71: $i,SV821: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV821 @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV821 @ SV821 @ SV71 ) @ ( c_HOL_Ozero__class_Ozero @ SV71 ) @ SV71 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5357]) ).
thf(5886,plain,
! [SV1937: $i,SV1494: $i,SV823: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ SV823 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV823 @ SV1494 @ tc_nat ) @ SV1937 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV76 @ SV1494 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV823 @ SV76 @ tc_nat ) @ SV1494 @ tc_nat ) @ SV1937 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5887,plain,
! [SV1938: $i,SV1495: $i,SV824: $i,SV77: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5359]) ).
thf(5888,plain,
! [SV1939: $i,SV1496: $i,SV825: $i,SV78: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5360]) ).
thf(5889,plain,
! [SV1940: $i,SV1497: $i,SV826: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring @ SV79 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5890,plain,
! [SV1941: $i,SV1498: $i,SV827: $i,SV80: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring @ SV80 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(5891,plain,
! [SV1942: $i,SV1500: $i,SV831: $i,SV84: $i] :
( ( ( class_Divides_Osemiring__div @ SV84 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5892,plain,
! [SV1943: $i,SV1501: $i,SV832: $i,SV85: $i] :
( ( ( class_Divides_Osemiring__div @ SV85 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5365]) ).
thf(5893,plain,
! [SV1944: $i,SV1502: $i,SV833: $i,SV86: $i] :
( ( ( class_Divides_Osemiring__div @ SV86 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5894,plain,
! [SV1945: $i,SV1503: $i,SV834: $i,SV87: $i] :
( ( ( class_Divides_Osemiring__div @ SV87 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(5895,plain,
! [SV2211: $i,SV2155: $i,SV1946: $i,SV1504: $i,SV835: $i,SV88: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2155 @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2155 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5368]) ).
thf(5896,plain,
! [SV2212: $i,SV2156: $i,SV1947: $i,SV1505: $i,SV836: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 )
| ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SV2156 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5369]) ).
thf(5897,plain,
! [SV2213: $i,SV2157: $i,SV1948: $i,SV1506: $i,SV837: $i,SV90: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2157 @ SV1506 @ SV90 ) @ SV2213 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SV2157 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SV2213 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5370]) ).
thf(5898,plain,
! [SV2214: $i,SV2158: $i,SV1949: $i,SV1507: $i,SV838: $i,SV91: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ SV2214 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SV2214 @ SV91 ) @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5371]) ).
thf(5899,plain,
! [SV1950: $i,SV1508: $i,SV843: $i,SV96: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5900,plain,
! [SV1951: $i,SV1509: $i,SV844: $i,SV97: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
| ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5373]) ).
thf(5901,plain,
! [SV845: $i,SV1510: $i,SV98: $i] :
( ( ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SV1510 @ SV845 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV845 @ SV1510 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SV845 @ tc_nat ) @ SV1510 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5902,plain,
! [SV846: $i,SV1511: $i,SV99: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SV1511 @ tc_nat ) @ SV846 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1511 @ SV846 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1511 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5903,plain,
! [SV2159: $i,SV1952: $i,SV1512: $i,SV850: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1952 @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1952 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV103 @ SV1952 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5376]) ).
thf(5904,plain,
! [SV2160: $i,SV1953: $i,SV1513: $i,SV851: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SV1953 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1513 @ SV851 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5377]) ).
thf(5905,plain,
! [SV2161: $i,SV1954: $i,SV1514: $i,SV852: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1954 @ SV852 @ tc_nat ) @ SV2161 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SV1954 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SV2161 @ tc_nat )
| ~ ( c_lessequals @ SV1954 @ SV105 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5378]) ).
thf(5906,plain,
! [SV2162: $i,SV1955: $i,SV1515: $i,SV853: $i,SV106: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ SV2162 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SV2162 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5379]) ).
thf(5907,plain,
! [SV2163: $i,SV1956: $i,SV1516: $i,SV854: $i,SV107: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV107 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV1516 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1956 @ SV854 @ SV107 ) @ SV1516 @ SV107 ) @ SV2163 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1956 @ SV1516 @ SV107 ) @ SV2163 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5380]) ).
thf(5908,plain,
! [SV109: $i,SV1518: $i,SV856: $i] :
( ( ( c_lessequals @ SV856 @ SV1518 @ SV109 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV856 @ SV109 ) @ SV1518 @ SV109 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5382]) ).
thf(5909,plain,
! [SV2164: $i,SV1957: $i,SV1519: $i,SV857: $i,SV110: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5383]) ).
thf(5910,plain,
! [SV1958: $i,SV1520: $i,SV858: $i,SV111: $i] :
( ( ( class_Divides_Osemiring__div @ SV111 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV858 @ SV1520 @ SV111 ) @ SV1958 @ SV111 ) @ SV1520 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV858 @ SV1958 @ SV111 ) @ SV1520 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5384]) ).
thf(5911,plain,
! [SV1959: $i,SV1521: $i,SV859: $i,SV112: $i] :
( ( ( class_Orderings_Olinorder @ SV112 )
= $false )
| ( ( ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1959 @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5385]) ).
thf(5912,plain,
! [SV1960: $i,SV1522: $i,SV860: $i,SV113: $i] :
( ( ( class_Orderings_Olinorder @ SV113 )
= $false )
| ( ( ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1960 @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5386]) ).
thf(5913,plain,
! [SV1961: $i,SV1523: $i,SV861: $i,SV114: $i] :
( ( ( class_Orderings_Olinorder @ SV114 )
= $false )
| ( ( ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1961 @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5387]) ).
thf(5914,plain,
! [SV1530: $i,SV121: $i,SV868: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV868 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1530 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ( c_lessequals @ SV868 @ SV1530 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5394]) ).
thf(5915,plain,
! [SV122: $i,SV1531: $i,SV869: $i] :
( ( ( c_lessequals @ SV869 @ SV1531 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV869 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1531 @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5395]) ).
thf(5916,plain,
! [SV1962: $i,SV1532: $i,SV871: $i,SV124: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV124 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV124 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5917,plain,
! [SV1963: $i,SV1533: $i,SV872: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV125 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV125 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5918,plain,
! [SV2165: $i,SV1964: $i,SV1538: $i,SV877: $i,SV131: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV131 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5400]) ).
thf(5919,plain,
! [SV135: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5401]) ).
thf(5920,plain,
! [SV1965: $i,SV1543: $i,SV884: $i,SV140: $i] :
( ( ( class_Divides_Osemiring__div @ SV140 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV884 @ SV1543 @ SV140 ) @ SV1965 @ SV140 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV884 @ SV1965 @ SV140 ) @ ( c_Divides_Odiv__class_Omod @ SV1543 @ SV1965 @ SV140 ) @ SV140 ) @ SV1965 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5404]) ).
thf(5921,plain,
! [SV1966: $i,SV1544: $i,SV885: $i,SV142: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV142 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV885 @ ( c_HOL_Oplus__class_Oplus @ SV1544 @ SV1966 @ SV142 ) @ SV142 )
= ( c_HOL_Oplus__class_Oplus @ SV1544 @ ( c_HOL_Oplus__class_Oplus @ SV885 @ SV1966 @ SV142 ) @ SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5405]) ).
thf(5922,plain,
! [SV1967: $i,SV1545: $i,SV886: $i,SV143: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV143 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV886 @ SV1545 @ SV143 ) @ SV1967 @ SV143 )
= ( c_HOL_Oplus__class_Oplus @ SV886 @ ( c_HOL_Oplus__class_Oplus @ SV1545 @ SV1967 @ SV143 ) @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5923,plain,
! [SV1968: $i,SV1546: $i,SV887: $i,SV144: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SV1546 @ SV1968 @ SV144 ) @ SV144 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SV1968 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5924,plain,
! [SV1969: $i,SV1547: $i,SV888: $i,SV145: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SV1547 @ SV1969 @ SV145 ) @ SV145 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SV1547 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5408]) ).
thf(5925,plain,
! [SV1970: $i,SV1548: $i,SV889: $i,SV146: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SV1548 @ SV146 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SV1970 @ SV146 ) @ SV1548 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5926,plain,
! [SV1971: $i,SV1549: $i,SV890: $i,SV147: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SV1549 @ SV147 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1971 @ SV890 @ SV147 ) @ SV1549 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5410]) ).
thf(5927,plain,
! [SV1972: $i,SV1550: $i,SV891: $i,SV148: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5928,plain,
! [SV894: $i,SV1551: $i,SV151: $i,SV1973: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1973 @ SV151 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1551 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SV1551 @ tc_nat ) @ tc_nat ) @ SV1973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SV1551 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5412]) ).
thf(5929,plain,
! [SV1974: $i,SV1552: $i,SV895: $i,SV152: $i] :
( ( ( class_Ring__and__Field_Omult__mono1 @ SV152 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
| ~ ( c_lessequals @ SV1552 @ SV1974 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5413]) ).
thf(5930,plain,
! [SV1975: $i,SV1553: $i,SV896: $i,SV153: $i] :
( ( ( class_Ring__and__Field_Omult__mono @ SV153 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
| ~ ( c_lessequals @ SV1553 @ SV1975 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(5931,plain,
! [SV1976: $i,SV1554: $i,SV897: $i,SV154: $i] :
( ( ( class_Ring__and__Field_Omult__mono @ SV154 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
| ~ ( c_lessequals @ SV897 @ SV1976 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5932,plain,
! [SV1977: $i,SV1555: $i,SV898: $i,SV155: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV155 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV1977 @ SV1555 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5416]) ).
thf(5933,plain,
! [SV1978: $i,SV1556: $i,SV899: $i,SV156: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV156 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1978 @ SV899 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5934,plain,
! [SV2166: $i,SV1979: $i,SV1557: $i,SV901: $i,SV158: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5418]) ).
thf(5935,plain,
! [SV1980: $i,SV1563: $i,SV907: $i,SV164: $i] :
( ( ( class_Divides_Osemiring__div @ SV164 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ ( c_Divides_Odiv__class_Omod @ SV1563 @ SV1980 @ SV164 ) @ SV164 ) @ SV1980 @ SV164 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV907 @ SV1563 @ SV164 ) @ SV1980 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5424]) ).
thf(5936,plain,
! [SV1981: $i,SV1564: $i,SV908: $i,SV165: $i] :
( ( ( class_Divides_Osemiring__div @ SV165 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV908 @ SV1564 @ SV165 ) @ SV1981 @ SV165 ) @ SV1564 @ SV165 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV908 @ SV1981 @ SV165 ) @ SV1564 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5425]) ).
thf(5937,plain,
! [SV2215: $i,SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV166 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5426]) ).
thf(5938,plain,
! [SV2216: $i,SV2168: $i,SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ~ ( class_Ring__and__Field_Odvd @ SV167 )
| ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5427]) ).
thf(5939,plain,
! [SV1567: $i,SV911: $i,SV168: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5428]) ).
thf(5940,plain,
! [SV1568: $i,SV912: $i,SV169: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
= $true )
| ( ( ~ ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
| ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5429]) ).
thf(5941,plain,
! [SV1569: $i,SV913: $i,SV170: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
= $true )
| ( ( ~ ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
| ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5942,plain,
! [SV1570: $i,SV915: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5431]) ).
thf(5943,plain,
! [SV1571: $i,SV916: $i,SV173: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
= $true )
| ( ( ~ ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
| ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5432]) ).
thf(5944,plain,
! [SV1572: $i,SV917: $i,SV174: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5433]) ).
thf(5945,plain,
! [SV1984: $i,SV1574: $i,SV919: $i,SV176: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__mult @ SV176 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV919 @ SV1574 @ SV176 ) @ SV1984 @ SV176 )
= ( c_HOL_Otimes__class_Otimes @ SV919 @ ( c_HOL_Otimes__class_Otimes @ SV1574 @ SV1984 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5435]) ).
thf(5946,plain,
! [SV1985: $i,SV1575: $i,SV920: $i,SV177: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV177 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1575 @ SV177 ) @ SV1985 @ SV177 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV920 @ SV1985 @ SV177 ) @ SV1575 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5947,plain,
! [SV1986: $i,SV1576: $i,SV921: $i,SV178: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV178 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV921 @ SV1576 @ SV178 ) @ SV1986 @ SV178 )
= ( c_HOL_Otimes__class_Otimes @ SV921 @ ( c_HOL_Otimes__class_Otimes @ SV1576 @ SV1986 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5948,plain,
! [SV1987: $i,SV1577: $i,SV922: $i,SV179: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV179 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV922 @ ( c_HOL_Otimes__class_Otimes @ SV1577 @ SV1987 @ SV179 ) @ SV179 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV922 @ SV1577 @ SV179 ) @ SV1987 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5949,plain,
! [SV1988: $i,SV1578: $i,SV923: $i,SV180: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV180 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV923 @ ( c_HOL_Otimes__class_Otimes @ SV1578 @ SV1988 @ SV180 ) @ SV180 )
= ( c_HOL_Otimes__class_Otimes @ SV1578 @ ( c_HOL_Otimes__class_Otimes @ SV923 @ SV1988 @ SV180 ) @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5439]) ).
thf(5950,plain,
! [SV1989: $i,SV1580: $i,SV925: $i,SV182: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV182 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV925 @ ( c_HOL_Otimes__class_Otimes @ SV1580 @ SV1989 @ SV182 ) @ SV182 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV925 @ SV1580 @ SV182 ) @ SV1989 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5440]) ).
thf(5951,plain,
! [SV1990: $i,SV1581: $i,SV926: $i,SV183: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV183 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV926 @ SV1581 @ SV183 ) @ SV1990 @ SV183 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV926 @ SV1990 @ SV183 ) @ ( c_HOL_Otimes__class_Otimes @ SV1581 @ SV1990 @ SV183 ) @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5441]) ).
thf(5952,plain,
! [SV1991: $i,SV1582: $i,SV927: $i,SV184: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV184 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV927 @ ( c_HOL_Oplus__class_Oplus @ SV1582 @ SV1991 @ SV184 ) @ SV184 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1582 @ SV184 ) @ ( c_HOL_Otimes__class_Otimes @ SV927 @ SV1991 @ SV184 ) @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5953,plain,
! [SV1992: $i,SV1583: $i,SV928: $i,SV185: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV185 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV928 @ ( c_HOL_Oplus__class_Oplus @ SV1583 @ SV1992 @ SV185 ) @ SV185 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1583 @ SV185 ) @ ( c_HOL_Otimes__class_Otimes @ SV928 @ SV1992 @ SV185 ) @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5954,plain,
! [SV1993: $i,SV1584: $i,SV929: $i,SV186: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV186 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV929 @ SV1584 @ SV186 ) @ SV1993 @ SV186 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV929 @ SV1993 @ SV186 ) @ ( c_HOL_Otimes__class_Otimes @ SV1584 @ SV1993 @ SV186 ) @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5444]) ).
thf(5955,plain,
! [SV1994: $i,SV1585: $i,SV930: $i,SV187: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV187 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV930 @ SV1585 @ SV187 ) @ SV1994 @ SV187 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV930 @ SV1994 @ SV187 ) @ ( c_HOL_Otimes__class_Otimes @ SV1585 @ SV1994 @ SV187 ) @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5956,plain,
! [SV1995: $i,SV1588: $i,SV933: $i,SV190: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV190 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV933 @ ( c_HOL_Oplus__class_Oplus @ SV1588 @ SV1995 @ SV190 ) @ SV190 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1588 @ SV190 ) @ ( c_HOL_Otimes__class_Otimes @ SV933 @ SV1995 @ SV190 ) @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5957,plain,
! [SV1996: $i,SV1589: $i,SV934: $i,SV191: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring @ SV191 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV934 @ SV1589 @ SV191 ) @ SV1996 @ SV191 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV934 @ SV1996 @ SV191 ) @ ( c_HOL_Otimes__class_Otimes @ SV1589 @ SV1996 @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5958,plain,
! [SV937: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV937 @ SV194 ) @ SV194 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV937 @ SV194 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5959,plain,
! [SV938: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV938 @ SV195 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV938 @ SV195 ) @ SV195 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5449]) ).
thf(5960,plain,
! [SV1590: $i,SV196: $i,SV939: $i] :
( ( ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SV1590 @ SV196 ) @ SV196 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5450]) ).
thf(5961,plain,
! [SV1591: $i,SV197: $i,SV940: $i] :
( ( ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1591 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SV1591 @ SV940 @ SV197 ) @ SV197 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5451]) ).
thf(5962,plain,
! [SV1592: $i,SV198: $i,SV941: $i] :
( ( ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1592 @ SV198 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SV1592 @ SV198 ) @ SV198 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5452]) ).
thf(5963,plain,
! [SV1593: $i,SV199: $i,SV942: $i] :
( ( ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SV1593 @ SV942 @ SV199 ) @ SV199 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5453]) ).
thf(5964,plain,
! [SV1997: $i,SV1594: $i,SV943: $i,SV201: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV201 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV943 @ SV1594 @ SV201 ) @ ( c_HOL_Otimes__class_Otimes @ SV1997 @ SV1594 @ SV201 ) @ SV201 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV943 @ SV1997 @ SV201 ) @ SV1594 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5454]) ).
thf(5965,plain,
! [SV1595: $i,SV202: $i,SV1998: $i,SV944: $i] :
( ( ( ~ ( c_lessequals @ SV944 @ SV1998 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV202 @ SV1595 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1595 @ SV1998 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5455]) ).
thf(5966,plain,
! [SV2169: $i,SV1999: $i,SV1596: $i,SV945: $i,SV204: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV204 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5456]) ).
thf(5967,plain,
! [SV2170: $i,SV2000: $i,SV1597: $i,SV946: $i,SV205: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__semiring @ SV205 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5457]) ).
thf(5968,plain,
! [SV948: $i,SV207: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV207 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV948 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV207 @ SV948 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5458]) ).
thf(5969,plain,
! [SV949: $i,SV208: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV208 @ SV949 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV949 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV208 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5459]) ).
thf(5970,plain,
! [SV209: $i,SV950: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV950 @ SV209 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV950 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV209 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5971,plain,
! [SV951: $i,SV210: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV210 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV951 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV210 @ SV951 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5972,plain,
! [SV953: $i,SV212: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV212 @ SV953 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV953 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV212 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(5973,plain,
! [SV213: $i,SV954: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV954 @ SV213 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV954 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV213 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5463]) ).
thf(5974,plain,
! [SV955: $i,SV214: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV214 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV955 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV214 @ SV955 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(5975,plain,
! [SV215: $i,SV956: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV956 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV215 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV215 @ SV956 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5465]) ).
thf(5976,plain,
! [SV217: $i,SV958: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV958 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV217 @ tc_nat ) @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV217 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5466]) ).
thf(5977,plain,
! [SV2001: $i,SV1598: $i,SV960: $i,SV219: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV2001 @ SV219 ) @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5468]) ).
thf(5978,plain,
! [SV2002: $i,SV1599: $i,SV961: $i,SV220: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SV2002 @ SV961 @ SV220 ) @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5469]) ).
thf(5979,plain,
! [SV2003: $i,SV1600: $i,SV962: $i,SV221: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5470]) ).
thf(5980,plain,
! [SV2171: $i,SV2004: $i,SV1601: $i,SV963: $i,SV223: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1601 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV2004 @ SV2171 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV2004 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV1601 @ SV2171 @ SV223 ) @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5471]) ).
thf(5981,plain,
! [SV2005: $i,SV1602: $i,SV965: $i,SV225: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV225 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Orderings_Oord__class_Omin @ SV965 @ SV1602 @ SV225 ) @ SV2005 @ SV225 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Oplus__class_Oplus @ SV965 @ SV2005 @ SV225 ) @ ( c_HOL_Oplus__class_Oplus @ SV1602 @ SV2005 @ SV225 ) @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5472]) ).
thf(5982,plain,
! [SV2006: $i,SV1603: $i,SV967: $i,SV227: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV227 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV967 @ ( c_HOL_Oplus__class_Oplus @ SV1603 @ SV2006 @ SV227 ) @ SV227 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1603 @ SV227 ) @ SV2006 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5983,plain,
! [SV2007: $i,SV1604: $i,SV968: $i,SV228: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV228 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV968 @ ( c_HOL_Oplus__class_Oplus @ SV1604 @ SV2007 @ SV228 ) @ SV228 )
= ( c_HOL_Oplus__class_Oplus @ SV1604 @ ( c_HOL_Oplus__class_Oplus @ SV968 @ SV2007 @ SV228 ) @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5984,plain,
! [SV2008: $i,SV1607: $i,SV971: $i,SV231: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV231 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV971 @ SV1607 @ SV231 ) @ SV2008 @ SV231 )
= ( c_HOL_Oplus__class_Oplus @ SV971 @ ( c_HOL_Oplus__class_Oplus @ SV1607 @ SV2008 @ SV231 ) @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5476]) ).
thf(5985,plain,
! [SV2009: $i,SV1608: $i,SV972: $i,SV232: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV232 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV972 @ ( c_HOL_Oplus__class_Oplus @ SV1608 @ SV2009 @ SV232 ) @ SV232 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV972 @ SV1608 @ SV232 ) @ SV2009 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5477]) ).
thf(5986,plain,
! [SV2010: $i,SV1609: $i,SV973: $i,SV233: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV233 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV1609 @ SV233 ) @ SV2010 @ SV233 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV973 @ SV2010 @ SV233 ) @ SV1609 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5987,plain,
! [SV2011: $i,SV1610: $i,SV974: $i,SV234: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV234 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV974 @ ( c_HOL_Oplus__class_Oplus @ SV1610 @ SV2011 @ SV234 ) @ SV234 )
= ( c_HOL_Oplus__class_Oplus @ SV1610 @ ( c_HOL_Oplus__class_Oplus @ SV974 @ SV2011 @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5479]) ).
thf(5988,plain,
! [SV2012: $i,SV1611: $i,SV975: $i,SV235: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV235 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SV1611 @ SV235 ) @ SV2012 @ SV235 )
= ( c_HOL_Oplus__class_Oplus @ SV975 @ ( c_HOL_Oplus__class_Oplus @ SV1611 @ SV2012 @ SV235 ) @ SV235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5480]) ).
thf(5989,plain,
! [SV2013: $i,SV1619: $i,SV984: $i,SV246: $i] :
( ( ( class_Divides_Osemiring__div @ SV246 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ SV1619 @ SV246 ) @ SV2013 @ SV246 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV984 @ ( c_Divides_Odiv__class_Omod @ SV1619 @ SV2013 @ SV246 ) @ SV246 ) @ SV2013 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5489]) ).
thf(5990,plain,
! [SV2014: $i,SV1620: $i,SV985: $i,SV247: $i] :
( ( ( class_Divides_Osemiring__div @ SV247 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV985 @ SV1620 @ SV247 ) @ SV2014 @ SV247 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV985 @ SV2014 @ SV247 ) @ SV1620 @ SV247 ) @ SV2014 @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5490]) ).
thf(5991,plain,
! [SV2015: $i,SV1621: $i,SV986: $i,SV248: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
| ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5992,plain,
! [SV2016: $i,SV1624: $i,SV990: $i,SV252: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
= $false )
| ( ( ( c_lessequals @ SV990 @ SV1624 @ SV252 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5993,plain,
! [SV2017: $i,SV1625: $i,SV991: $i,SV253: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
= $false )
| ( ( ( c_lessequals @ SV991 @ SV1625 @ SV253 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5994,plain,
! [SV2018: $i,SV1626: $i,SV992: $i,SV254: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
| ~ ( c_lessequals @ SV1626 @ SV2018 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5496]) ).
thf(5995,plain,
! [SV2019: $i,SV1627: $i,SV993: $i,SV255: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
= $false )
| ( ( ( c_lessequals @ SV993 @ SV1627 @ SV255 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5996,plain,
! [SV2020: $i,SV1628: $i,SV994: $i,SV256: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
| ~ ( c_lessequals @ SV2020 @ SV1628 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5997,plain,
! [SV2021: $i,SV1629: $i,SV995: $i,SV257: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
= $false )
| ( ( ( c_lessequals @ SV995 @ SV1629 @ SV257 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5998,plain,
! [SV258: $i,SV1630: $i,SV996: $i] :
( ( ( c_lessequals @ SV996 @ SV1630 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV996 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV1630 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5500]) ).
thf(5999,plain,
! [SV997: $i,SV259: $i,SV1631: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV997 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1631 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV259 @ SV997 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5501]) ).
thf(6000,plain,
! [SV998: $i,SV260: $i,SV1632: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1632 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV998 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV260 @ SV998 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5502]) ).
thf(6001,plain,
! [SV999: $i,SV261: $i,SV1633: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1633 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SV1633 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV999 @ SV1633 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV261 @ SV999 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5503]) ).
thf(6002,plain,
! [SV2172: $i,SV2022: $i,SV1634: $i,SV1000: $i,SV263: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__algebra @ SV263 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1634 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ SV2172 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SV2172 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ SV2172 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SV2172 @ SV263 ) @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5504]) ).
thf(6003,plain,
! [SV2173: $i,SV2023: $i,SV1636: $i,SV1002: $i,SV267: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring @ SV267 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1636 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2023 @ SV1636 @ SV267 ) @ SV2173 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV1002 @ SV2023 @ SV267 ) @ SV1636 @ SV267 ) @ SV2173 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5506]) ).
thf(6004,plain,
! [SV271: $i,SV1638: $i,SV1006: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
| ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5507]) ).
thf(6005,plain,
! [SV1639: $i,SV272: $i,SV1007: $i] :
( ( ( SV1007
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1639 @ SV1639 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SV1007 @ SV1007 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5508]) ).
thf(6006,plain,
! [SV1640: $i,SV273: $i,SV1008: $i] :
( ( ( SV1008
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1008 @ SV1008 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1640 @ SV1640 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5509]) ).
thf(6007,plain,
! [SV1015: $i,SV282: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV1015 @ SV282 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ SV1015 @ SV282 )
= SV1015 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(6008,plain,
! [SV2025: $i,SV1644: $i,SV1016: $i,SV283: $i] :
( ( ( class_Divides_Osemiring__div @ SV283 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ SV1644 @ SV283 ) @ SV2025 @ SV283 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1016 @ ( c_Divides_Odiv__class_Omod @ SV1644 @ SV2025 @ SV283 ) @ SV283 ) @ SV2025 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(6009,plain,
! [SV2026: $i,SV1645: $i,SV1017: $i,SV284: $i] :
( ( ( class_Divides_Osemiring__div @ SV284 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1017 @ SV1645 @ SV284 ) @ SV2026 @ SV284 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1017 @ SV2026 @ SV284 ) @ SV1645 @ SV284 ) @ SV2026 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5516]) ).
thf(6010,plain,
! [SV1648: $i,SV1020: $i,SV287: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV287 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1020 @ SV1020 @ SV287 ) @ ( c_HOL_Otimes__class_Otimes @ SV1648 @ SV1648 @ SV287 ) @ SV287 ) @ SV287 )
= $true )
| ( ( SV1648
= ( c_HOL_Ozero__class_Ozero @ SV287 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5519]) ).
thf(6011,plain,
! [SV1649: $i,SV1021: $i,SV288: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV288 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1021 @ SV1021 @ SV288 ) @ ( c_HOL_Otimes__class_Otimes @ SV1649 @ SV1649 @ SV288 ) @ SV288 ) @ SV288 )
= $true )
| ( ( SV1021
= ( c_HOL_Ozero__class_Ozero @ SV288 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5520]) ).
thf(6012,plain,
! [SV2027: $i,SV1652: $i,SV1026: $i,SV298: $i] :
( ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5522]) ).
thf(6013,plain,
! [SV2028: $i,SV1653: $i,SV1027: $i,SV299: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5523]) ).
thf(6014,plain,
! [SV2029: $i,SV1654: $i,SV1028: $i,SV300: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(6015,plain,
! [SV2030: $i,SV1655: $i,SV1029: $i,SV301: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(6016,plain,
! [SV2031: $i,SV1656: $i,SV1030: $i,SV302: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(6017,plain,
! [SV2032: $i,SV1657: $i,SV1031: $i,SV303: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5527]) ).
thf(6018,plain,
! [SV2033: $i,SV1658: $i,SV1032: $i,SV304: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5528]) ).
thf(6019,plain,
! [SV2034: $i,SV1659: $i,SV1033: $i,SV305: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5529]) ).
thf(6020,plain,
! [SV2035: $i,SV1660: $i,SV1034: $i,SV306: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5530]) ).
thf(6021,plain,
! [SV2036: $i,SV1661: $i,SV1035: $i,SV307: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(6022,plain,
! [SV2037: $i,SV1662: $i,SV1036: $i,SV308: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5532]) ).
thf(6023,plain,
! [SV2038: $i,SV1663: $i,SV1037: $i,SV309: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(6024,plain,
! [SV2039: $i,SV1664: $i,SV1038: $i,SV310: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5534]) ).
thf(6025,plain,
! [SV311: $i,SV1665: $i,SV1039: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV1665 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1039 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1665 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5535]) ).
thf(6026,plain,
! [SV1040: $i,SV312: $i,SV1666: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV1040 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1666 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV312 @ SV1040 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(6027,plain,
! [SV1667: $i,SV313: $i,SV1041: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1041 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1667 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SV1041 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1667 @ SV1041 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5537]) ).
thf(6028,plain,
! [SV1668: $i,SV1042: $i,SV314: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1668 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1042 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1668 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5538]) ).
thf(6029,plain,
! [SV315: $i,SV1669: $i,SV1043: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1043 @ SV1669 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1043 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5539]) ).
thf(6030,plain,
! [SV1044: $i,SV1670: $i,SV316: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV316 @ SV1670 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1044 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SV1044 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1670 @ SV1044 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5540]) ).
thf(6031,plain,
! [SV2040: $i,SV1671: $i,SV1045: $i,SV317: $i] :
( ( ( class_Divides_Osemiring__div @ SV317 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1045 @ ( c_HOL_Otimes__class_Otimes @ SV1671 @ SV2040 @ SV317 ) @ SV317 ) @ SV1671 @ SV317 )
= ( c_Divides_Odiv__class_Omod @ SV1045 @ SV1671 @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(6032,plain,
! [SV2041: $i,SV1672: $i,SV1046: $i,SV318: $i] :
( ( ( class_Divides_Osemiring__div @ SV318 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1046 @ ( c_HOL_Otimes__class_Otimes @ SV1672 @ SV2041 @ SV318 ) @ SV318 ) @ SV2041 @ SV318 )
= ( c_Divides_Odiv__class_Omod @ SV1046 @ SV2041 @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5542]) ).
thf(6033,plain,
! [SV2042: $i,SV1674: $i,SV1048: $i,SV320: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV320 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
| ( SV2042
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SV2042 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SV2042 @ SV320 ) @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5543]) ).
thf(6034,plain,
! [SV2043: $i,SV1675: $i,SV1049: $i,SV321: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV321 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
| ( SV2043
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1675 @ SV321 ) @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5544]) ).
thf(6035,plain,
! [SV1050: $i,SV322: $i,SV1676: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV322 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1676 @ SV1050 @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV1676
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV322 @ SV1050 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5545]) ).
thf(6036,plain,
! [SV323: $i,SV1677: $i,SV1051: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
= $true )
| ( ( ~ ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5546]) ).
thf(6037,plain,
! [SV324: $i,SV1678: $i,SV1052: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 )
| ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(6038,plain,
! [SV325: $i,SV1679: $i,SV1053: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
= $true )
| ( ( ~ ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(6039,plain,
! [SV326: $i,SV1680: $i,SV1054: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 )
| ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5549]) ).
thf(6040,plain,
! [SV327: $i,SV1681: $i,SV1055: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
= $true )
| ( ( ~ ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5550]) ).
thf(6041,plain,
! [SV328: $i,SV1682: $i,SV1056: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 )
| ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(6042,plain,
! [SV329: $i,SV1683: $i,SV1057: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
= $true )
| ( ( ~ ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5552]) ).
thf(6043,plain,
! [SV1684: $i,SV1058: $i,SV331: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5553]) ).
thf(6044,plain,
! [SV1685: $i,SV1059: $i,SV332: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5554]) ).
thf(6045,plain,
! [SV333: $i,SV1686: $i,SV1060: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1060 @ SV1686 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1686 @ SV1060 @ SV333 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5555]) ).
thf(6046,plain,
! [SV1061: $i,SV334: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV334 ) @ SV1061 @ SV334 )
= $false )
| ( ( SV1061
= ( c_HOL_Ozero__class_Ozero @ SV334 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5556]) ).
thf(6047,plain,
! [SV336: $i,SV1062: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1062 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV336 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV336 @ SV1062 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(6048,plain,
! [SV2044: $i,SV1687: $i,SV1064: $i,SV338: $i] :
( ( ( class_Orderings_Olinorder @ SV338 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ ( c_Orderings_Oord__class_Omin @ SV1064 @ SV1687 @ SV338 ) @ SV2044 @ SV338 )
= ( c_Orderings_Oord__class_Omin @ SV1064 @ ( c_Orderings_Oord__class_Omin @ SV1687 @ SV2044 @ SV338 ) @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(6049,plain,
! [SV2045: $i,SV1688: $i,SV1065: $i,SV339: $i] :
( ( ( class_Orderings_Olinorder @ SV339 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1065 @ ( c_Orderings_Oord__class_Omin @ SV1688 @ SV2045 @ SV339 ) @ SV339 )
= ( c_Orderings_Oord__class_Omin @ SV1688 @ ( c_Orderings_Oord__class_Omin @ SV1065 @ SV2045 @ SV339 ) @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5559]) ).
thf(6050,plain,
! [SV1066: $i,SV1689: $i,SV340: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5560]) ).
thf(6051,plain,
! [SV342: $i,SV1690: $i,SV1068: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1068 @ SV1690 @ SV342 )
= SV1068 )
= $true )
| ( ( ~ ( c_lessequals @ SV1068 @ SV1690 @ SV342 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5561]) ).
thf(6052,plain,
! [SV343: $i,SV1691: $i,SV1069: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1069 @ SV1691 @ SV343 )
= SV1691 )
= $true )
| ( ( ~ ( c_lessequals @ SV1691 @ SV1069 @ SV343 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5562]) ).
thf(6053,plain,
! [SV1692: $i,SV1072: $i,SV346: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5563]) ).
thf(6054,plain,
! [SV1693: $i,SV350: $i,SV2046: $i,SV1075: $i] :
( ( ( ~ ( c_lessequals @ SV1075 @ SV2046 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV350 @ SV1693 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1693 @ SV2046 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5564]) ).
thf(6055,plain,
! [SV2174: $i,SV2047: $i,SV1694: $i,SV1076: $i,SV351: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SV1694 @ SV2174 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5565]) ).
thf(6056,plain,
! [SV2175: $i,SV2048: $i,SV1695: $i,SV1077: $i,SV352: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2048 @ SV1077 @ tc_nat ) @ SV2175 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SV2048 @ tc_nat ) @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ SV2175 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2048 @ SV352 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5566]) ).
thf(6057,plain,
! [SV2176: $i,SV2049: $i,SV1696: $i,SV1078: $i,SV353: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV1078 @ tc_nat ) @ SV1696 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2049 @ SV1078 @ tc_nat ) @ SV2176 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1696 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2049 @ SV353 @ tc_nat ) @ SV1078 @ tc_nat ) @ SV2176 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV353 @ SV2049 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(6058,plain,
! [SV1079: $i,SV354: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ ( c_HOL_Oplus__class_Oplus @ SV1079 @ SV1079 @ SV354 ) @ SV354 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV354 ) @ SV1079 @ SV354 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(6059,plain,
! [SV1080: $i,SV355: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ SV1080 @ SV355 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV355 ) @ ( c_HOL_Oplus__class_Oplus @ SV1080 @ SV1080 @ SV355 ) @ SV355 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5569]) ).
thf(6060,plain,
! [SV2177: $i,SV2050: $i,SV1698: $i,SV1082: $i,SV357: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1082 @ SV1698 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SV2050 @ SV2177 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1082 @ SV2050 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1698 @ SV2177 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5571]) ).
thf(6061,plain,
! [SV2051: $i,SV1699: $i,SV1083: $i,SV358: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
| ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5572]) ).
thf(6062,plain,
! [SV360: $i,SV1700: $i,SV1085: $i] :
( ( ( c_lessequals @ SV1085 @ SV1700 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5573]) ).
thf(6063,plain,
! [SV361: $i,SV1086: $i,SV1701: $i] :
( ( ( c_lessequals @ SV1701 @ SV1086 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5574]) ).
thf(6064,plain,
! [SV2178: $i,SV2052: $i,SV1702: $i,SV1087: $i,SV362: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV362 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1702 @ SV362 ) @ SV2052 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2178 @ SV1702 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV2178 @ SV362 ) @ SV1702 @ SV362 ) @ SV2052 @ SV362 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5575]) ).
thf(6065,plain,
! [SV2053: $i,SV1704: $i,SV1089: $i,SV364: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV364 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV1704 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV2053 @ SV364 ) @ SV364 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1704 @ SV2053 @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5577]) ).
thf(6066,plain,
! [SV2054: $i,SV1705: $i,SV1090: $i,SV365: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV365 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SV1705 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SV2054 @ SV1705 @ SV365 ) @ SV365 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SV2054 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5578]) ).
thf(6067,plain,
! [SV2055: $i,SV1709: $i,SV1103: $i,SV378: $i] :
( ( ( class_Divides_Osemiring__div @ SV378 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1103 @ SV1709 @ SV378 ) @ SV2055 @ SV378 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1103 @ SV2055 @ SV378 ) @ ( c_Divides_Odiv__class_Omod @ SV1709 @ SV2055 @ SV378 ) @ SV378 ) @ SV2055 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5583]) ).
thf(6068,plain,
! [SV2056: $i,SV1710: $i,SV1104: $i,SV379: $i] :
( ( ( class_Orderings_Olinorder @ SV379 )
= $false )
| ( ( ( c_lessequals @ SV1104 @ SV1710 @ SV379 )
| ~ ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SV1710 @ SV2056 @ SV379 ) @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5584]) ).
thf(6069,plain,
! [SV2057: $i,SV1711: $i,SV1105: $i,SV380: $i] :
( ( ( class_Orderings_Olinorder @ SV380 )
= $false )
| ( ( ( c_lessequals @ SV1105 @ SV1711 @ SV380 )
| ~ ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SV2057 @ SV1711 @ SV380 ) @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5585]) ).
thf(6070,plain,
! [SV2058: $i,SV1712: $i,SV1106: $i,SV381: $i] :
( ( ( class_Orderings_Olinorder @ SV381 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SV1712 @ SV381 ) @ SV2058 @ SV381 )
| ~ ( c_lessequals @ SV1106 @ SV2058 @ SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5586]) ).
thf(6071,plain,
! [SV2059: $i,SV1713: $i,SV1107: $i,SV382: $i] :
( ( ( class_Orderings_Olinorder @ SV382 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SV1713 @ SV382 ) @ SV2059 @ SV382 )
| ~ ( c_lessequals @ SV1713 @ SV2059 @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(6072,plain,
! [SV2060: $i,SV1714: $i,SV1108: $i,SV383: $i] :
( ( ( class_Orderings_Olinorder @ SV383 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SV1714 @ SV383 ) @ SV2060 @ SV383 )
| ~ ( c_lessequals @ SV1108 @ SV2060 @ SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5588]) ).
thf(6073,plain,
! [SV2061: $i,SV1715: $i,SV1109: $i,SV384: $i] :
( ( ( class_Orderings_Olinorder @ SV384 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SV1715 @ SV384 ) @ SV2061 @ SV384 )
| ~ ( c_lessequals @ SV1715 @ SV2061 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5589]) ).
thf(6074,plain,
! [SV2062: $i,SV1716: $i,SV1110: $i,SV385: $i] :
( ( ( class_Orderings_Olinorder @ SV385 )
= $false )
| ( ( ( c_lessequals @ SV1110 @ SV1716 @ SV385 )
| ~ ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SV1716 @ SV2062 @ SV385 ) @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(6075,plain,
! [SV2063: $i,SV1717: $i,SV1111: $i,SV386: $i] :
( ( ( class_Orderings_Olinorder @ SV386 )
= $false )
| ( ( ( c_lessequals @ SV1111 @ SV1717 @ SV386 )
| ~ ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SV2063 @ SV1717 @ SV386 ) @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5591]) ).
thf(6076,plain,
! [SV2064: $i,SV1718: $i,SV1113: $i,SV388: $i] :
( ( ( class_Orderings_Olinorder @ SV388 )
= $false )
| ( ( ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
| ( c_lessequals @ SV2064 @ SV1718 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2064 @ SV1113 @ SV388 ) @ SV1718 @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5592]) ).
thf(6077,plain,
! [SV2065: $i,SV1719: $i,SV1114: $i,SV389: $i] :
( ( ( c_lessequals @ SV389 @ SV1114 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV389 @ SV1719 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1114 @ SV389 @ tc_nat ) @ SV1719 @ tc_nat ) @ SV2065 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1114 @ SV1719 @ tc_nat ) @ SV2065 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5593]) ).
thf(6078,plain,
! [SV2179: $i,SV2066: $i,SV1722: $i,SV1117: $i,SV392: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ SV2179 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SV2179 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5596]) ).
thf(6079,plain,
! [SV2180: $i,SV2067: $i,SV1723: $i,SV1118: $i,SV393: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2067 @ SV1118 @ tc_nat ) @ SV2180 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SV2067 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SV2180 @ tc_nat )
| ~ ( c_lessequals @ SV2067 @ SV393 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5597]) ).
thf(6080,plain,
! [SV2181: $i,SV2068: $i,SV1724: $i,SV1119: $i,SV394: $i] :
( ( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SV2068 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1724 @ SV1119 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5598]) ).
thf(6081,plain,
! [SV2182: $i,SV2069: $i,SV1725: $i,SV1120: $i,SV395: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2069 @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2069 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV395 @ SV2069 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5599]) ).
thf(6082,plain,
! [SV1129: $i,SV404: $i] :
( ( ( class_Int_Onumber__ring @ SV404 )
= $false )
| ( ( SV1129
= ( c_HOL_Oplus__class_Oplus @ SV1129 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5601]) ).
thf(6083,plain,
! [SV2183: $i,SV2070: $i,SV1728: $i,SV1134: $i,SV412: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SV1728 @ SV2183 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5602]) ).
thf(6084,plain,
! [SV2184: $i,SV2071: $i,SV1729: $i,SV1135: $i,SV413: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5603]) ).
thf(6085,plain,
! [SV1136: $i,SV1730: $i,SV414: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5604]) ).
thf(6086,plain,
! [SV1137: $i,SV415: $i,SV1731: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5605]) ).
thf(6087,plain,
! [SV2072: $i,SV1732: $i,SV1138: $i,SV416: $i] :
( ( ( class_Orderings_Oorder @ SV416 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
| ~ ( c_lessequals @ SV1138 @ SV2072 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5606]) ).
thf(6088,plain,
! [SV2073: $i,SV1733: $i,SV1139: $i,SV417: $i] :
( ( ( class_Orderings_Oorder @ SV417 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 )
| ~ ( c_lessequals @ SV2073 @ SV1733 @ SV417 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5607]) ).
thf(6089,plain,
! [SV2074: $i,SV1734: $i,SV1140: $i,SV418: $i] :
( ( ( class_Orderings_Opreorder @ SV418 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
| ~ ( c_lessequals @ SV2074 @ SV1734 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5608]) ).
thf(6090,plain,
! [SV2075: $i,SV1735: $i,SV1141: $i,SV419: $i] :
( ( ( class_Orderings_Opreorder @ SV419 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 )
| ~ ( c_lessequals @ SV1141 @ SV2075 @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5609]) ).
thf(6091,plain,
! [SV2076: $i,SV1736: $i,SV1142: $i,SV420: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SV1736 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SV2076 @ SV1736 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SV1142 @ SV2076 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5610]) ).
thf(6092,plain,
! [SV2077: $i,SV1737: $i,SV1143: $i,SV421: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SV1737 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SV2077 @ SV1737 @ SV421 ) @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SV1143 @ SV2077 @ SV421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5611]) ).
thf(6093,plain,
! [SV2078: $i,SV1738: $i,SV1144: $i,SV422: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1738 @ SV422 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SV2078 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SV1738 @ SV2078 @ SV422 ) @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5612]) ).
thf(6094,plain,
! [SV2079: $i,SV1739: $i,SV1145: $i,SV423: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV1739 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV2079 @ SV423 ) @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SV2079 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5613]) ).
thf(6095,plain,
! [SV2080: $i,SV1740: $i,SV1146: $i,SV424: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV1740 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV2080 @ SV424 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SV2080 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5614]) ).
thf(6096,plain,
! [SV2081: $i,SV1741: $i,SV1147: $i,SV425: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1147 @ SV1741 @ SV425 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1741 @ SV425 ) @ SV425 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5615]) ).
thf(6097,plain,
! [SV426: $i,SV1742: $i,SV1148: $i] :
( ( ( c_lessequals @ SV1148 @ SV1742 @ SV426 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1148 @ SV1742 @ SV426 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV426 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5616]) ).
thf(6098,plain,
! [SV427: $i,SV1743: $i,SV1149: $i] :
( ( ( c_lessequals @ SV1149 @ SV1743 @ SV427 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1149 @ SV1743 @ SV427 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5617]) ).
thf(6099,plain,
! [SV2185: $i,SV2082: $i,SV1744: $i,SV1150: $i,SV428: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5618]) ).
thf(6100,plain,
! [SV429: $i,SV1745: $i,SV1151: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1745 @ SV429 )
= $true )
| ( ( ( c_lessequals @ SV1745 @ SV1151 @ SV429 )
| ~ ( c_lessequals @ SV1151 @ SV1745 @ SV429 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5619]) ).
thf(6101,plain,
! [SV2083: $i,SV1746: $i,SV1152: $i,SV430: $i] :
( ( ( class_Orderings_Olinorder @ SV430 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
| ( c_HOL_Oord__class_Oless @ SV2083 @ SV1746 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2083 @ SV1152 @ SV430 ) @ SV1746 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5620]) ).
thf(6102,plain,
! [SV431: $i,SV1747: $i,SV1153: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1153 @ SV1747 @ SV431 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1153 @ SV431 ) @ SV1747 @ SV431 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(6103,plain,
! [SV2084: $i,SV1748: $i,SV1154: $i,SV432: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SV2084 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SV2084 @ SV432 ) @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5622]) ).
thf(6104,plain,
! [SV2085: $i,SV1749: $i,SV1155: $i,SV433: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
| ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1155 @ SV433 ) @ SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5623]) ).
thf(6105,plain,
! [SV434: $i,SV1750: $i,SV1156: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1750 @ SV434 )
= $true )
| ( ( ( SV1750 = SV1156 )
| ~ ( c_lessequals @ SV1156 @ SV1750 @ SV434 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5624]) ).
thf(6106,plain,
! [SV435: $i,SV1751: $i,SV1157: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1751 @ SV435 )
= $true )
| ( ( ~ ( c_lessequals @ SV1157 @ SV1751 @ SV435 )
| ( SV1751 = SV1157 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5625]) ).
thf(6107,plain,
! [SV436: $i,SV1752: $i,SV1158: $i] :
( ( ( SV1158 = SV1752 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1752 @ SV436 )
| ~ ( c_lessequals @ SV1158 @ SV1752 @ SV436 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5626]) ).
thf(6108,plain,
! [SV437: $i,SV1753: $i,SV1159: $i] :
( ( ( SV1159 = SV1753 )
= $true )
| ( ( ~ ( c_lessequals @ SV1159 @ SV1753 @ SV437 )
| ( c_HOL_Oord__class_Oless @ SV1159 @ SV1753 @ SV437 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV437 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5627]) ).
thf(6109,plain,
! [SV438: $i,SV1754: $i,SV1160: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV1754 @ SV438 )
= $true )
| ( ( ~ ( c_lessequals @ SV1160 @ SV1754 @ SV438 )
| ( SV1160 = SV1754 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5628]) ).
thf(6110,plain,
! [SV439: $i,SV1755: $i,SV1161: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1755 @ SV439 )
= $true )
| ( ( ( SV1161 = SV1755 )
| ~ ( c_lessequals @ SV1161 @ SV1755 @ SV439 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV439 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5629]) ).
thf(6111,plain,
! [SV440: $i,SV1756: $i,SV1162: $i] :
( ( ( SV1162 = SV1756 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1162 @ SV1756 @ SV440 )
| ~ ( c_lessequals @ SV1162 @ SV1756 @ SV440 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5630]) ).
thf(6112,plain,
! [SV441: $i,SV1757: $i,SV1163: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV1757 @ SV441 )
= $true )
| ( ( ( SV1163 = SV1757 )
| ~ ( c_lessequals @ SV1163 @ SV1757 @ SV441 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5631]) ).
thf(6113,plain,
! [SV2086: $i,SV1758: $i,SV1164: $i,SV442: $i] :
( ( ( class_Orderings_Olinorder @ SV442 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(6114,plain,
! [SV443: $i,SV1759: $i,SV1165: $i] :
( ( ( ~ ( c_lessequals @ SV1165 @ SV1759 @ SV443 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1759 @ SV1165 @ SV443 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV443 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5633]) ).
thf(6115,plain,
! [SV444: $i,SV1760: $i,SV1166: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1166 @ SV1760 @ SV444 )
= $true )
| ( ( c_lessequals @ SV1760 @ SV1166 @ SV444 )
= $true )
| ( ( class_Orderings_Olinorder @ SV444 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5634]) ).
thf(6116,plain,
! [SV445: $i,SV1167: $i] :
( ( ( c_lessequals @ SV1167 @ SV1167 @ SV445 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1167 @ SV1167 @ SV445 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5635]) ).
thf(6117,plain,
! [SV447: $i,SV1761: $i,SV1169: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1169 @ SV1761 @ SV447 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1761 @ SV1169 @ SV447 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5637]) ).
thf(6118,plain,
! [SV448: $i,SV1762: $i,SV1170: $i] :
( ( ( c_lessequals @ SV1170 @ SV1762 @ SV448 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1762 @ SV1170 @ SV448 )
= $true )
| ( ( class_Orderings_Olinorder @ SV448 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5638]) ).
thf(6119,plain,
! [SV449: $i,SV1763: $i,SV1171: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1171 @ SV1763 @ SV449 )
= $true )
| ( ( c_lessequals @ SV1763 @ SV1171 @ SV449 )
= $true )
| ( ( class_Orderings_Olinorder @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5639]) ).
thf(6120,plain,
! [SV450: $i,SV1764: $i,SV1172: $i] :
( ( ( ~ ( c_lessequals @ SV1172 @ SV1764 @ SV450 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1764 @ SV1172 @ SV450 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV450 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5640]) ).
thf(6121,plain,
! [SV2087: $i,SV1765: $i,SV1173: $i,SV451: $i] :
( ( ( class_Orderings_Olinorder @ SV451 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SV1765 @ SV451 ) @ SV2087 @ SV451 )
| ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2087 @ SV451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5641]) ).
thf(6122,plain,
! [SV2088: $i,SV1766: $i,SV1174: $i,SV452: $i] :
( ( ( class_Orderings_Olinorder @ SV452 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SV1766 @ SV452 ) @ SV2088 @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2088 @ SV452 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5642]) ).
thf(6123,plain,
! [SV2089: $i,SV1767: $i,SV1175: $i,SV453: $i] :
( ( ( class_Orderings_Olinorder @ SV453 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV1767 @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SV2089 @ SV1767 @ SV453 ) @ SV453 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(6124,plain,
! [SV2090: $i,SV1768: $i,SV1176: $i,SV454: $i] :
( ( ( class_Orderings_Olinorder @ SV454 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1176 @ SV1768 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2090 @ SV454 ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5644]) ).
thf(6125,plain,
! [SV2091: $i,SV1769: $i,SV1177: $i,SV455: $i] :
( ( ( class_Orderings_Olinorder @ SV455 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SV1769 @ SV455 ) @ SV2091 @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1769 @ SV2091 @ SV455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5645]) ).
thf(6126,plain,
! [SV2092: $i,SV1770: $i,SV1178: $i,SV456: $i] :
( ( ( class_Orderings_Olinorder @ SV456 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SV1770 @ SV456 ) @ SV2092 @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV2092 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5646]) ).
thf(6127,plain,
! [SV2093: $i,SV1771: $i,SV1179: $i,SV457: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV457 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SV1771 @ SV2093 @ SV457 ) @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1771 @ SV457 ) @ SV457 ) @ SV2093 @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5647]) ).
thf(6128,plain,
! [SV2217: $i,SV2186: $i,SV2094: $i,SV1772: $i,SV1180: $i,SV458: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2186 @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2186 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5648]) ).
thf(6129,plain,
! [SV2218: $i,SV2187: $i,SV2095: $i,SV1773: $i,SV1181: $i,SV459: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 )
| ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SV2187 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5649]) ).
thf(6130,plain,
! [SV2219: $i,SV2188: $i,SV2096: $i,SV1774: $i,SV1182: $i,SV460: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2188 @ SV1774 @ SV460 ) @ SV2219 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV2188 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SV2219 @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5650]) ).
thf(6131,plain,
! [SV2220: $i,SV2189: $i,SV2097: $i,SV1775: $i,SV1183: $i,SV461: $i] :
( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ SV2220 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SV2220 @ SV461 ) @ SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5651]) ).
thf(6132,plain,
! [SV2098: $i,SV1776: $i,SV1184: $i,SV462: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV462 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5652]) ).
thf(6133,plain,
! [SV2099: $i,SV1777: $i,SV1185: $i,SV463: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV463 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omin @ SV1185 @ SV1777 @ SV463 ) @ SV2099 @ SV463 )
= ( c_Orderings_Oord__class_Omin @ ( c_HOL_Ominus__class_Ominus @ SV1185 @ SV2099 @ SV463 ) @ ( c_HOL_Ominus__class_Ominus @ SV1777 @ SV2099 @ SV463 ) @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5653]) ).
thf(6134,plain,
! [SV2100: $i,SV1778: $i,SV1186: $i,SV464: $i] :
( ( ( class_Divides_Oring__div @ SV464 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ SV1778 @ SV464 ) @ SV2100 @ SV464 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1186 @ ( c_Divides_Odiv__class_Omod @ SV1778 @ SV2100 @ SV464 ) @ SV464 ) @ SV2100 @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5654]) ).
thf(6135,plain,
! [SV2101: $i,SV1779: $i,SV1187: $i,SV465: $i] :
( ( ( class_Divides_Oring__div @ SV465 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1187 @ SV1779 @ SV465 ) @ SV2101 @ SV465 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1187 @ SV2101 @ SV465 ) @ SV1779 @ SV465 ) @ SV2101 @ SV465 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5655]) ).
thf(6136,plain,
! [SV2102: $i,SV1780: $i,SV1188: $i,SV466: $i] :
( ( ( class_Divides_Oring__div @ SV466 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1188 @ SV1780 @ SV466 ) @ SV2102 @ SV466 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV1188 @ SV2102 @ SV466 ) @ ( c_Divides_Odiv__class_Omod @ SV1780 @ SV2102 @ SV466 ) @ SV466 ) @ SV2102 @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5656]) ).
thf(6137,plain,
! [SV2103: $i,SV1782: $i,SV1190: $i,SV468: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5658]) ).
thf(6138,plain,
! [SV1195: $i,SV473: $i] :
( ( ( class_Int_Onumber__ring @ SV473 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1195 @ SV1195 @ SV473 )
= ( c_HOL_Ozero__class_Ozero @ SV473 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5659]) ).
thf(6139,plain,
! [SV2104: $i,SV1784: $i,SV1197: $i,SV475: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV475 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1197 @ ( c_HOL_Ominus__class_Ominus @ SV1784 @ SV2104 @ SV475 ) @ SV475 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV1784 @ SV475 ) @ ( c_HOL_Otimes__class_Otimes @ SV1197 @ SV2104 @ SV475 ) @ SV475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5661]) ).
thf(6140,plain,
! [SV2105: $i,SV1785: $i,SV1198: $i,SV476: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV476 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1198 @ ( c_HOL_Ominus__class_Ominus @ SV1785 @ SV2105 @ SV476 ) @ SV476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV1785 @ SV476 ) @ ( c_HOL_Otimes__class_Otimes @ SV1198 @ SV2105 @ SV476 ) @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(6141,plain,
! [SV2106: $i,SV1786: $i,SV1199: $i,SV477: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV477 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1199 @ SV1786 @ SV477 ) @ SV2106 @ SV477 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1199 @ SV2106 @ SV477 ) @ ( c_HOL_Otimes__class_Otimes @ SV1786 @ SV2106 @ SV477 ) @ SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(6142,plain,
! [SV2107: $i,SV1787: $i,SV1200: $i,SV478: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV478 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1200 @ SV1787 @ SV478 ) @ SV2107 @ SV478 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1200 @ SV2107 @ SV478 ) @ ( c_HOL_Otimes__class_Otimes @ SV1787 @ SV2107 @ SV478 ) @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(6143,plain,
! [SV2190: $i,SV2108: $i,SV1788: $i,SV1201: $i,SV479: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV479 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1201 @ SV1788 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SV2108 @ SV2190 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ SV2108 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SV1788 @ SV2190 @ SV479 ) @ SV479 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5665]) ).
thf(6144,plain,
! [SV1793: $i,SV489: $i,SV2109: $i,SV1210: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1210 @ SV2109 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1793 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1793 @ SV2109 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5670]) ).
thf(6145,plain,
! [SV1795: $i,SV509: $i,SV1226: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1226 @ SV509 ) @ SV1795 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV1226 @ SV1795 @ SV509 ) @ SV509 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SV1795 @ SV509 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5674]) ).
thf(6146,plain,
! [SV512: $i,SV1796: $i,SV1229: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1229 @ SV1796 @ SV512 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1229 @ SV512 ) @ SV1796 @ SV512 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV512 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5675]) ).
thf(6147,plain,
! [SV1797: $i,SV513: $i,SV1230: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1230 @ SV513 ) @ SV1797 @ SV513 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1230 @ SV1797 @ SV513 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV513 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5676]) ).
thf(6148,plain,
! [SV514: $i,SV1798: $i,SV1231: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ SV1798 @ SV514 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ ( c_HOL_Oabs__class_Oabs @ SV1798 @ SV514 ) @ SV514 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5677]) ).
thf(6149,plain,
! [SV515: $i,SV1799: $i,SV1232: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ ( c_HOL_Oabs__class_Oabs @ SV1799 @ SV515 ) @ SV515 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ SV1799 @ SV515 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV515 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5678]) ).
thf(6150,plain,
! [SV1800: $i,SV1234: $i,SV517: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5679]) ).
thf(6151,plain,
! [SV522: $i,SV1239: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1239 @ SV522 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1239 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SV1239 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5680]) ).
thf(6152,plain,
! [SV523: $i,SV1801: $i,SV1240: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1240 @ SV1801 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
= $true )
| ( ( ~ ( c_lessequals @ SV1240 @ SV1801 @ SV523 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5681]) ).
thf(6153,plain,
! [SV524: $i,SV1802: $i,SV1241: $i] :
( ( ( c_lessequals @ SV1241 @ SV1802 @ SV524 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1241 @ SV1802 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5682]) ).
thf(6154,plain,
! [SV1246: $i,SV529: $i,SV1803: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1803 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV1246 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SV1246 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5684]) ).
thf(6155,plain,
! [SV1247: $i,SV530: $i,SV1804: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV1247 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1804 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SV1247 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5685]) ).
thf(6156,plain,
! [SV531: $i,SV1805: $i,SV1248: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1248 @ SV1805 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1248 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1805 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5686]) ).
thf(6157,plain,
! [SV1251: $i,SV534: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV534 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1251 @ SV534 ) @ SV534 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1251 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV534 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5689]) ).
thf(6158,plain,
! [SV535: $i,SV1252: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1252 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV535 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1252 @ SV535 ) @ SV535 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV535 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(6159,plain,
! [SV2191: $i,SV2110: $i,SV1808: $i,SV1253: $i,SV536: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5691]) ).
thf(6160,plain,
! [SV2192: $i,SV2111: $i,SV1809: $i,SV1254: $i,SV537: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5692]) ).
thf(6161,plain,
! [SV1258: $i,SV541: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV541 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1258 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV541 @ ( c_HOL_Otimes__class_Otimes @ SV541 @ SV1258 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(6162,plain,
! [SV1259: $i,SV542: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV542 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1259 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV542 @ ( c_HOL_Otimes__class_Otimes @ SV1259 @ SV542 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(6163,plain,
! [SV2112: $i,SV1811: $i,SV1260: $i,SV544: $i] :
( ( ( class_Divides_Osemiring__div @ SV544 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SV1811 @ SV544 ) @ SV2112 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SV2112 @ SV544 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV2112 @ SV1811 @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(6164,plain,
! [SV545: $i,SV1261: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1261 @ SV1261 @ SV545 ) @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
= $false )
| ( ( c_lessequals @ SV1261 @ ( c_HOL_Ozero__class_Ozero @ SV545 ) @ SV545 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(6165,plain,
! [SV546: $i,SV1262: $i] :
( ( ( c_lessequals @ SV1262 @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1262 @ SV1262 @ SV546 ) @ ( c_HOL_Ozero__class_Ozero @ SV546 ) @ SV546 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV546 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(6166,plain,
! [SV1263: $i,SV547: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 )
= $false )
| ( ( ( ( c_HOL_Oabs__class_Oabs @ SV1263 @ SV547 )
= SV1263 )
| ( c_HOL_Oord__class_Oless @ SV1263 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV547 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5699]) ).
thf(6167,plain,
! [SV2193: $i,SV2113: $i,SV1812: $i,SV1265: $i,SV549: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5701]) ).
thf(6168,plain,
! [SV1268: $i,SV553: $i] :
( ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV553 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1268 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Otimes__class_Otimes @ SV553 @ SV1268 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5703]) ).
thf(6169,plain,
! [SV557: $i,SV1271: $i,SV1814: $i] :
( ( ( c_lessequals @ SV1814 @ SV1271 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV557 @ SV1814 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV557 @ SV1271 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(6170,plain,
! [SV2194: $i,SV2114: $i,SV1815: $i,SV1272: $i,SV559: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV559 ) )
= $true )
| ( ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SV2194 @ SV2114 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5705]) ).
thf(6171,plain,
! [SV2115: $i,SV1816: $i,SV1273: $i,SV560: $i] :
( ( ( class_Orderings_Opreorder @ SV560 )
= $false )
| ( ( ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV2115 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV1273 @ SV2115 @ SV560 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(6172,plain,
! [SV561: $i,SV1817: $i,SV1274: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $true )
| ( ( ~ ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
| ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5707]) ).
thf(6173,plain,
! [SV2116: $i,SV1818: $i,SV1275: $i,SV562: $i] :
( ( ( class_Orderings_Oorder @ SV562 )
= $false )
| ( ( ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
| ~ ( c_lessequals @ SV1275 @ SV2116 @ SV562 )
| ~ ( c_lessequals @ SV2116 @ SV1818 @ SV562 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(6174,plain,
! [SV567: $i,SV1280: $i] :
( ( ( c_lessequals @ SV1280 @ SV567 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV567 @ ( c_Suc @ SV1280 ) @ tc_nat )
= $false )
| ( ( SV567 = SV1280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5712]) ).
thf(6175,plain,
! [SV2117: $i,SV1821: $i,SV1281: $i,SV569: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV2117 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1281 @ SV569 ) @ SV569 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5713]) ).
thf(6176,plain,
! [SV2118: $i,SV1822: $i,SV1282: $i,SV570: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
| ( c_HOL_Oord__class_Oless @ SV1822 @ SV2118 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV2118 @ SV570 ) @ SV570 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5714]) ).
thf(6177,plain,
! [SV2119: $i,SV1823: $i,SV1283: $i,SV571: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SV2119 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV2119 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SV2119 @ SV571 ) @ SV571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5715]) ).
thf(6178,plain,
! [SV2120: $i,SV1824: $i,SV1284: $i,SV572: $i] :
( ( ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
| ( c_HOL_Oord__class_Oless @ SV1824 @ SV2120 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SV2120 @ SV1284 @ SV572 ) @ SV572 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5716]) ).
thf(6179,plain,
! [SV2121: $i,SV1825: $i,SV1285: $i,SV573: $i] :
( ( ( class_Divides_Osemiring__div @ SV573 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV1825 @ SV573 ) @ ( c_HOL_Otimes__class_Otimes @ SV1285 @ SV2121 @ SV573 ) @ SV573 )
= ( c_HOL_Otimes__class_Otimes @ SV1285 @ ( c_Divides_Odiv__class_Omod @ SV1825 @ SV2121 @ SV573 ) @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(6180,plain,
! [SV2122: $i,SV1826: $i,SV1286: $i,SV574: $i] :
( ( ( class_Divides_Osemiring__div @ SV574 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV1286 @ SV1826 @ SV574 ) @ ( c_HOL_Otimes__class_Otimes @ SV2122 @ SV1826 @ SV574 ) @ SV574 )
= ( c_HOL_Otimes__class_Otimes @ ( c_Divides_Odiv__class_Omod @ SV1286 @ SV2122 @ SV574 ) @ SV1826 @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5718]) ).
thf(6181,plain,
! [SV1287: $i,SV575: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV575 @ SV1287 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1287 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV575 @ SV1287 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(6182,plain,
! [SV579: $i,SV1827: $i,SV1291: $i] :
( ( ( c_lessequals @ SV1291 @ SV1827 @ SV579 )
= $true )
| ( ( c_lessequals @ SV1827 @ SV1291 @ SV579 )
= $true )
| ( ( class_Orderings_Olinorder @ SV579 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5720]) ).
thf(6183,plain,
! [SV580: $i,SV1292: $i,SV1828: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV1292 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV580 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1828 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5721]) ).
thf(6184,plain,
! [SV581: $i,SV1293: $i,SV1829: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1829 @ SV1293 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1829 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SV1829 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5722]) ).
thf(6185,plain,
! [SV598: $i,SV1305: $i,SV1832: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1832 @ SV1305 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV598 @ SV1832 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SV1305 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5730]) ).
thf(6186,plain,
! [SV609: $i,SV1838: $i,SV1316: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1316 @ SV1838 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1316 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1838 @ SV609 ) @ SV609 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1838 @ SV1316 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV609 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(6187,plain,
! [SV1324: $i,SV1843: $i,SV618: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1843 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1324 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SV1324 @ SV1843 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5738]) ).
thf(6188,plain,
! [SV1325: $i,SV1844: $i,SV621: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1844 @ SV1325 @ tc_nat )
| ~ ( c_lessequals @ SV1844 @ SV621 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5739]) ).
thf(6189,plain,
! [SV1326: $i,SV1845: $i,SV622: $i] :
( ( ( c_lessequals @ SV622 @ SV1845 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1326 @ SV1845 @ tc_nat )
| ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5740]) ).
thf(6190,plain,
! [SV1331: $i,SV628: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ SV628 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV1331 @ tc_nat )
= $false )
| ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV628 @ SV1331 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(6191,plain,
! [SV632: $i,SV1851: $i,SV1335: $i] :
( ( ( c_lessequals @ SV1335 @ SV1851 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1335 @ SV632 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1335 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1851 @ SV1335 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1851 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(6192,plain,
! [SV635: $i,SV1852: $i,SV1338: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1338 @ SV1852 @ SV635 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1338 @ SV1852 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5745]) ).
thf(6193,plain,
! [SV636: $i,SV1853: $i,SV1339: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1339 @ SV1853 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1339 @ SV1853 @ SV636 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV636 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5746]) ).
thf(6194,plain,
! [SV2123: $i,SV1854: $i,SV1340: $i,SV637: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV637 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SV1854 @ SV637 ) @ SV2123 @ SV637 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV2123 @ SV1340 @ SV637 ) @ SV637 ) @ SV1854 @ SV637 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(6195,plain,
! [SV1855: $i,SV638: $i,SV1341: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1341 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1855 @ SV638 ) @ SV638 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1341 @ SV1855 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5748]) ).
thf(6196,plain,
! [SV639: $i,SV1856: $i,SV1342: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1342 @ SV1856 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1342 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1856 @ SV639 ) @ SV639 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5749]) ).
thf(6197,plain,
! [SV641: $i,SV1344: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1344 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV641 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV641 @ SV1344 @ tc_nat ) @ SV641 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(6198,plain,
! [SV1345: $i,SV642: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV642 @ SV1345 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SV1345 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV1345 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5751]) ).
thf(6199,plain,
! [SV643: $i,SV1346: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1346 @ SV643 @ tc_nat )
= $true )
| ( ( ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV1346 @ SV643 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV1346 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5752]) ).
thf(6200,plain,
! [SV1349: $i,SV1859: $i,SV646: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1859 @ SV1349 @ tc_nat )
| ~ ( c_lessequals @ SV1859 @ SV646 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(6201,plain,
! [SV1350: $i,SV1860: $i,SV647: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1350 @ SV1860 @ tc_nat )
| ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(6202,plain,
! [SV1861: $i,SV652: $i,SV1355: $i] :
( ( ( c_lessequals @ SV1355 @ SV652 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV652 @ SV1861 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SV1355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1861 @ SV1355 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(6203,plain,
! [SV654: $i,SV1862: $i,SV1357: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV1862 @ SV654 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1862 @ SV1357 @ SV654 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV654 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5758]) ).
thf(6204,plain,
! [SV655: $i,SV1863: $i,SV1358: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1358 @ SV1863 @ SV655 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1863 @ SV1358 @ SV655 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV655 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5759]) ).
thf(6205,plain,
! [SV656: $i,SV1864: $i,SV1359: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1359 @ SV1864 @ SV656 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1864 @ SV1359 @ SV656 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV656 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5760]) ).
thf(6206,plain,
! [SV657: $i,SV1865: $i,SV1360: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1360 @ SV1865 @ SV657 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1865 @ SV1360 @ SV657 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV657 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5761]) ).
thf(6207,plain,
! [SV1365: $i,SV664: $i,SV1867: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1867 @ SV664 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1867 @ SV1365 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1867 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(6208,plain,
! [SV665: $i,SV1868: $i,SV1366: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1366 @ SV1868 @ SV665 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1868 @ SV1366 @ SV665 )
| ( SV1868 = SV1366 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5767]) ).
thf(6209,plain,
! [SV666: $i,SV1869: $i,SV1367: $i] :
( ( ( SV1367 = SV1869 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1869 @ SV1367 @ SV666 )
| ( c_HOL_Oord__class_Oless @ SV1367 @ SV1869 @ SV666 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV666 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5768]) ).
thf(6210,plain,
! [SV667: $i,SV1870: $i,SV1368: $i] :
( ( ( SV1368 = SV1870 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1368 @ SV1870 @ SV667 )
| ( c_HOL_Oord__class_Oless @ SV1870 @ SV1368 @ SV667 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV667 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5769]) ).
thf(6211,plain,
! [SV668: $i,SV1871: $i,SV1369: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1369 @ SV1871 @ SV668 )
= $true )
| ( ( ( SV1871 = SV1369 )
| ( c_HOL_Oord__class_Oless @ SV1871 @ SV1369 @ SV668 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV668 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5770]) ).
thf(6212,plain,
! [SV671: $i,SV1872: $i,SV1372: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1372 @ SV1872 @ SV671 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1872 @ SV1372 @ SV671 )
| ( SV1872 = SV1372 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV671 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5771]) ).
thf(6213,plain,
! [SV2124: $i,SV1873: $i,SV1373: $i,SV672: $i] :
( ( ( class_Orderings_Oorder @ SV672 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(6214,plain,
! [SV2125: $i,SV1874: $i,SV1374: $i,SV673: $i] :
( ( ( class_Orderings_Opreorder @ SV673 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(6215,plain,
! [SV679: $i,SV1378: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1378 @ SV679 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1378 = SV679 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV679 @ SV1378 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5776]) ).
thf(6216,plain,
! [SV1878: $i,SV681: $i,SV1380: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1380 @ SV1380 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SV1878 @ SV1878 @ SV681 ) @ SV681 )
!= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
= $true )
| ( ( SV1380
= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV681 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5778]) ).
thf(6217,plain,
! [SV2126: $i,SV1879: $i,SV1381: $i,SV682: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV682 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV682 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
| ( SV1879 = SV2126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5779]) ).
thf(6218,plain,
! [SV2195: $i,SV2127: $i,SV1880: $i,SV1382: $i,SV683: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV1880 @ tc_nat ) @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV2127 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2195 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV683 @ SV1382 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SV2127 @ SV1382 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5780]) ).
thf(6219,plain,
! [SV1881: $i,SV684: $i,SV1383: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1383 @ SV684 )
!= ( c_HOL_Oabs__class_Oabs @ SV1881 @ SV684 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1383 @ SV1881 @ SV684 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV684 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(6220,plain,
! [SV2128: $i,SV1882: $i,SV1384: $i,SV685: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV1882 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV2128 @ SV685 ) )
| ( SV1882 = SV2128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(6221,plain,
! [SV686: $i,SV1883: $i,SV1385: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
!= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5783]) ).
thf(6222,plain,
! [SV2196: $i,SV2129: $i,SV1884: $i,SV1387: $i,SV688: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV688 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
| ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SV2196 @ SV2129 @ SV688 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5785]) ).
thf(6223,plain,
! [SV689: $i,SV1885: $i,SV1388: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SV1885 @ SV689 )
!= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
= $true )
| ( ( ( SV1885
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(6224,plain,
! [SV2197: $i,SV2130: $i,SV1886: $i,SV1389: $i,SV690: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV690 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
| ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5787]) ).
thf(6225,plain,
! [SV691: $i,SV1887: $i,SV1390: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1390 @ SV1887 @ SV691 )
!= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
= $true )
| ( ( SV1390 = SV1887 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV691 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5788]) ).
thf(6226,plain,
! [SV693: $i,SV1888: $i,SV1391: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SV1888 @ SV693 )
!= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
= $true )
| ( ( ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1888
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5789]) ).
thf(6227,plain,
! [SV2131: $i,SV1889: $i,SV1393: $i,SV696: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV696 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SV1889 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SV2131 @ SV2131 @ SV696 ) )
| ( SV1393 = SV1889 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5791]) ).
thf(6228,plain,
! [SV1890: $i,SV1395: $i,SV698: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV698 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SV1395 = SV1890 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV698 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5793]) ).
thf(6229,plain,
! [SV2198: $i,SV2132: $i,SV1891: $i,SV1397: $i,SV702: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV702 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2132 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2198 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SV2132 @ SV702 )
= SV2198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5794]) ).
thf(6230,plain,
! [SV704: $i,SV1892: $i,SV1399: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1399 @ SV1892 @ SV704 )
!= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1892 @ SV1399 @ SV704 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV704 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(6231,plain,
! [SV705: $i,SV1893: $i,SV1400: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
!= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5797]) ).
thf(6232,plain,
! [SV2133: $i,SV1894: $i,SV1402: $i,SV708: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV708 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SV1894 @ SV2133 @ SV708 ) )
| ( SV1894 = SV2133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5799]) ).
thf(6233,plain,
! [SV2199: $i,SV2134: $i,SV1895: $i,SV1403: $i,SV709: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV709 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5800]) ).
thf(6234,plain,
! [SV2200: $i,SV2135: $i,SV1896: $i,SV1404: $i,SV710: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV710 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5801]) ).
thf(6235,plain,
! [SV711: $i,SV1405: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1405 @ SV1405 @ SV711 )
= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
= $false )
| ( ( SV1405
= ( c_HOL_Ozero__class_Ozero @ SV711 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV711 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5802]) ).
thf(6236,plain,
! [SV2136: $i,SV1897: $i,SV1406: $i,SV712: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1897 @ SV2136 @ tc_nat ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1897 @ SV1406 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV712 @ SV2136 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(6237,plain,
! [SV2221: $i,SV2201: $i,SV2137: $i,SV1898: $i,SV1407: $i,SV713: $i] :
( ( ~ ( class_Divides_Oring__div @ SV713 )
| ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5804]) ).
thf(6238,plain,
! [SV1899: $i,SV715: $i,SV1409: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1409 @ SV715 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1899 @ SV715 ) )
= $true )
| ( ( SV1409 = SV1899 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV715 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5806]) ).
thf(6239,plain,
! [SV1900: $i,SV720: $i,SV1414: $i] :
( ( ( SV1414
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV720 = SV1900 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV720 @ SV1414 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV1900 @ SV1414 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5807]) ).
thf(6240,plain,
! [SV1902: $i,SV1416: $i,SV722: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV722 ) )
= $true )
| ( ( ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
| ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV722 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5809]) ).
thf(6241,plain,
! [SV724: $i,SV1903: $i,SV1418: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SV1903 @ SV724 )
!= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
= $true )
| ( ( ( SV1903
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5811]) ).
thf(6242,plain,
! [SV2138: $i,SV1904: $i,SV1419: $i,SV725: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SV1904 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SV2138 @ SV1904 @ SV725 ) )
| ( SV1419 = SV2138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5812]) ).
thf(6243,plain,
! [SV1905: $i,SV1421: $i,SV727: $i] :
( ( ( SV727
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1421 = SV1905 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1421 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV727 @ SV1905 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5813]) ).
thf(6244,plain,
! [SV2222: $i,SV2202: $i,SV2139: $i,SV1907: $i,SV1423: $i,SV729: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV729 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2202 @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
| ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2202 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5815]) ).
thf(6245,plain,
! [SV730: $i,SV1424: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1424 @ SV730 )
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $false )
| ( ( SV1424
= ( c_HOL_Ozero__class_Ozero @ SV730 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV730 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(6246,plain,
! [SV732: $i,SV1908: $i,SV1426: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1426 @ SV1908 @ SV732 )
!= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
= $true )
| ( ( SV1426 = SV1908 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV732 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5817]) ).
thf(6247,plain,
! [SV734: $i,SV1909: $i,SV1428: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1428 @ SV1909 @ SV734 )
!= SV1428 )
= $true )
| ( ( c_lessequals @ SV1428 @ SV1909 @ SV734 )
= $true )
| ( ( class_Orderings_Olinorder @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5819]) ).
thf(6248,plain,
! [SV735: $i,SV1910: $i,SV1429: $i] :
( ( ( ~ ( c_lessequals @ SV1429 @ SV1910 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
| ( SV735 = SV1910 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5820]) ).
thf(6249,plain,
! [SV2203: $i,SV2140: $i,SV1911: $i,SV1432: $i,SV738: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2140 @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV738 @ SV2140 @ tc_nat )
| ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2140 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5821]) ).
thf(6250,plain,
! [SV2204: $i,SV2141: $i,SV1912: $i,SV1434: $i,SV741: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV741 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5822]) ).
thf(6251,plain,
! [SV2223: $i,SV2205: $i,SV2142: $i,SV1913: $i,SV1435: $i,SV742: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV742 )
| ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5823]) ).
thf(6252,plain,
! [SV2224: $i,SV2206: $i,SV2143: $i,SV1914: $i,SV1436: $i,SV743: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV743 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2206 @ SV1914 @ SV743 ) @ SV2224 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SV2206 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SV2224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5824]) ).
thf(6253,plain,
! [SV744: $i,SV1915: $i,SV1437: $i] :
( ( ( SV1437 = SV1915 )
= $true )
| ( ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1437 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV744 @ SV1915 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5825]) ).
thf(6254,plain,
! [SV1916: $i,SV1438: $i,SV745: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat ) )
= $true )
| ( ( SV1438 = SV1916 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1438 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1916 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5826]) ).
thf(6255,plain,
! [SV2144: $i,SV1917: $i,SV1439: $i,SV746: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV1439 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV2144 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV2144 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV1439 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( ( SV1439 = SV2144 )
| ( SV746 = SV1917 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(6256,plain,
! [SV1918: $i,SV747: $i,SV1440: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1440 @ SV1440 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SV1918 @ SV1918 @ SV747 ) @ SV747 )
!= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
= $true )
| ( ( SV1918
= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5828]) ).
thf(6257,plain,
! [SV2207: $i,SV2145: $i,SV1919: $i,SV1441: $i,SV748: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV748 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5829]) ).
thf(6258,plain,
! [SV2225: $i,SV2208: $i,SV2146: $i,SV1920: $i,SV1442: $i,SV749: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV749 )
| ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5830]) ).
thf(6259,plain,
! [SV2147: $i,SV1921: $i,SV1443: $i,SV750: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV1921 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV2147 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( ( SV1921 = SV2147 )
| ( SV1443
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(6260,plain,
! [SV2148: $i,SV1922: $i,SV1444: $i,SV751: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV1922 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV2148 @ SV751 ) )
| ( SV1922 = SV2148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(6261,plain,
! [SV2149: $i,SV1923: $i,SV1445: $i,SV752: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV1445 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV2149 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV2149 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV1445 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( ( SV1445 = SV2149 )
| ( SV752 = SV1923 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5833]) ).
thf(6262,plain,
! [SV2209: $i,SV2150: $i,SV1924: $i,SV1446: $i,SV753: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2150 @ SV1446 @ tc_nat ) @ SV2209 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2150 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV2150 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SV2209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5834]) ).
thf(6263,plain,
! [SV2210: $i,SV2151: $i,SV1925: $i,SV1447: $i,SV754: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV754 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
| ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5835]) ).
thf(6264,plain,
! [SV755: $i,SV1448: $i,SV1: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5836]) ).
thf(6265,plain,
! [SV756: $i,SV1449: $i,SV2: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5837]) ).
thf(6266,plain,
! [SV760: $i,SV6: $i,SV1451: $i] :
( ( ( ~ ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5839]) ).
thf(6267,plain,
! [SV761: $i,SV7: $i,SV1452: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5840]) ).
thf(6268,plain,
! [SV2152: $i,SV1926: $i,SV1455: $i,SV764: $i,SV11: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV11 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1455 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1926 @ SV2152 @ SV11 ) @ SV11 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV764 @ SV1926 @ SV11 ) @ ( c_HOL_Otimes__class_Otimes @ SV1455 @ SV2152 @ SV11 ) @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5841]) ).
thf(6269,plain,
! [SV2153: $i,SV1927: $i,SV1456: $i,SV765: $i,SV12: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV12 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV765 @ SV1456 @ SV12 ) @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SV2153 @ SV12 ) @ SV12 )
= ( c_HOL_Otimes__class_Otimes @ SV765 @ ( c_HOL_Otimes__class_Otimes @ SV1456 @ ( c_HOL_Otimes__class_Otimes @ SV1927 @ SV2153 @ SV12 ) @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5842]) ).
thf(6270,plain,
! [SV2154: $i,SV1928: $i,SV1457: $i,SV766: $i,SV13: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV13 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ ( c_HOL_Otimes__class_Otimes @ SV1928 @ SV2154 @ SV13 ) @ SV13 )
= ( c_HOL_Otimes__class_Otimes @ SV1928 @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ SV766 @ SV1457 @ SV13 ) @ SV2154 @ SV13 ) @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(6271,plain,
! [SV16: $i,SV1929: $i,SV1458: $i,SV769: $i] :
( ( ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SV1458 @ ( c_HOL_Oabs__class_Oabs @ SV1929 @ SV16 ) @ SV16 ) @ SV16 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SV1929 @ SV16 ) @ SV1458 @ SV16 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5845]) ).
thf(6272,plain,
! [SV18: $i,SV770: $i,SV1459: $i] :
( ( ( ~ ( c_lessequals @ SV1459 @ SV770 @ SV18 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV770 @ SV1459 @ SV18 ) )
= $true )
| ( ( SV770 = SV1459 )
= $true )
| ( ( class_Orderings_Oorder @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5846]) ).
thf(6273,plain,
! [SV19: $i,SV771: $i,SV1460: $i] :
( ( ( ~ ( c_lessequals @ SV1460 @ SV771 @ SV19 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV771 @ SV1460 @ SV19 ) )
= $true )
| ( ( SV771 = SV1460 )
= $true )
| ( ( class_Orderings_Oorder @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5847]) ).
thf(6274,plain,
! [SV28: $i,SV1461: $i,SV780: $i] :
( ( ( ~ ( c_lessequals @ SV780 @ SV1461 @ SV28 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1461 @ SV780 @ SV28 ) )
= $true )
| ( ( SV780 = SV1461 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5856]) ).
thf(6275,plain,
! [SV782: $i,SV1462: $i,SV30: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV1462 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1462 @ SV782 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV30 @ SV782 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(6276,plain,
! [SV31: $i,SV783: $i,SV1463: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(6277,plain,
! [SV1930: $i,SV35: $i,SV1464: $i,SV786: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5861]) ).
thf(6278,plain,
! [SV1931: $i,SV43: $i,SV1471: $i,SV794: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1471 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1931 @ SV43 ) @ SV43 )
= $true )
| ( ( ~ ( c_lessequals @ SV1471 @ SV1931 @ SV43 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5862]) ).
thf(6279,plain,
! [SV1932: $i,SV44: $i,SV1472: $i,SV795: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SV1472 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SV1932 @ SV1472 @ SV44 ) @ SV44 )
= $true )
| ( ( ~ ( c_lessequals @ SV795 @ SV1932 @ SV44 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(6280,plain,
! [SV1933: $i,SV45: $i,SV1473: $i,SV796: $i] :
( ( ( c_lessequals @ SV796 @ SV1473 @ SV45 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV1473 @ SV45 ) @ SV45 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5864]) ).
thf(6281,plain,
! [SV1934: $i,SV46: $i,SV1474: $i,SV797: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1474 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1934 @ SV46 ) @ SV46 )
= $true )
| ( ( ~ ( c_lessequals @ SV1474 @ SV1934 @ SV46 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5865]) ).
thf(6282,plain,
! [SV1935: $i,SV47: $i,SV1475: $i,SV798: $i] :
( ( ( c_lessequals @ SV798 @ SV1475 @ SV47 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SV1935 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SV1475 @ SV1935 @ SV47 ) @ SV47 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5866]) ).
thf(6283,plain,
! [SV1936: $i,SV48: $i,SV1476: $i,SV799: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SV1476 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SV1936 @ SV1476 @ SV48 ) @ SV48 )
= $true )
| ( ( ~ ( c_lessequals @ SV799 @ SV1936 @ SV48 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5867]) ).
thf(6284,plain,
! [SV801: $i,SV1478: $i,SV50: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5868]) ).
thf(6285,plain,
! [SV802: $i,SV51: $i,SV1479: $i] :
( ( ( ~ ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5869]) ).
thf(6286,plain,
! [SV803: $i,SV1480: $i,SV52: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5870]) ).
thf(6287,plain,
! [SV804: $i,SV53: $i,SV1481: $i] :
( ( ( ~ ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5871]) ).
thf(6288,plain,
! [SV1485: $i,SV808: $i,SV58: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SV1485 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 ) )
= $true )
| ( ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5872]) ).
thf(6289,plain,
! [SV809: $i,SV1486: $i,SV59: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV1486 @ SV59 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5873]) ).
thf(6290,plain,
! [SV810: $i,SV60: $i,SV1487: $i] :
( ( ( c_lessequals @ SV1487 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV1487 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 ) )
= $true )
| ( ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5874]) ).
thf(6291,plain,
! [SV1488: $i,SV61: $i,SV811: $i] :
( ( ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1488 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5875]) ).
thf(6292,plain,
! [SV812: $i,SV1489: $i,SV62: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5876]) ).
thf(6293,plain,
! [SV813: $i,SV63: $i,SV1490: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5877]) ).
thf(6294,plain,
! [SV1491: $i,SV64: $i,SV814: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5878]) ).
thf(6295,plain,
! [SV815: $i,SV1492: $i,SV65: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5879]) ).
thf(6296,plain,
! [SV816: $i,SV66: $i,SV1493: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5880]) ).
thf(6297,plain,
! [SV1938: $i,SV77: $i,SV1495: $i,SV824: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5887]) ).
thf(6298,plain,
! [SV1939: $i,SV78: $i,SV1496: $i,SV825: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5888]) ).
thf(6299,plain,
! [SV1940: $i,SV79: $i,SV1497: $i,SV826: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5889]) ).
thf(6300,plain,
! [SV1941: $i,SV80: $i,SV1498: $i,SV827: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5890]) ).
thf(6301,plain,
! [SV1942: $i,SV84: $i,SV1500: $i,SV831: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5891]) ).
thf(6302,plain,
! [SV85: $i,SV1943: $i,SV1501: $i,SV832: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5892]) ).
thf(6303,plain,
! [SV1944: $i,SV86: $i,SV1502: $i,SV833: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5893]) ).
thf(6304,plain,
! [SV87: $i,SV1945: $i,SV1503: $i,SV834: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5894]) ).
thf(6305,plain,
! [SV2211: $i,SV2155: $i,SV1946: $i,SV1504: $i,SV835: $i,SV88: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV88 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2155 @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2155 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5895]) ).
thf(6306,plain,
! [SV2212: $i,SV2156: $i,SV1947: $i,SV1505: $i,SV836: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV89 ) )
= $true )
| ( ( ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SV2156 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5896]) ).
thf(6307,plain,
! [SV2213: $i,SV2157: $i,SV1948: $i,SV1506: $i,SV837: $i,SV90: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV90 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2157 @ SV1506 @ SV90 ) @ SV2213 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SV2157 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SV2213 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5897]) ).
thf(6308,plain,
! [SV2214: $i,SV2158: $i,SV1949: $i,SV1507: $i,SV838: $i,SV91: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV91 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ SV2214 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SV2214 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5898]) ).
thf(6309,plain,
! [SV1950: $i,SV1508: $i,SV843: $i,SV96: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 ) )
= $true )
| ( ( ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5899]) ).
thf(6310,plain,
! [SV1951: $i,SV1509: $i,SV844: $i,SV97: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV97 ) )
= $true )
| ( ( ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5900]) ).
thf(6311,plain,
! [SV98: $i,SV1510: $i,SV845: $i] :
( ( ( c_lessequals @ SV845 @ SV1510 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV98 @ ( c_HOL_Ominus__class_Ominus @ SV1510 @ SV845 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV98 @ SV845 @ tc_nat ) @ SV1510 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5901]) ).
thf(6312,plain,
! [SV99: $i,SV846: $i,SV1511: $i] :
( ( ( c_lessequals @ SV1511 @ SV846 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV99 @ SV1511 @ tc_nat ) @ SV846 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV99 @ ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1511 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5902]) ).
thf(6313,plain,
! [SV2159: $i,SV850: $i,SV103: $i,SV1952: $i,SV1512: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1952 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV103 @ SV1952 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1952 @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5903]) ).
thf(6314,plain,
! [SV2160: $i,SV851: $i,SV104: $i,SV1953: $i,SV1513: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SV1953 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1513 @ SV851 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5904]) ).
thf(6315,plain,
! [SV2161: $i,SV1514: $i,SV852: $i,SV1954: $i,SV105: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SV1954 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SV2161 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1954 @ SV105 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1954 @ SV852 @ tc_nat ) @ SV2161 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5905]) ).
thf(6316,plain,
! [SV2162: $i,SV853: $i,SV1955: $i,SV1515: $i,SV106: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SV2162 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ SV2162 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5906]) ).
thf(6317,plain,
! [SV2163: $i,SV1956: $i,SV1516: $i,SV854: $i,SV107: $i] :
( ( ( class_Ring__and__Field_Oring @ SV107 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV854 @ SV1516 @ SV107 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1956 @ SV854 @ SV107 ) @ SV1516 @ SV107 ) @ SV2163 @ SV107 ) @ SV107 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1956 @ SV1516 @ SV107 ) @ SV2163 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5907]) ).
thf(6318,plain,
! [SV1518: $i,SV109: $i,SV856: $i] :
( ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ SV856 @ SV109 ) @ SV1518 @ SV109 )
= $false )
| ( ( c_lessequals @ SV856 @ SV1518 @ SV109 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(6319,plain,
! [SV2164: $i,SV1957: $i,SV1519: $i,SV857: $i,SV110: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5909]) ).
thf(6320,plain,
! [SV112: $i,SV1959: $i,SV1521: $i,SV859: $i] :
( ( ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
= $true )
| ( ( ~ ( c_lessequals @ SV859 @ SV1959 @ SV112 )
| ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5911]) ).
thf(6321,plain,
! [SV113: $i,SV1960: $i,SV1522: $i,SV860: $i] :
( ( ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
= $true )
| ( ( ~ ( c_lessequals @ SV860 @ SV1960 @ SV113 )
| ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5912]) ).
thf(6322,plain,
! [SV114: $i,SV1961: $i,SV1523: $i,SV861: $i] :
( ( ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
= $true )
| ( ( ~ ( c_lessequals @ SV861 @ SV1961 @ SV114 )
| ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5913]) ).
thf(6323,plain,
! [SV121: $i,SV1530: $i,SV868: $i] :
( ( ( c_lessequals @ SV868 @ SV1530 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV868 @ SV121 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1530 @ SV121 ) @ SV121 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5914]) ).
thf(6324,plain,
! [SV1531: $i,SV122: $i,SV869: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV869 @ SV122 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1531 @ SV122 ) @ SV122 )
= $false )
| ( ( c_lessequals @ SV869 @ SV1531 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(6325,plain,
! [SV1962: $i,SV1532: $i,SV871: $i,SV124: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV124 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ SV124 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5916]) ).
thf(6326,plain,
! [SV1963: $i,SV1533: $i,SV872: $i,SV125: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV125 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ SV125 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5917]) ).
thf(6327,plain,
! [SV2165: $i,SV1964: $i,SV1538: $i,SV877: $i,SV131: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV131 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(6328,plain,
! [SV135: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5919]) ).
thf(6329,plain,
! [SV144: $i,SV1968: $i,SV1546: $i,SV887: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SV1546 @ SV1968 @ SV144 ) @ SV144 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SV1968 @ SV144 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5923]) ).
thf(6330,plain,
! [SV145: $i,SV1969: $i,SV1547: $i,SV888: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SV1547 @ SV1969 @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SV1547 @ SV145 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5924]) ).
thf(6331,plain,
! [SV1970: $i,SV146: $i,SV1548: $i,SV889: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SV1548 @ SV146 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SV1970 @ SV146 ) @ SV1548 @ SV146 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5925]) ).
thf(6332,plain,
! [SV1971: $i,SV147: $i,SV1549: $i,SV890: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SV1549 @ SV147 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1971 @ SV890 @ SV147 ) @ SV1549 @ SV147 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5926]) ).
thf(6333,plain,
! [SV148: $i,SV1972: $i,SV1550: $i,SV891: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5927]) ).
thf(6334,plain,
! [SV894: $i,SV1551: $i,SV151: $i,SV1973: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1973 @ SV151 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1551 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SV1551 @ tc_nat ) @ tc_nat ) @ SV1973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SV1551 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5928]) ).
thf(6335,plain,
! [SV1974: $i,SV152: $i,SV1552: $i,SV895: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
| ~ ( c_lessequals @ SV1552 @ SV1974 @ SV152 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5929]) ).
thf(6336,plain,
! [SV1975: $i,SV153: $i,SV1553: $i,SV896: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
| ~ ( c_lessequals @ SV1553 @ SV1975 @ SV153 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5930]) ).
thf(6337,plain,
! [SV1976: $i,SV154: $i,SV1554: $i,SV897: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
| ~ ( c_lessequals @ SV897 @ SV1976 @ SV154 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5931]) ).
thf(6338,plain,
! [SV1977: $i,SV155: $i,SV1555: $i,SV898: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
= $true )
| ( ( ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
| ~ ( c_lessequals @ SV1977 @ SV1555 @ SV155 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5932]) ).
thf(6339,plain,
! [SV1978: $i,SV156: $i,SV1556: $i,SV899: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
= $true )
| ( ( ~ ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
| ~ ( c_lessequals @ SV1978 @ SV899 @ SV156 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5933]) ).
thf(6340,plain,
! [SV2166: $i,SV1979: $i,SV1557: $i,SV901: $i,SV158: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5934]) ).
thf(6341,plain,
! [SV2215: $i,SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV166 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5937]) ).
thf(6342,plain,
! [SV2216: $i,SV2168: $i,SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ( ~ ( class_Ring__and__Field_Odvd @ SV167 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5938]) ).
thf(6343,plain,
! [SV911: $i,SV1567: $i,SV168: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5939]) ).
thf(6344,plain,
! [SV912: $i,SV169: $i,SV1568: $i] :
( ( ( ~ ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5940]) ).
thf(6345,plain,
! [SV913: $i,SV170: $i,SV1569: $i] :
( ( ( ~ ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5941]) ).
thf(6346,plain,
! [SV915: $i,SV1570: $i,SV172: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5942]) ).
thf(6347,plain,
! [SV916: $i,SV173: $i,SV1571: $i] :
( ( ( ~ ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5943]) ).
thf(6348,plain,
! [SV917: $i,SV1572: $i,SV174: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5944]) ).
thf(6349,plain,
! [SV1590: $i,SV939: $i,SV196: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SV1590 @ SV196 ) @ SV196 ) )
= $true )
| ( ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5960]) ).
thf(6350,plain,
! [SV940: $i,SV1591: $i,SV197: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1591 @ SV197 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SV1591 @ SV940 @ SV197 ) @ SV197 ) )
= $true )
| ( ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5961]) ).
thf(6351,plain,
! [SV941: $i,SV1592: $i,SV198: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1592 @ SV198 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SV1592 @ SV198 ) @ SV198 ) )
= $true )
| ( ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5962]) ).
thf(6352,plain,
! [SV1593: $i,SV942: $i,SV199: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SV1593 @ SV942 @ SV199 ) @ SV199 ) )
= $true )
| ( ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5963]) ).
thf(6353,plain,
! [SV1595: $i,SV202: $i,SV1998: $i,SV944: $i] :
( ( ( c_lessequals @ SV944 @ SV1998 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV202 @ SV1595 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1595 @ SV1998 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5965]) ).
thf(6354,plain,
! [SV2169: $i,SV1999: $i,SV1596: $i,SV945: $i,SV204: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5966]) ).
thf(6355,plain,
! [SV2170: $i,SV2000: $i,SV1597: $i,SV946: $i,SV205: $i] :
( ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5967]) ).
thf(6356,plain,
! [SV2001: $i,SV1598: $i,SV219: $i,SV960: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV2001 @ SV219 ) @ SV219 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5977]) ).
thf(6357,plain,
! [SV2002: $i,SV1599: $i,SV220: $i,SV961: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SV2002 @ SV961 @ SV220 ) @ SV220 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5978]) ).
thf(6358,plain,
! [SV221: $i,SV2003: $i,SV1600: $i,SV962: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5979]) ).
thf(6359,plain,
! [SV2171: $i,SV2004: $i,SV1601: $i,SV963: $i,SV223: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV223 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV1601 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV2004 @ SV2171 @ SV223 ) @ SV223 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV963 @ SV2004 @ SV223 ) @ ( c_HOL_Oplus__class_Oplus @ SV1601 @ SV2171 @ SV223 ) @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(6360,plain,
! [SV2015: $i,SV1621: $i,SV986: $i,SV248: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV248 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5991]) ).
thf(6361,plain,
! [SV2016: $i,SV252: $i,SV1624: $i,SV990: $i] :
( ( ( c_lessequals @ SV990 @ SV1624 @ SV252 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5992]) ).
thf(6362,plain,
! [SV2017: $i,SV253: $i,SV1625: $i,SV991: $i] :
( ( ( c_lessequals @ SV991 @ SV1625 @ SV253 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 )
| ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5993]) ).
thf(6363,plain,
! [SV2018: $i,SV254: $i,SV1626: $i,SV992: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
= $true )
| ( ( ~ ( c_lessequals @ SV1626 @ SV2018 @ SV254 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5994]) ).
thf(6364,plain,
! [SV2019: $i,SV255: $i,SV1627: $i,SV993: $i] :
( ( ( c_lessequals @ SV993 @ SV1627 @ SV255 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5995]) ).
thf(6365,plain,
! [SV2020: $i,SV256: $i,SV1628: $i,SV994: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
= $true )
| ( ( ~ ( c_lessequals @ SV2020 @ SV1628 @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5996]) ).
thf(6366,plain,
! [SV2021: $i,SV257: $i,SV1629: $i,SV995: $i] :
( ( ( c_lessequals @ SV995 @ SV1629 @ SV257 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 )
| ~ ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5997]) ).
thf(6367,plain,
! [SV1630: $i,SV996: $i,SV258: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV258 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV996 @ SV1630 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV996 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV258 @ SV1630 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5998]) ).
thf(6368,plain,
! [SV997: $i,SV259: $i,SV1631: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1631 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV259 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1631 @ SV997 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV259 @ SV997 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5999]) ).
thf(6369,plain,
! [SV998: $i,SV260: $i,SV1632: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV260 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1632 @ SV998 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1632 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV260 @ SV998 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6000]) ).
thf(6370,plain,
! [SV999: $i,SV1633: $i,SV261: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV261 @ SV1633 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV999 @ SV1633 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1633 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV261 @ SV999 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6001]) ).
thf(6371,plain,
! [SV2172: $i,SV2022: $i,SV1634: $i,SV1000: $i,SV263: $i] :
( ( ( class_RealVector_Oreal__normed__algebra @ SV263 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ SV1000 @ SV1634 @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ SV2172 @ SV263 ) @ SV263 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SV2172 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1000 @ SV2022 @ SV263 ) @ SV2172 @ SV263 ) @ SV263 ) @ ( c_HOL_Otimes__class_Otimes @ SV2022 @ ( c_HOL_Ominus__class_Ominus @ SV1634 @ SV2172 @ SV263 ) @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6002]) ).
thf(6372,plain,
! [SV2173: $i,SV2023: $i,SV1636: $i,SV1002: $i,SV267: $i] :
( ( ( class_Ring__and__Field_Osemiring @ SV267 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1002 @ SV1636 @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2023 @ SV1636 @ SV267 ) @ SV2173 @ SV267 ) @ SV267 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ SV1002 @ SV2023 @ SV267 ) @ SV1636 @ SV267 ) @ SV2173 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6003]) ).
thf(6373,plain,
! [SV1006: $i,SV271: $i,SV1638: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6004]) ).
thf(6374,plain,
! [SV1007: $i,SV272: $i,SV1639: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1639 @ SV1639 @ SV272 ) @ ( c_HOL_Otimes__class_Otimes @ SV1007 @ SV1007 @ SV272 ) @ SV272 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) @ SV272 )
= $false )
| ( ( SV1007
= ( c_HOL_Ozero__class_Ozero @ SV272 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6005]) ).
thf(6375,plain,
! [SV1640: $i,SV273: $i,SV1008: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1008 @ SV1008 @ SV273 ) @ ( c_HOL_Otimes__class_Otimes @ SV1640 @ SV1640 @ SV273 ) @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV273 )
= $false )
| ( ( SV1008
= ( c_HOL_Ozero__class_Ozero @ SV273 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6006]) ).
thf(6376,plain,
! [SV2027: $i,SV298: $i,SV1652: $i,SV1026: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6012]) ).
thf(6377,plain,
! [SV2028: $i,SV299: $i,SV1653: $i,SV1027: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6013]) ).
thf(6378,plain,
! [SV2029: $i,SV300: $i,SV1654: $i,SV1028: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6014]) ).
thf(6379,plain,
! [SV2030: $i,SV301: $i,SV1655: $i,SV1029: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6015]) ).
thf(6380,plain,
! [SV2031: $i,SV302: $i,SV1656: $i,SV1030: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
| ~ ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6016]) ).
thf(6381,plain,
! [SV2032: $i,SV303: $i,SV1657: $i,SV1031: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 )
| ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6017]) ).
thf(6382,plain,
! [SV2033: $i,SV304: $i,SV1658: $i,SV1032: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6018]) ).
thf(6383,plain,
! [SV2034: $i,SV305: $i,SV1659: $i,SV1033: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
| ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6019]) ).
thf(6384,plain,
! [SV2035: $i,SV306: $i,SV1660: $i,SV1034: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
| ~ ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6020]) ).
thf(6385,plain,
! [SV2036: $i,SV307: $i,SV1661: $i,SV1035: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6021]) ).
thf(6386,plain,
! [SV2037: $i,SV308: $i,SV1662: $i,SV1036: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6022]) ).
thf(6387,plain,
! [SV2038: $i,SV309: $i,SV1663: $i,SV1037: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 )
| ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6023]) ).
thf(6388,plain,
! [SV2039: $i,SV310: $i,SV1664: $i,SV1038: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 )
| ~ ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6024]) ).
thf(6389,plain,
! [SV1665: $i,SV1039: $i,SV311: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV311 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV1665 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1039 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV311 @ SV1665 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6025]) ).
thf(6390,plain,
! [SV1040: $i,SV312: $i,SV1666: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1666 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV312 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1666 @ SV1040 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV312 @ SV1040 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(6391,plain,
! [SV1041: $i,SV1667: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV313 @ SV1667 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1041 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV313 @ SV1041 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1667 @ SV1041 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6027]) ).
thf(6392,plain,
! [SV314: $i,SV1668: $i,SV1042: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1042 @ SV1668 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV314 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1042 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV314 @ SV1668 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6028]) ).
thf(6393,plain,
! [SV1669: $i,SV1043: $i,SV315: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV315 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1043 @ SV1669 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1043 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV315 @ SV1669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6029]) ).
thf(6394,plain,
! [SV1670: $i,SV316: $i,SV1044: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1044 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV316 @ SV1670 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV316 @ SV1044 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1670 @ SV1044 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6030]) ).
thf(6395,plain,
! [SV2042: $i,SV320: $i,SV1674: $i,SV1048: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
= $true )
| ( ( ( SV2042
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SV2042 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SV2042 @ SV320 ) @ SV320 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6033]) ).
thf(6396,plain,
! [SV2043: $i,SV321: $i,SV1675: $i,SV1049: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
= $true )
| ( ( ( SV2043
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1675 @ SV321 ) @ SV321 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6034]) ).
thf(6397,plain,
! [SV1051: $i,SV323: $i,SV1677: $i] :
( ( ( ~ ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6036]) ).
thf(6398,plain,
! [SV1052: $i,SV1678: $i,SV324: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6037]) ).
thf(6399,plain,
! [SV1053: $i,SV325: $i,SV1679: $i] :
( ( ( ~ ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6038]) ).
thf(6400,plain,
! [SV1054: $i,SV1680: $i,SV326: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6039]) ).
thf(6401,plain,
! [SV1055: $i,SV327: $i,SV1681: $i] :
( ( ( ~ ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6040]) ).
thf(6402,plain,
! [SV1056: $i,SV1682: $i,SV328: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6041]) ).
thf(6403,plain,
! [SV1683: $i,SV329: $i,SV1057: $i] :
( ( ( ~ ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6042]) ).
thf(6404,plain,
! [SV1058: $i,SV1684: $i,SV331: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6043]) ).
thf(6405,plain,
! [SV1059: $i,SV1685: $i,SV332: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6044]) ).
thf(6406,plain,
! [SV333: $i,SV1060: $i,SV1686: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1686 @ SV1060 @ SV333 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1060 @ SV1686 @ SV333 )
= ( c_HOL_Ozero__class_Ozero @ SV333 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6407,plain,
! [SV1066: $i,SV340: $i,SV1689: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6050]) ).
thf(6408,plain,
! [SV342: $i,SV1690: $i,SV1068: $i] :
( ( ( c_lessequals @ SV1068 @ SV1690 @ SV342 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1068 @ SV1690 @ SV342 )
= SV1068 )
= $true )
| ( ( class_Orderings_Olinorder @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6051]) ).
thf(6409,plain,
! [SV343: $i,SV1069: $i,SV1691: $i] :
( ( ( c_lessequals @ SV1691 @ SV1069 @ SV343 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omin @ SV1069 @ SV1691 @ SV343 )
= SV1691 )
= $true )
| ( ( class_Orderings_Olinorder @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6052]) ).
thf(6410,plain,
! [SV1072: $i,SV1692: $i,SV346: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6053]) ).
thf(6411,plain,
! [SV1693: $i,SV350: $i,SV2046: $i,SV1075: $i] :
( ( ( c_lessequals @ SV1075 @ SV2046 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV350 @ SV1693 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1693 @ SV2046 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6054]) ).
thf(6412,plain,
! [SV2174: $i,SV2047: $i,SV1694: $i,SV1076: $i,SV351: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
| ~ ( c_lessequals @ SV1694 @ SV2174 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6055]) ).
thf(6413,plain,
! [SV2175: $i,SV1695: $i,SV1077: $i,SV352: $i,SV2048: $i] :
( ( ( c_lessequals @ SV2048 @ SV352 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV352 @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2048 @ SV1077 @ tc_nat ) @ SV2175 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV352 @ SV2048 @ tc_nat ) @ SV1077 @ tc_nat ) @ SV1695 @ tc_nat ) @ SV2175 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6056]) ).
thf(6414,plain,
! [SV2176: $i,SV1696: $i,SV1078: $i,SV2049: $i,SV353: $i] :
( ( ( c_lessequals @ SV353 @ SV2049 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV353 @ SV1078 @ tc_nat ) @ SV1696 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2049 @ SV1078 @ tc_nat ) @ SV2176 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1696 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2049 @ SV353 @ tc_nat ) @ SV1078 @ tc_nat ) @ SV2176 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6057]) ).
thf(6415,plain,
! [SV2177: $i,SV2050: $i,SV1698: $i,SV1082: $i,SV357: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add__abs @ SV357 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1082 @ SV1698 @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ SV2050 @ SV2177 @ SV357 ) @ SV357 ) @ SV357 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1082 @ SV2050 @ SV357 ) @ SV357 ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1698 @ SV2177 @ SV357 ) @ SV357 ) @ SV357 ) @ SV357 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6060]) ).
thf(6416,plain,
! [SV2051: $i,SV1699: $i,SV1083: $i,SV358: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV358 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6061]) ).
thf(6417,plain,
! [SV1085: $i,SV1700: $i,SV360: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1085 @ SV1700 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6062]) ).
thf(6418,plain,
! [SV1086: $i,SV1701: $i,SV361: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1701 @ SV1086 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6063]) ).
thf(6419,plain,
! [SV2178: $i,SV2052: $i,SV1702: $i,SV1087: $i,SV362: $i] :
( ( ( class_Ring__and__Field_Oring @ SV362 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1087 @ SV1702 @ SV362 ) @ SV2052 @ SV362 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2178 @ SV1702 @ SV362 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1087 @ SV2178 @ SV362 ) @ SV1702 @ SV362 ) @ SV2052 @ SV362 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6064]) ).
thf(6420,plain,
! [SV2053: $i,SV364: $i,SV1704: $i,SV1089: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV1704 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV2053 @ SV364 ) @ SV364 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1704 @ SV2053 @ SV364 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV364 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6065]) ).
thf(6421,plain,
! [SV2054: $i,SV365: $i,SV1705: $i,SV1090: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SV1705 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SV2054 @ SV1705 @ SV365 ) @ SV365 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SV2054 @ SV365 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV365 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6066]) ).
thf(6422,plain,
! [SV2056: $i,SV379: $i,SV1710: $i,SV1104: $i] :
( ( ( c_lessequals @ SV1104 @ SV1710 @ SV379 )
= $true )
| ( ( ~ ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SV1710 @ SV2056 @ SV379 ) @ SV379 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6068]) ).
thf(6423,plain,
! [SV2057: $i,SV380: $i,SV1711: $i,SV1105: $i] :
( ( ( c_lessequals @ SV1105 @ SV1711 @ SV380 )
= $true )
| ( ( ~ ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SV2057 @ SV1711 @ SV380 ) @ SV380 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6069]) ).
thf(6424,plain,
! [SV2058: $i,SV381: $i,SV1712: $i,SV1106: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SV1712 @ SV381 ) @ SV2058 @ SV381 )
= $true )
| ( ( ~ ( c_lessequals @ SV1106 @ SV2058 @ SV381 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6070]) ).
thf(6425,plain,
! [SV2059: $i,SV382: $i,SV1713: $i,SV1107: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SV1713 @ SV382 ) @ SV2059 @ SV382 )
= $true )
| ( ( ~ ( c_lessequals @ SV1713 @ SV2059 @ SV382 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6071]) ).
thf(6426,plain,
! [SV2060: $i,SV383: $i,SV1714: $i,SV1108: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SV1714 @ SV383 ) @ SV2060 @ SV383 )
= $true )
| ( ( ~ ( c_lessequals @ SV1108 @ SV2060 @ SV383 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6072]) ).
thf(6427,plain,
! [SV2061: $i,SV384: $i,SV1715: $i,SV1109: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SV1715 @ SV384 ) @ SV2061 @ SV384 )
= $true )
| ( ( ~ ( c_lessequals @ SV1715 @ SV2061 @ SV384 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6073]) ).
thf(6428,plain,
! [SV2062: $i,SV385: $i,SV1716: $i,SV1110: $i] :
( ( ( c_lessequals @ SV1110 @ SV1716 @ SV385 )
= $true )
| ( ( ~ ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SV1716 @ SV2062 @ SV385 ) @ SV385 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV385 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6074]) ).
thf(6429,plain,
! [SV2063: $i,SV386: $i,SV1717: $i,SV1111: $i] :
( ( ( c_lessequals @ SV1111 @ SV1717 @ SV386 )
= $true )
| ( ( ~ ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SV2063 @ SV1717 @ SV386 ) @ SV386 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV386 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6075]) ).
thf(6430,plain,
! [SV2064: $i,SV388: $i,SV1718: $i,SV1113: $i] :
( ( ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
= $true )
| ( ( ( c_lessequals @ SV2064 @ SV1718 @ SV388 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2064 @ SV1113 @ SV388 ) @ SV1718 @ SV388 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6076]) ).
thf(6431,plain,
! [SV2179: $i,SV1117: $i,SV2066: $i,SV1722: $i,SV392: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SV2179 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ SV2179 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6078]) ).
thf(6432,plain,
! [SV2180: $i,SV1723: $i,SV1118: $i,SV2067: $i,SV393: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SV2067 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SV2180 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2067 @ SV393 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2067 @ SV1118 @ tc_nat ) @ SV2180 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6079]) ).
thf(6433,plain,
! [SV2181: $i,SV1119: $i,SV394: $i,SV2068: $i,SV1724: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SV2068 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1724 @ SV1119 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6080]) ).
thf(6434,plain,
! [SV2182: $i,SV1120: $i,SV395: $i,SV2069: $i,SV1725: $i] :
( ( ( ~ ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2069 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV395 @ SV2069 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2069 @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6081]) ).
thf(6435,plain,
! [SV2183: $i,SV2070: $i,SV1728: $i,SV1134: $i,SV412: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
| ~ ( c_lessequals @ SV1728 @ SV2183 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6083]) ).
thf(6436,plain,
! [SV2184: $i,SV2071: $i,SV1729: $i,SV1135: $i,SV413: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6084]) ).
thf(6437,plain,
! [SV1136: $i,SV414: $i,SV1730: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6085]) ).
thf(6438,plain,
! [SV1137: $i,SV415: $i,SV1731: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6086]) ).
thf(6439,plain,
! [SV2072: $i,SV416: $i,SV1732: $i,SV1138: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
= $true )
| ( ( ~ ( c_lessequals @ SV1138 @ SV2072 @ SV416 )
| ~ ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6087]) ).
thf(6440,plain,
! [SV2073: $i,SV417: $i,SV1733: $i,SV1139: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 )
| ~ ( c_lessequals @ SV2073 @ SV1733 @ SV417 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6088]) ).
thf(6441,plain,
! [SV2074: $i,SV418: $i,SV1734: $i,SV1140: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
= $true )
| ( ( ~ ( c_lessequals @ SV2074 @ SV1734 @ SV418 )
| ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6089]) ).
thf(6442,plain,
! [SV2075: $i,SV419: $i,SV1735: $i,SV1141: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 )
| ~ ( c_lessequals @ SV1141 @ SV2075 @ SV419 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6090]) ).
thf(6443,plain,
! [SV2076: $i,SV420: $i,SV1736: $i,SV1142: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SV1736 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SV2076 @ SV1736 @ SV420 ) @ SV420 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1142 @ SV2076 @ SV420 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6091]) ).
thf(6444,plain,
! [SV2077: $i,SV421: $i,SV1737: $i,SV1143: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SV1737 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SV2077 @ SV1737 @ SV421 ) @ SV421 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1143 @ SV2077 @ SV421 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6092]) ).
thf(6445,plain,
! [SV2078: $i,SV422: $i,SV1738: $i,SV1144: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1738 @ SV422 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SV2078 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SV1738 @ SV2078 @ SV422 ) @ SV422 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6093]) ).
thf(6446,plain,
! [SV2079: $i,SV423: $i,SV1739: $i,SV1145: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV1739 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV2079 @ SV423 ) @ SV423 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SV2079 @ SV423 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6094]) ).
thf(6447,plain,
! [SV2080: $i,SV424: $i,SV1740: $i,SV1146: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV1740 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV2080 @ SV424 ) @ SV424 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SV2080 @ SV424 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6095]) ).
thf(6448,plain,
! [SV2081: $i,SV425: $i,SV1741: $i,SV1147: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1147 @ SV1741 @ SV425 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1741 @ SV425 ) @ SV425 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6096]) ).
thf(6449,plain,
! [SV426: $i,SV1742: $i,SV1148: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1148 @ SV1742 @ SV426 )
= $false )
| ( ( c_lessequals @ SV1148 @ SV1742 @ SV426 )
= $true )
| ( ( class_Orderings_Opreorder @ SV426 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6097]) ).
thf(6450,plain,
! [SV427: $i,SV1743: $i,SV1149: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1149 @ SV1743 @ SV427 )
= $false )
| ( ( c_lessequals @ SV1149 @ SV1743 @ SV427 )
= $true )
| ( ( class_Orderings_Oorder @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6098]) ).
thf(6451,plain,
! [SV2185: $i,SV2082: $i,SV1744: $i,SV1150: $i,SV428: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6099]) ).
thf(6452,plain,
! [SV429: $i,SV1151: $i,SV1745: $i] :
( ( ( c_lessequals @ SV1745 @ SV1151 @ SV429 )
= $true )
| ( ( ~ ( c_lessequals @ SV1151 @ SV1745 @ SV429 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1745 @ SV429 )
= $true )
| ( ( class_Orderings_Opreorder @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6100]) ).
thf(6453,plain,
! [SV2083: $i,SV430: $i,SV1746: $i,SV1152: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2083 @ SV1746 @ SV430 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2083 @ SV1152 @ SV430 ) @ SV1746 @ SV430 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6454,plain,
! [SV1747: $i,SV431: $i,SV1153: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1153 @ SV431 ) @ SV1747 @ SV431 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1153 @ SV1747 @ SV431 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV431 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6102]) ).
thf(6455,plain,
! [SV2084: $i,SV432: $i,SV1748: $i,SV1154: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SV2084 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SV2084 @ SV432 ) @ SV432 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6103]) ).
thf(6456,plain,
! [SV2085: $i,SV433: $i,SV1749: $i,SV1155: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1155 @ SV433 ) @ SV433 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6104]) ).
thf(6457,plain,
! [SV434: $i,SV1156: $i,SV1750: $i] :
( ( ( SV1750 = SV1156 )
= $true )
| ( ( ~ ( c_lessequals @ SV1156 @ SV1750 @ SV434 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1750 @ SV434 )
= $true )
| ( ( class_Orderings_Oorder @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6105]) ).
thf(6458,plain,
! [SV435: $i,SV1751: $i,SV1157: $i] :
( ( ( ~ ( c_lessequals @ SV1157 @ SV1751 @ SV435 ) )
= $true )
| ( ( SV1751 = SV1157 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1751 @ SV435 )
= $true )
| ( ( class_Orderings_Oorder @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6106]) ).
thf(6459,plain,
! [SV436: $i,SV1752: $i,SV1158: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1752 @ SV436 )
= $true )
| ( ( ~ ( c_lessequals @ SV1158 @ SV1752 @ SV436 ) )
= $true )
| ( ( SV1158 = SV1752 )
= $true )
| ( ( class_Orderings_Olinorder @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6107]) ).
thf(6460,plain,
! [SV437: $i,SV1753: $i,SV1159: $i] :
( ( ( ~ ( c_lessequals @ SV1159 @ SV1753 @ SV437 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1159 @ SV1753 @ SV437 )
= $true )
| ( ( SV1159 = SV1753 )
= $true )
| ( ( class_Orderings_Olinorder @ SV437 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6108]) ).
thf(6461,plain,
! [SV438: $i,SV1754: $i,SV1160: $i] :
( ( ( ~ ( c_lessequals @ SV1160 @ SV1754 @ SV438 ) )
= $true )
| ( ( SV1160 = SV1754 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV1754 @ SV438 )
= $true )
| ( ( class_Orderings_Oorder @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6109]) ).
thf(6462,plain,
! [SV439: $i,SV1755: $i,SV1161: $i] :
( ( ( SV1161 = SV1755 )
= $true )
| ( ( ~ ( c_lessequals @ SV1161 @ SV1755 @ SV439 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1755 @ SV439 )
= $true )
| ( ( class_Orderings_Oorder @ SV439 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6110]) ).
thf(6463,plain,
! [SV440: $i,SV1756: $i,SV1162: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1162 @ SV1756 @ SV440 )
= $true )
| ( ( ~ ( c_lessequals @ SV1162 @ SV1756 @ SV440 ) )
= $true )
| ( ( SV1162 = SV1756 )
= $true )
| ( ( class_Orderings_Oorder @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6111]) ).
thf(6464,plain,
! [SV441: $i,SV1757: $i,SV1163: $i] :
( ( ( SV1163 = SV1757 )
= $true )
| ( ( ~ ( c_lessequals @ SV1163 @ SV1757 @ SV441 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV1757 @ SV441 )
= $true )
| ( ( class_Orderings_Oorder @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6112]) ).
thf(6465,plain,
! [SV442: $i,SV2086: $i,SV1758: $i,SV1164: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6113]) ).
thf(6466,plain,
! [SV443: $i,SV1759: $i,SV1165: $i] :
( ( ( c_lessequals @ SV1165 @ SV1759 @ SV443 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1759 @ SV1165 @ SV443 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6114]) ).
thf(6467,plain,
! [SV445: $i,SV1167: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1167 @ SV1167 @ SV445 )
= $false )
| ( ( c_lessequals @ SV1167 @ SV1167 @ SV445 )
= $false )
| ( ( class_Orderings_Olinorder @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6116]) ).
thf(6468,plain,
! [SV447: $i,SV1761: $i,SV1169: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1169 @ SV1761 @ SV447 )
= $false )
| ( ( ~ ( c_lessequals @ SV1761 @ SV1169 @ SV447 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6117]) ).
thf(6469,plain,
! [SV450: $i,SV1764: $i,SV1172: $i] :
( ( ( c_lessequals @ SV1172 @ SV1764 @ SV450 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1764 @ SV1172 @ SV450 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(6470,plain,
! [SV2087: $i,SV451: $i,SV1765: $i,SV1173: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SV1765 @ SV451 ) @ SV2087 @ SV451 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1765 @ SV2087 @ SV451 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6121]) ).
thf(6471,plain,
! [SV2088: $i,SV452: $i,SV1766: $i,SV1174: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SV1766 @ SV452 ) @ SV2088 @ SV452 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1174 @ SV2088 @ SV452 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV452 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6122]) ).
thf(6472,plain,
! [SV2089: $i,SV453: $i,SV1767: $i,SV1175: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV1767 @ SV453 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SV2089 @ SV1767 @ SV453 ) @ SV453 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6123]) ).
thf(6473,plain,
! [SV2090: $i,SV454: $i,SV1768: $i,SV1176: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1176 @ SV1768 @ SV454 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2090 @ SV454 ) @ SV454 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV454 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6124]) ).
thf(6474,plain,
! [SV2091: $i,SV455: $i,SV1769: $i,SV1177: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SV1769 @ SV455 ) @ SV2091 @ SV455 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1769 @ SV2091 @ SV455 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6125]) ).
thf(6475,plain,
! [SV2092: $i,SV456: $i,SV1770: $i,SV1178: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SV1770 @ SV456 ) @ SV2092 @ SV456 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1178 @ SV2092 @ SV456 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6126]) ).
thf(6476,plain,
! [SV457: $i,SV2093: $i,SV1771: $i,SV1179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SV1771 @ SV2093 @ SV457 ) @ SV457 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1771 @ SV457 ) @ SV457 ) @ SV2093 @ SV457 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6127]) ).
thf(6477,plain,
! [SV2217: $i,SV2186: $i,SV2094: $i,SV1772: $i,SV1180: $i,SV458: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV458 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2186 @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2186 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6128]) ).
thf(6478,plain,
! [SV2218: $i,SV2187: $i,SV2095: $i,SV1773: $i,SV1181: $i,SV459: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV459 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SV2187 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6129]) ).
thf(6479,plain,
! [SV2219: $i,SV2188: $i,SV2096: $i,SV1774: $i,SV1182: $i,SV460: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV460 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2188 @ SV1774 @ SV460 ) @ SV2219 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV2188 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SV2219 @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6130]) ).
thf(6480,plain,
! [SV2220: $i,SV2189: $i,SV2097: $i,SV1775: $i,SV1183: $i,SV461: $i] :
( ( ( ~ ( class_Ring__and__Field_Opordered__ring @ SV461 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ SV2220 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SV2220 @ SV461 ) @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6131]) ).
thf(6481,plain,
! [SV2098: $i,SV462: $i,SV1776: $i,SV1184: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6132]) ).
thf(6482,plain,
! [SV468: $i,SV2103: $i,SV1782: $i,SV1190: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6137]) ).
thf(6483,plain,
! [SV2190: $i,SV2108: $i,SV1788: $i,SV1201: $i,SV479: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV479 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1201 @ SV1788 @ SV479 ) @ ( c_HOL_Oplus__class_Oplus @ SV2108 @ SV2190 @ SV479 ) @ SV479 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1201 @ SV2108 @ SV479 ) @ ( c_HOL_Ominus__class_Ominus @ SV1788 @ SV2190 @ SV479 ) @ SV479 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6143]) ).
thf(6484,plain,
! [SV1793: $i,SV489: $i,SV2109: $i,SV1210: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1210 @ SV2109 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1793 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1793 @ SV2109 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6144]) ).
thf(6485,plain,
! [SV1226: $i,SV1795: $i,SV509: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV509 ) @ SV1795 @ SV509 )
= $false )
| ( ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV1226 @ SV509 ) @ SV1795 @ SV509 )
= ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV1226 @ SV1795 @ SV509 ) @ SV509 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(6486,plain,
! [SV1796: $i,SV512: $i,SV1229: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1229 @ SV512 ) @ SV1796 @ SV512 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1229 @ SV1796 @ SV512 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV512 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(6487,plain,
! [SV513: $i,SV1797: $i,SV1230: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1230 @ SV1797 @ SV513 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oabs__class_Oabs @ SV1230 @ SV513 ) @ SV1797 @ SV513 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV513 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(6488,plain,
! [SV514: $i,SV1798: $i,SV1231: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ ( c_HOL_Oabs__class_Oabs @ SV1798 @ SV514 ) @ SV514 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1231 @ SV1798 @ SV514 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6148]) ).
thf(6489,plain,
! [SV515: $i,SV1799: $i,SV1232: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ SV1799 @ SV515 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1232 @ ( c_HOL_Oabs__class_Oabs @ SV1799 @ SV515 ) @ SV515 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV515 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6149]) ).
thf(6490,plain,
! [SV1234: $i,SV1800: $i,SV517: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6150]) ).
thf(6491,plain,
! [SV522: $i,SV1239: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1239 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1239 @ SV522 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV522 @ SV1239 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6151]) ).
thf(6492,plain,
! [SV523: $i,SV1801: $i,SV1240: $i] :
( ( ( c_lessequals @ SV1240 @ SV1801 @ SV523 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1240 @ SV1801 @ SV523 ) @ ( c_HOL_Ozero__class_Ozero @ SV523 ) @ SV523 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6152]) ).
thf(6493,plain,
! [SV524: $i,SV1802: $i,SV1241: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1241 @ SV1802 @ SV524 ) @ ( c_HOL_Ozero__class_Ozero @ SV524 ) @ SV524 )
= $false )
| ( ( c_lessequals @ SV1241 @ SV1802 @ SV524 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6153]) ).
thf(6494,plain,
! [SV1246: $i,SV529: $i,SV1803: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV529 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1803 @ SV1246 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1803 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV529 @ SV1246 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6154]) ).
thf(6495,plain,
! [SV1247: $i,SV530: $i,SV1804: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1804 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV530 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1804 @ SV1247 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV530 @ SV1247 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6155]) ).
thf(6496,plain,
! [SV1805: $i,SV1248: $i,SV531: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV531 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1248 @ SV1805 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1248 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV531 @ SV1805 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6156]) ).
thf(6497,plain,
! [SV2191: $i,SV2110: $i,SV1808: $i,SV1253: $i,SV536: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6159]) ).
thf(6498,plain,
! [SV2192: $i,SV2111: $i,SV1809: $i,SV1254: $i,SV537: $i] :
( ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6160]) ).
thf(6499,plain,
! [SV2112: $i,SV544: $i,SV1811: $i,SV1260: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SV1811 @ SV544 ) @ SV2112 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SV2112 @ SV544 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV2112 @ SV1811 @ SV544 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV544 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6163]) ).
thf(6500,plain,
! [SV547: $i,SV1263: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1263 @ SV547 )
= SV1263 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1263 @ ( c_HOL_Ozero__class_Ozero @ SV547 ) @ SV547 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV547 )
= $false )
| ( ( class_Orderings_Olinorder @ SV547 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6166]) ).
thf(6501,plain,
! [SV2193: $i,SV2113: $i,SV1812: $i,SV1265: $i,SV549: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6167]) ).
thf(6502,plain,
! [SV1271: $i,SV1814: $i,SV557: $i] :
( ( ( c_lessequals @ SV557 @ SV1814 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1814 @ SV1271 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV557 @ SV1271 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6169]) ).
thf(6503,plain,
! [SV2194: $i,SV2114: $i,SV1815: $i,SV1272: $i,SV559: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
= $false )
| ( ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
| ~ ( c_lessequals @ SV2194 @ SV2114 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6170]) ).
thf(6504,plain,
! [SV2115: $i,SV560: $i,SV1816: $i,SV1273: $i] :
( ( ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
= $true )
| ( ( ~ ( c_lessequals @ SV2115 @ SV1816 @ SV560 )
| ~ ( c_lessequals @ SV1273 @ SV2115 @ SV560 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV560 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6171]) ).
thf(6505,plain,
! [SV1274: $i,SV561: $i,SV1817: $i] :
( ( ( ~ ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6172]) ).
thf(6506,plain,
! [SV2116: $i,SV562: $i,SV1818: $i,SV1275: $i] :
( ( ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
= $true )
| ( ( ~ ( c_lessequals @ SV1275 @ SV2116 @ SV562 )
| ~ ( c_lessequals @ SV2116 @ SV1818 @ SV562 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6173]) ).
thf(6507,plain,
! [SV2117: $i,SV569: $i,SV1821: $i,SV1281: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV2117 @ SV569 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1281 @ SV569 ) @ SV569 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6175]) ).
thf(6508,plain,
! [SV2118: $i,SV1822: $i,SV570: $i,SV1282: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1822 @ SV2118 @ SV570 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV2118 @ SV570 ) @ SV570 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6176]) ).
thf(6509,plain,
! [SV2119: $i,SV571: $i,SV1823: $i,SV1283: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SV2119 @ SV571 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV2119 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SV2119 @ SV571 ) @ SV571 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6177]) ).
thf(6510,plain,
! [SV2120: $i,SV1824: $i,SV572: $i,SV1284: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1824 @ SV2120 @ SV572 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SV2120 @ SV1284 @ SV572 ) @ SV572 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6178]) ).
thf(6511,plain,
! [SV1292: $i,SV580: $i,SV1828: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV580 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1828 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV1292 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6183]) ).
thf(6512,plain,
! [SV581: $i,SV1293: $i,SV1829: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1829 @ SV1293 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1829 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SV1829 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6184]) ).
thf(6513,plain,
! [SV1305: $i,SV1832: $i,SV598: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV598 @ SV1832 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1832 @ SV1305 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV598 ) @ SV1305 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6185]) ).
thf(6514,plain,
! [SV609: $i,SV1316: $i,SV1838: $i] :
( ( ( c_lessequals @ SV1838 @ SV1316 @ tc_nat )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1316 @ SV1838 @ tc_nat ) @ SV609 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1316 @ SV609 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1838 @ SV609 ) @ SV609 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6186]) ).
thf(6515,plain,
! [SV1843: $i,SV1324: $i,SV618: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1324 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ SV1843 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV618 @ ( c_HOL_Ominus__class_Ominus @ SV1324 @ SV1843 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6187]) ).
thf(6516,plain,
! [SV621: $i,SV1325: $i,SV1844: $i] :
( ( ( ~ ( c_lessequals @ SV1844 @ SV1325 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1844 @ SV621 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6188]) ).
thf(6517,plain,
! [SV622: $i,SV1845: $i,SV1326: $i] :
( ( ( ~ ( c_lessequals @ SV1326 @ SV1845 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV622 @ SV1845 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6189]) ).
thf(6518,plain,
! [SV1851: $i,SV632: $i,SV1335: $i] :
( ( ( c_lessequals @ SV1335 @ SV632 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1335 @ SV1851 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1335 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1851 @ SV1335 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV632 @ SV1851 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6191]) ).
thf(6519,plain,
! [SV635: $i,SV1852: $i,SV1338: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1338 @ SV1852 @ SV635 ) @ ( c_HOL_Ozero__class_Ozero @ SV635 ) @ SV635 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1338 @ SV1852 @ SV635 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6192]) ).
thf(6520,plain,
! [SV636: $i,SV1853: $i,SV1339: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1339 @ SV1853 @ SV636 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1339 @ SV1853 @ SV636 ) @ ( c_HOL_Ozero__class_Ozero @ SV636 ) @ SV636 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV636 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6193]) ).
thf(6521,plain,
! [SV2123: $i,SV637: $i,SV1854: $i,SV1340: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SV1854 @ SV637 ) @ SV2123 @ SV637 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV2123 @ SV1340 @ SV637 ) @ SV637 ) @ SV1854 @ SV637 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6194]) ).
thf(6522,plain,
! [SV638: $i,SV1855: $i,SV1341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1341 @ SV1855 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1341 @ SV638 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1855 @ SV638 ) @ SV638 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6195]) ).
thf(6523,plain,
! [SV1856: $i,SV639: $i,SV1342: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1342 @ SV639 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1856 @ SV639 ) @ SV639 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1342 @ SV1856 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6196]) ).
thf(6524,plain,
! [SV1345: $i,SV642: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV642 @ SV1345 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV642 @ SV1345 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV1345 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV642 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6198]) ).
thf(6525,plain,
! [SV643: $i,SV1346: $i] :
( ( ( c_Parity_Oeven__odd__class_Oeven @ ( c_HOL_Ominus__class_Ominus @ SV1346 @ SV643 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1346 @ SV643 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV1346 @ tc_nat )
= $true )
| ( ( c_Parity_Oeven__odd__class_Oeven @ SV643 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6199]) ).
thf(6526,plain,
! [SV646: $i,SV1349: $i,SV1859: $i] :
( ( ( ~ ( c_lessequals @ SV1859 @ SV1349 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1859 @ SV646 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6200]) ).
thf(6527,plain,
! [SV647: $i,SV1860: $i,SV1350: $i] :
( ( ( ~ ( c_lessequals @ SV1350 @ SV1860 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6201]) ).
thf(6528,plain,
! [SV1355: $i,SV1861: $i,SV652: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV652 @ SV1861 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1355 @ SV652 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV652 @ SV1355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1861 @ SV1355 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6202]) ).
thf(6529,plain,
! [SV654: $i,SV1862: $i,SV1357: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV1862 @ SV654 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1862 @ SV1357 @ SV654 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV654 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6203]) ).
thf(6530,plain,
! [SV655: $i,SV1863: $i,SV1358: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1358 @ SV1863 @ SV655 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1863 @ SV1358 @ SV655 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV655 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6204]) ).
thf(6531,plain,
! [SV656: $i,SV1864: $i,SV1359: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1359 @ SV1864 @ SV656 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1864 @ SV1359 @ SV656 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV656 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6205]) ).
thf(6532,plain,
! [SV657: $i,SV1865: $i,SV1360: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1360 @ SV1865 @ SV657 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1865 @ SV1360 @ SV657 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6206]) ).
thf(6533,plain,
! [SV664: $i,SV1365: $i,SV1867: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1867 @ SV1365 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1867 @ SV664 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV664 @ SV1867 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6207]) ).
thf(6534,plain,
! [SV665: $i,SV1366: $i,SV1868: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1868 @ SV1366 @ SV665 )
= $true )
| ( ( SV1868 = SV1366 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1366 @ SV1868 @ SV665 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6208]) ).
thf(6535,plain,
! [SV666: $i,SV1367: $i,SV1869: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1869 @ SV1367 @ SV666 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1367 @ SV1869 @ SV666 )
= $true )
| ( ( SV1367 = SV1869 )
= $true )
| ( ( class_Orderings_Olinorder @ SV666 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6209]) ).
thf(6536,plain,
! [SV667: $i,SV1870: $i,SV1368: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1368 @ SV1870 @ SV667 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1870 @ SV1368 @ SV667 )
= $true )
| ( ( SV1368 = SV1870 )
= $true )
| ( ( class_Orderings_Olinorder @ SV667 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6210]) ).
thf(6537,plain,
! [SV668: $i,SV1369: $i,SV1871: $i] :
( ( ( SV1871 = SV1369 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1871 @ SV1369 @ SV668 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1369 @ SV1871 @ SV668 )
= $true )
| ( ( class_Orderings_Olinorder @ SV668 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6211]) ).
thf(6538,plain,
! [SV671: $i,SV1372: $i,SV1872: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1872 @ SV1372 @ SV671 )
= $true )
| ( ( SV1872 = SV1372 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1372 @ SV1872 @ SV671 )
= $true )
| ( ( class_Orderings_Olinorder @ SV671 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6212]) ).
thf(6539,plain,
! [SV2124: $i,SV672: $i,SV1873: $i,SV1373: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 )
| ~ ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6213]) ).
thf(6540,plain,
! [SV2125: $i,SV673: $i,SV1874: $i,SV1374: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 )
| ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6214]) ).
thf(6541,plain,
! [SV1878: $i,SV681: $i,SV1380: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1380 @ SV1380 @ SV681 ) @ ( c_HOL_Otimes__class_Otimes @ SV1878 @ SV1878 @ SV681 ) @ SV681 )
= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
= $false )
| ( ( SV1380
= ( c_HOL_Ozero__class_Ozero @ SV681 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV681 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(6542,plain,
! [SV2126: $i,SV1879: $i,SV1381: $i,SV682: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV682 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
| ( SV1879 = SV2126 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV682 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6217]) ).
thf(6543,plain,
! [SV2195: $i,SV2127: $i,SV1880: $i,SV1382: $i,SV683: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV683 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV1880 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV2127 @ ( c_HOL_Otimes__class_Otimes @ SV1382 @ SV2195 @ tc_nat ) @ tc_nat ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV683 @ SV1382 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ SV2127 @ SV1382 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6218]) ).
thf(6544,plain,
! [SV1881: $i,SV684: $i,SV1383: $i] :
( ( ( ( c_HOL_Oabs__class_Oabs @ SV1383 @ SV684 )
= ( c_HOL_Oabs__class_Oabs @ SV1881 @ SV684 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1383 @ SV1881 @ SV684 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV684 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6219]) ).
thf(6545,plain,
! [SV2128: $i,SV685: $i,SV1882: $i,SV1384: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV1882 @ SV685 )
!= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV2128 @ SV685 ) )
= $true )
| ( ( SV1882 = SV2128 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6220]) ).
thf(6546,plain,
! [SV686: $i,SV1883: $i,SV1385: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6221]) ).
thf(6547,plain,
! [SV2196: $i,SV2129: $i,SV1884: $i,SV1387: $i,SV688: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
| ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SV2196 @ SV2129 @ SV688 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6222]) ).
thf(6548,plain,
! [SV689: $i,SV1885: $i,SV1388: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SV1885 @ SV689 )
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
= $false )
| ( ( ( SV1885
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
| ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6223]) ).
thf(6549,plain,
! [SV2197: $i,SV2130: $i,SV1886: $i,SV1389: $i,SV690: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
| ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6224]) ).
thf(6550,plain,
! [SV691: $i,SV1887: $i,SV1390: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1390 @ SV1887 @ SV691 )
= ( c_HOL_Ozero__class_Ozero @ SV691 ) )
= $false )
| ( ( SV1390 = SV1887 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV691 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6225]) ).
thf(6551,plain,
! [SV693: $i,SV1888: $i,SV1391: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SV1888 @ SV693 )
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
= $false )
| ( ( ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
| ( SV1888
= ( c_HOL_Ozero__class_Ozero @ SV693 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6226]) ).
thf(6552,plain,
! [SV2131: $i,SV696: $i,SV1889: $i,SV1393: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SV1889 @ SV696 )
!= ( c_HOL_Ominus__class_Ominus @ SV2131 @ SV2131 @ SV696 ) )
= $true )
| ( ( SV1393 = SV1889 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV696 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6227]) ).
thf(6553,plain,
! [SV1890: $i,SV1395: $i,SV698: $i] :
( ( ( class_Int_Onumber__ring @ SV698 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
| ( SV1395 = SV1890 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV698 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6228]) ).
thf(6554,plain,
! [SV2198: $i,SV2132: $i,SV1891: $i,SV1397: $i,SV702: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV702 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2132 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2198 @ SV702 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SV2132 @ SV702 )
= SV2198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6229]) ).
thf(6555,plain,
! [SV704: $i,SV1892: $i,SV1399: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1399 @ SV1892 @ SV704 )
= ( c_HOL_Ozero__class_Ozero @ SV704 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1892 @ SV1399 @ SV704 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV704 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6230]) ).
thf(6556,plain,
! [SV705: $i,SV1893: $i,SV1400: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6231]) ).
thf(6557,plain,
! [SV2133: $i,SV1894: $i,SV708: $i,SV1402: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
!= ( c_HOL_Ominus__class_Ominus @ SV1894 @ SV2133 @ SV708 ) )
= $true )
| ( ( SV1894 = SV2133 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV708 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6232]) ).
thf(6558,plain,
! [SV2199: $i,SV2134: $i,SV1895: $i,SV1403: $i,SV709: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV709 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV709 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6233]) ).
thf(6559,plain,
! [SV2200: $i,SV2135: $i,SV1896: $i,SV1404: $i,SV710: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
| ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6234]) ).
thf(6560,plain,
! [SV2136: $i,SV712: $i,SV1406: $i,SV1897: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1897 @ SV1406 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV712 @ SV2136 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1897 @ SV2136 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6236]) ).
thf(6561,plain,
! [SV2221: $i,SV2201: $i,SV2137: $i,SV1898: $i,SV1407: $i,SV713: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV713 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6237]) ).
thf(6562,plain,
! [SV1899: $i,SV715: $i,SV1409: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1409 @ SV715 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1899 @ SV715 ) )
= $false )
| ( ( SV1409 = SV1899 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV715 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6238]) ).
thf(6563,plain,
! [SV1902: $i,SV1416: $i,SV722: $i] :
( ( ( class_Int_Onumber__ring @ SV722 )
= $false )
| ( ( ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
| ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV722 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(6564,plain,
! [SV724: $i,SV1903: $i,SV1418: $i] :
( ( ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SV1903 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
= $false )
| ( ( ( SV1903
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
| ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6241]) ).
thf(6565,plain,
! [SV2138: $i,SV725: $i,SV1904: $i,SV1419: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SV1904 @ SV725 )
!= ( c_HOL_Oplus__class_Oplus @ SV2138 @ SV1904 @ SV725 ) )
= $true )
| ( ( SV1419 = SV2138 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6242]) ).
thf(6566,plain,
! [SV2222: $i,SV2202: $i,SV2139: $i,SV1907: $i,SV1423: $i,SV729: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV729 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2202 @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
| ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2202 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6244]) ).
thf(6567,plain,
! [SV732: $i,SV1908: $i,SV1426: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1426 @ SV1908 @ SV732 )
= ( c_HOL_Ozero__class_Ozero @ SV732 ) )
= $false )
| ( ( SV1426 = SV1908 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV732 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6246]) ).
thf(6568,plain,
! [SV734: $i,SV1909: $i,SV1428: $i] :
( ( ( ( c_Orderings_Oord__class_Omin @ SV1428 @ SV1909 @ SV734 )
= SV1428 )
= $false )
| ( ( c_lessequals @ SV1428 @ SV1909 @ SV734 )
= $true )
| ( ( class_Orderings_Olinorder @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6247]) ).
thf(6569,plain,
! [SV735: $i,SV1910: $i,SV1429: $i] :
( ( ( c_lessequals @ SV1429 @ SV1910 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
| ( SV735 = SV1910 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6248]) ).
thf(6570,plain,
! [SV2203: $i,SV2140: $i,SV1911: $i,SV1432: $i,SV738: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2140 @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV738 @ SV2140 @ tc_nat )
| ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2140 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6249]) ).
thf(6571,plain,
! [SV2204: $i,SV2141: $i,SV1912: $i,SV1434: $i,SV741: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
| ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6250]) ).
thf(6572,plain,
! [SV2223: $i,SV2205: $i,SV2142: $i,SV1913: $i,SV1435: $i,SV742: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV742 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6251]) ).
thf(6573,plain,
! [SV2224: $i,SV2206: $i,SV2143: $i,SV1914: $i,SV1436: $i,SV743: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV743 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2206 @ SV1914 @ SV743 ) @ SV2224 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SV2206 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SV2224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6252]) ).
thf(6574,plain,
! [SV1916: $i,SV1438: $i,SV745: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV745 @ tc_nat )
= $false )
| ( ( SV1438 = SV1916 )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1438 @ tc_nat )
= ( c_HOL_Otimes__class_Otimes @ SV745 @ SV1916 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6254]) ).
thf(6575,plain,
! [SV1917: $i,SV746: $i,SV2144: $i,SV1439: $i] :
( ( ( SV1439 = SV2144 )
= $true )
| ( ( SV746 = SV1917 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV1439 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV2144 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV746 @ SV2144 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1917 @ SV1439 @ tc_nat ) @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6255]) ).
thf(6576,plain,
! [SV1918: $i,SV747: $i,SV1440: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1440 @ SV1440 @ SV747 ) @ ( c_HOL_Otimes__class_Otimes @ SV1918 @ SV1918 @ SV747 ) @ SV747 )
= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
= $false )
| ( ( SV1918
= ( c_HOL_Ozero__class_Ozero @ SV747 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV747 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6256]) ).
thf(6577,plain,
! [SV2207: $i,SV2145: $i,SV1919: $i,SV1441: $i,SV748: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV748 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV748 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6257]) ).
thf(6578,plain,
! [SV2225: $i,SV2208: $i,SV2146: $i,SV1920: $i,SV1442: $i,SV749: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV749 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6258]) ).
thf(6579,plain,
! [SV750: $i,SV1443: $i,SV2147: $i,SV1921: $i] :
( ( ( SV1921 = SV2147 )
= $true )
| ( ( SV1443
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV1921 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV750 @ ( c_HOL_Otimes__class_Otimes @ SV1443 @ SV2147 @ tc_nat ) @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6259]) ).
thf(6580,plain,
! [SV2148: $i,SV751: $i,SV1922: $i,SV1444: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV1922 @ SV751 )
!= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV2148 @ SV751 ) )
= $true )
| ( ( SV1922 = SV2148 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6260]) ).
thf(6581,plain,
! [SV1923: $i,SV752: $i,SV2149: $i,SV1445: $i] :
( ( ( SV1445 = SV2149 )
= $true )
| ( ( SV752 = SV1923 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV1445 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV2149 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV752 @ SV2149 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1923 @ SV1445 @ tc_nat ) @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6261]) ).
thf(6582,plain,
! [SV2209: $i,SV2150: $i,SV1924: $i,SV1446: $i,SV753: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2150 @ SV1446 @ tc_nat ) @ SV2209 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV2150 @ SV753 @ tc_nat )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV2150 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SV2209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6262]) ).
thf(6583,plain,
! [SV2210: $i,SV2151: $i,SV1925: $i,SV1447: $i,SV754: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV754 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV754 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
| ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6263]) ).
thf(6584,plain,
! [SV755: $i,SV1448: $i,SV1: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6264]) ).
thf(6585,plain,
! [SV756: $i,SV1449: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6265]) ).
thf(6586,plain,
! [SV760: $i,SV6: $i,SV1451: $i] :
( ( ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6266]) ).
thf(6587,plain,
! [SV761: $i,SV7: $i,SV1452: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $false )
| ( ( ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6267]) ).
thf(6588,plain,
! [SV1458: $i,SV16: $i,SV1929: $i,SV769: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV769 @ SV1929 @ SV16 ) @ SV1458 @ SV16 )
= $false )
| ( ( c_lessequals @ SV769 @ ( c_HOL_Oplus__class_Oplus @ SV1458 @ ( c_HOL_Oabs__class_Oabs @ SV1929 @ SV16 ) @ SV16 ) @ SV16 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add__abs @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6271]) ).
thf(6589,plain,
! [SV18: $i,SV770: $i,SV1459: $i] :
( ( ( c_lessequals @ SV1459 @ SV770 @ SV18 )
= $false )
| ( ( ~ ( c_lessequals @ SV770 @ SV1459 @ SV18 ) )
= $true )
| ( ( SV770 = SV1459 )
= $true )
| ( ( class_Orderings_Oorder @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6272]) ).
thf(6590,plain,
! [SV19: $i,SV771: $i,SV1460: $i] :
( ( ( c_lessequals @ SV1460 @ SV771 @ SV19 )
= $false )
| ( ( ~ ( c_lessequals @ SV771 @ SV1460 @ SV19 ) )
= $true )
| ( ( SV771 = SV1460 )
= $true )
| ( ( class_Orderings_Oorder @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6273]) ).
thf(6591,plain,
! [SV28: $i,SV1461: $i,SV780: $i] :
( ( ( c_lessequals @ SV780 @ SV1461 @ SV28 )
= $false )
| ( ( ~ ( c_lessequals @ SV1461 @ SV780 @ SV28 ) )
= $true )
| ( ( SV780 = SV1461 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6274]) ).
thf(6592,plain,
! [SV783: $i,SV31: $i,SV1463: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6276]) ).
thf(6593,plain,
! [SV786: $i,SV35: $i,SV1464: $i,SV1930: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6277]) ).
thf(6594,plain,
! [SV794: $i,SV43: $i,SV1931: $i,SV1471: $i] :
( ( ( c_lessequals @ SV1471 @ SV1931 @ SV43 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1471 @ SV43 ) @ ( c_HOL_Oplus__class_Oplus @ SV794 @ SV1931 @ SV43 ) @ SV43 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6278]) ).
thf(6595,plain,
! [SV1472: $i,SV44: $i,SV1932: $i,SV795: $i] :
( ( ( c_lessequals @ SV795 @ SV1932 @ SV44 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV795 @ SV1472 @ SV44 ) @ ( c_HOL_Oplus__class_Oplus @ SV1932 @ SV1472 @ SV44 ) @ SV44 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6279]) ).
thf(6596,plain,
! [SV1473: $i,SV45: $i,SV796: $i,SV1933: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV796 @ SV45 ) @ ( c_HOL_Oplus__class_Oplus @ SV1933 @ SV1473 @ SV45 ) @ SV45 )
= $false )
| ( ( c_lessequals @ SV796 @ SV1473 @ SV45 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6280]) ).
thf(6597,plain,
! [SV797: $i,SV46: $i,SV1934: $i,SV1474: $i] :
( ( ( c_lessequals @ SV1474 @ SV1934 @ SV46 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1474 @ SV46 ) @ ( c_HOL_Oplus__class_Oplus @ SV797 @ SV1934 @ SV46 ) @ SV46 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(6598,plain,
! [SV1475: $i,SV47: $i,SV1935: $i,SV798: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV798 @ SV1935 @ SV47 ) @ ( c_HOL_Oplus__class_Oplus @ SV1475 @ SV1935 @ SV47 ) @ SV47 )
= $false )
| ( ( c_lessequals @ SV798 @ SV1475 @ SV47 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6282]) ).
thf(6599,plain,
! [SV1476: $i,SV48: $i,SV1936: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ SV1936 @ SV48 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV799 @ SV1476 @ SV48 ) @ ( c_HOL_Oplus__class_Oplus @ SV1936 @ SV1476 @ SV48 ) @ SV48 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6283]) ).
thf(6600,plain,
! [SV801: $i,SV1478: $i,SV50: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6284]) ).
thf(6601,plain,
! [SV802: $i,SV51: $i,SV1479: $i] :
( ( ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6285]) ).
thf(6602,plain,
! [SV803: $i,SV1480: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 )
= $false )
| ( ( ~ ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6286]) ).
thf(6603,plain,
! [SV804: $i,SV53: $i,SV1481: $i] :
( ( ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= $false )
| ( ( ~ ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 ) )
= $true )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6287]) ).
thf(6604,plain,
! [SV58: $i,SV1485: $i,SV808: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV808 @ SV1485 @ SV58 ) @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV808 @ SV58 )
= $true )
| ( ( c_lessequals @ SV808 @ ( c_HOL_Ozero__class_Ozero @ SV58 ) @ SV58 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6288]) ).
thf(6605,plain,
! [SV59: $i,SV809: $i,SV1486: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1486 @ SV809 @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV1486 @ SV59 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV809 @ SV59 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6289]) ).
thf(6606,plain,
! [SV60: $i,SV1487: $i,SV810: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV810 @ SV1487 @ SV60 ) @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
= $false )
| ( ( c_lessequals @ SV1487 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
= $true )
| ( ( c_lessequals @ SV810 @ ( c_HOL_Ozero__class_Ozero @ SV60 ) @ SV60 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6290]) ).
thf(6607,plain,
! [SV61: $i,SV811: $i,SV1488: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1488 @ SV811 @ SV61 ) @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= $false )
| ( ( c_lessequals @ SV811 @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV61 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ SV811 @ SV61 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6291]) ).
thf(6608,plain,
! [SV812: $i,SV1489: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6292]) ).
thf(6609,plain,
! [SV813: $i,SV63: $i,SV1490: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6293]) ).
thf(6610,plain,
! [SV1491: $i,SV64: $i,SV814: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6294]) ).
thf(6611,plain,
! [SV815: $i,SV1492: $i,SV65: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6295]) ).
thf(6612,plain,
! [SV816: $i,SV66: $i,SV1493: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6296]) ).
thf(6613,plain,
! [SV1495: $i,SV824: $i,SV1938: $i,SV77: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6297]) ).
thf(6614,plain,
! [SV1496: $i,SV825: $i,SV1939: $i,SV78: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6298]) ).
thf(6615,plain,
! [SV1497: $i,SV826: $i,SV1940: $i,SV79: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6299]) ).
thf(6616,plain,
! [SV1498: $i,SV827: $i,SV1941: $i,SV80: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6300]) ).
thf(6617,plain,
! [SV1500: $i,SV84: $i,SV1942: $i,SV831: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6301]) ).
thf(6618,plain,
! [SV1943: $i,SV85: $i,SV1501: $i,SV832: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6302]) ).
thf(6619,plain,
! [SV86: $i,SV1944: $i,SV1502: $i,SV833: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6303]) ).
thf(6620,plain,
! [SV1503: $i,SV87: $i,SV1945: $i,SV834: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6304]) ).
thf(6621,plain,
! [SV2211: $i,SV2155: $i,SV1946: $i,SV1504: $i,SV835: $i,SV88: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV88 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2155 @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 )
| ~ ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2155 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6305]) ).
thf(6622,plain,
! [SV2212: $i,SV2156: $i,SV1947: $i,SV1505: $i,SV836: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV89 )
= $false )
| ( ( ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SV2156 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6306]) ).
thf(6623,plain,
! [SV2213: $i,SV2157: $i,SV1948: $i,SV1506: $i,SV837: $i,SV90: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV90 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2157 @ SV1506 @ SV90 ) @ SV2213 @ SV90 ) @ SV90 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SV2157 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SV2213 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6307]) ).
thf(6624,plain,
! [SV2214: $i,SV2158: $i,SV1949: $i,SV1507: $i,SV838: $i,SV91: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV91 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ SV2214 @ SV91 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SV2214 @ SV91 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6308]) ).
thf(6625,plain,
! [SV1950: $i,SV1508: $i,SV843: $i,SV96: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
| ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6309]) ).
thf(6626,plain,
! [SV1951: $i,SV1509: $i,SV844: $i,SV97: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
= $false )
| ( ( ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
| ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6310]) ).
thf(6627,plain,
! [SV2159: $i,SV850: $i,SV103: $i,SV1952: $i,SV1512: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1952 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV103 @ SV1952 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1952 @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6313]) ).
thf(6628,plain,
! [SV2160: $i,SV851: $i,SV104: $i,SV1953: $i,SV1513: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SV1953 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1513 @ SV851 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6314]) ).
thf(6629,plain,
! [SV2161: $i,SV1514: $i,SV852: $i,SV1954: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SV1954 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SV2161 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1954 @ SV105 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1954 @ SV852 @ tc_nat ) @ SV2161 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6315]) ).
thf(6630,plain,
! [SV2162: $i,SV853: $i,SV1955: $i,SV1515: $i,SV106: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SV2162 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV853 @ SV106 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ SV2162 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6316]) ).
thf(6631,plain,
! [SV2164: $i,SV1957: $i,SV110: $i,SV1519: $i,SV857: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6319]) ).
thf(6632,plain,
! [SV1521: $i,SV112: $i,SV1959: $i,SV859: $i] :
( ( ( ~ ( c_lessequals @ SV859 @ SV1959 @ SV112 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) )
= $true )
| ( ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6320]) ).
thf(6633,plain,
! [SV1522: $i,SV113: $i,SV1960: $i,SV860: $i] :
( ( ( ~ ( c_lessequals @ SV860 @ SV1960 @ SV113 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) )
= $true )
| ( ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Orderings_Olinorder @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6321]) ).
thf(6634,plain,
! [SV1523: $i,SV114: $i,SV1961: $i,SV861: $i] :
( ( ( ~ ( c_lessequals @ SV861 @ SV1961 @ SV114 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) )
= $true )
| ( ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6322]) ).
thf(6635,plain,
! [SV1962: $i,SV1532: $i,SV871: $i,SV124: $i] :
( ( ( class_Int_Onumber__ring @ SV124 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ SV124 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1962 @ SV124 ) @ ( c_HOL_Otimes__class_Otimes @ SV871 @ SV1532 @ SV124 ) @ SV124 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6325]) ).
thf(6636,plain,
! [SV1963: $i,SV1533: $i,SV872: $i,SV125: $i] :
( ( ( class_Int_Onumber__ring @ SV125 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ SV125 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1963 @ SV125 ) @ ( c_HOL_Otimes__class_Otimes @ SV872 @ SV1533 @ SV125 ) @ SV125 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6326]) ).
thf(6637,plain,
! [SV2165: $i,SV1964: $i,SV1538: $i,SV131: $i,SV877: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6327]) ).
thf(6638,plain,
! [SV1546: $i,SV144: $i,SV1968: $i,SV887: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ SV1968 @ SV144 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV887 @ ( c_HOL_Otimes__class_Otimes @ SV1546 @ SV1968 @ SV144 ) @ SV144 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6329]) ).
thf(6639,plain,
! [SV1969: $i,SV145: $i,SV1547: $i,SV888: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ SV1547 @ SV145 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV888 @ ( c_HOL_Otimes__class_Otimes @ SV1547 @ SV1969 @ SV145 ) @ SV145 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6330]) ).
thf(6640,plain,
! [SV1548: $i,SV146: $i,SV1970: $i,SV889: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV889 @ SV1970 @ SV146 ) @ SV1548 @ SV146 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV889 @ SV1548 @ SV146 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6331]) ).
thf(6641,plain,
! [SV1549: $i,SV147: $i,SV890: $i,SV1971: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1971 @ SV890 @ SV147 ) @ SV1549 @ SV147 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV890 @ SV1549 @ SV147 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6332]) ).
thf(6642,plain,
! [SV1550: $i,SV148: $i,SV1972: $i,SV891: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6333]) ).
thf(6643,plain,
! [SV894: $i,SV151: $i,SV1973: $i,SV1551: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1551 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1973 @ SV151 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV151 @ ( c_Divides_Odiv__class_Omod @ SV894 @ SV1551 @ tc_nat ) @ tc_nat ) @ SV1973 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV151 @ SV1551 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6334]) ).
thf(6644,plain,
! [SV1974: $i,SV1552: $i,SV895: $i,SV152: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1552 @ SV1974 @ SV152 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6335]) ).
thf(6645,plain,
! [SV1975: $i,SV1553: $i,SV896: $i,SV153: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1553 @ SV1975 @ SV153 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6336]) ).
thf(6646,plain,
! [SV1976: $i,SV897: $i,SV1554: $i,SV154: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV897 @ SV1976 @ SV154 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6337]) ).
thf(6647,plain,
! [SV1555: $i,SV1977: $i,SV155: $i,SV898: $i] :
( ( ( ~ ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1977 @ SV1555 @ SV155 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6338]) ).
thf(6648,plain,
! [SV899: $i,SV1978: $i,SV156: $i,SV1556: $i] :
( ( ( ~ ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1978 @ SV899 @ SV156 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6339]) ).
thf(6649,plain,
! [SV2166: $i,SV1979: $i,SV158: $i,SV1557: $i,SV901: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6340]) ).
thf(6650,plain,
! [SV2215: $i,SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6341]) ).
thf(6651,plain,
! [SV2216: $i,SV2168: $i,SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6342]) ).
thf(6652,plain,
! [SV911: $i,SV1567: $i,SV168: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6343]) ).
thf(6653,plain,
! [SV912: $i,SV169: $i,SV1568: $i] :
( ( ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
= $false )
| ( ( ~ ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6344]) ).
thf(6654,plain,
! [SV913: $i,SV170: $i,SV1569: $i] :
( ( ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
= $false )
| ( ( ~ ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6345]) ).
thf(6655,plain,
! [SV915: $i,SV1570: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6346]) ).
thf(6656,plain,
! [SV916: $i,SV173: $i,SV1571: $i] :
( ( ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
= $false )
| ( ( ~ ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6347]) ).
thf(6657,plain,
! [SV917: $i,SV1572: $i,SV174: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6348]) ).
thf(6658,plain,
! [SV1590: $i,SV939: $i,SV196: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Otimes__class_Otimes @ SV939 @ SV1590 @ SV196 ) @ SV196 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV939 @ SV196 )
= $true )
| ( ( c_lessequals @ SV939 @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV196 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6349]) ).
thf(6659,plain,
! [SV940: $i,SV1591: $i,SV197: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ ( c_HOL_Otimes__class_Otimes @ SV1591 @ SV940 @ SV197 ) @ SV197 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1591 @ SV197 )
= $true )
| ( ( c_lessequals @ SV940 @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6350]) ).
thf(6660,plain,
! [SV1592: $i,SV941: $i,SV198: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ ( c_HOL_Otimes__class_Otimes @ SV941 @ SV1592 @ SV198 ) @ SV198 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1592 @ SV198 )
= $true )
| ( ( c_lessequals @ SV941 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6351]) ).
thf(6661,plain,
! [SV942: $i,SV1593: $i,SV199: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ ( c_HOL_Otimes__class_Otimes @ SV1593 @ SV942 @ SV199 ) @ SV199 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV942 @ SV199 )
= $true )
| ( ( c_lessequals @ SV942 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6352]) ).
thf(6662,plain,
! [SV1998: $i,SV944: $i,SV1595: $i,SV202: $i] :
( ( ( c_lessequals @ SV202 @ SV1595 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV944 @ SV1998 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV202 @ SV944 @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ SV1595 @ SV1998 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6353]) ).
thf(6663,plain,
! [SV2169: $i,SV1999: $i,SV204: $i,SV1596: $i,SV945: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6354]) ).
thf(6664,plain,
! [SV2170: $i,SV2000: $i,SV205: $i,SV1597: $i,SV946: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6355]) ).
thf(6665,plain,
! [SV2001: $i,SV1598: $i,SV960: $i,SV219: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV2001 @ SV219 ) @ SV219 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6356]) ).
thf(6666,plain,
! [SV2002: $i,SV1599: $i,SV961: $i,SV220: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SV2002 @ SV961 @ SV220 ) @ SV220 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6357]) ).
thf(6667,plain,
! [SV1600: $i,SV221: $i,SV2003: $i,SV962: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6358]) ).
thf(6668,plain,
! [SV2015: $i,SV1621: $i,SV986: $i,SV248: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6360]) ).
thf(6669,plain,
! [SV1624: $i,SV990: $i,SV2016: $i,SV252: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 ) )
= $true )
| ( ( c_lessequals @ SV990 @ SV1624 @ SV252 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6361]) ).
thf(6670,plain,
! [SV1625: $i,SV991: $i,SV2017: $i,SV253: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 ) )
= $true )
| ( ( c_lessequals @ SV991 @ SV1625 @ SV253 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6362]) ).
thf(6671,plain,
! [SV992: $i,SV254: $i,SV2018: $i,SV1626: $i] :
( ( ( ~ ( c_lessequals @ SV1626 @ SV2018 @ SV254 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6363]) ).
thf(6672,plain,
! [SV1627: $i,SV255: $i,SV993: $i,SV2019: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 ) )
= $true )
| ( ( c_lessequals @ SV993 @ SV1627 @ SV255 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6364]) ).
thf(6673,plain,
! [SV994: $i,SV256: $i,SV1628: $i,SV2020: $i] :
( ( ( ~ ( c_lessequals @ SV2020 @ SV1628 @ SV256 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6365]) ).
thf(6674,plain,
! [SV995: $i,SV257: $i,SV1629: $i,SV2021: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) )
= $true )
| ( ( c_lessequals @ SV995 @ SV1629 @ SV257 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6366]) ).
thf(6675,plain,
! [SV1006: $i,SV271: $i,SV1638: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6373]) ).
thf(6676,plain,
! [SV2027: $i,SV1652: $i,SV1026: $i,SV298: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6376]) ).
thf(6677,plain,
! [SV1653: $i,SV299: $i,SV1027: $i,SV2028: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6377]) ).
thf(6678,plain,
! [SV1654: $i,SV300: $i,SV2029: $i,SV1028: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6378]) ).
thf(6679,plain,
! [SV2030: $i,SV1029: $i,SV1655: $i,SV301: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6379]) ).
thf(6680,plain,
! [SV1030: $i,SV2031: $i,SV302: $i,SV1656: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6380]) ).
thf(6681,plain,
! [SV1031: $i,SV303: $i,SV1657: $i,SV2032: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6381]) ).
thf(6682,plain,
! [SV1032: $i,SV304: $i,SV2033: $i,SV1658: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6382]) ).
thf(6683,plain,
! [SV2034: $i,SV1659: $i,SV1033: $i,SV305: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6383]) ).
thf(6684,plain,
! [SV1660: $i,SV2035: $i,SV306: $i,SV1034: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6384]) ).
thf(6685,plain,
! [SV1035: $i,SV307: $i,SV2036: $i,SV1661: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6385]) ).
thf(6686,plain,
! [SV1662: $i,SV308: $i,SV1036: $i,SV2037: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6386]) ).
thf(6687,plain,
! [SV1037: $i,SV309: $i,SV1663: $i,SV2038: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6387]) ).
thf(6688,plain,
! [SV1038: $i,SV310: $i,SV1664: $i,SV2039: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6388]) ).
thf(6689,plain,
! [SV1674: $i,SV1048: $i,SV320: $i,SV2042: $i] :
( ( ( SV2042
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SV2042 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SV2042 @ SV320 ) @ SV320 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6395]) ).
thf(6690,plain,
! [SV1675: $i,SV1049: $i,SV321: $i,SV2043: $i] :
( ( ( SV2043
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1675 @ SV321 ) @ SV321 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6396]) ).
thf(6691,plain,
! [SV1051: $i,SV323: $i,SV1677: $i] :
( ( ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6397]) ).
thf(6692,plain,
! [SV1052: $i,SV1678: $i,SV324: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 )
= $false )
| ( ( ~ ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6398]) ).
thf(6693,plain,
! [SV1053: $i,SV325: $i,SV1679: $i] :
( ( ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6399]) ).
thf(6694,plain,
! [SV1054: $i,SV1680: $i,SV326: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 )
= $false )
| ( ( ~ ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6400]) ).
thf(6695,plain,
! [SV1055: $i,SV327: $i,SV1681: $i] :
( ( ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6401]) ).
thf(6696,plain,
! [SV1056: $i,SV1682: $i,SV328: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 )
= $false )
| ( ( ~ ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6402]) ).
thf(6697,plain,
! [SV1683: $i,SV329: $i,SV1057: $i] :
( ( ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6403]) ).
thf(6698,plain,
! [SV1058: $i,SV1684: $i,SV331: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6404]) ).
thf(6699,plain,
! [SV1059: $i,SV1685: $i,SV332: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6405]) ).
thf(6700,plain,
! [SV1066: $i,SV340: $i,SV1689: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6407]) ).
thf(6701,plain,
! [SV1072: $i,SV1692: $i,SV346: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6410]) ).
thf(6702,plain,
! [SV2046: $i,SV1075: $i,SV1693: $i,SV350: $i] :
( ( ( c_lessequals @ SV350 @ SV1693 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1075 @ SV2046 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV350 @ SV1075 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1693 @ SV2046 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6411]) ).
thf(6703,plain,
! [SV2174: $i,SV2047: $i,SV351: $i,SV1694: $i,SV1076: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
= $true )
| ( ( ~ ( c_lessequals @ SV1694 @ SV2174 @ SV351 )
| ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6412]) ).
thf(6704,plain,
! [SV2051: $i,SV1699: $i,SV1083: $i,SV358: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
| ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6416]) ).
thf(6705,plain,
! [SV1085: $i,SV1700: $i,SV360: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1085 @ SV1700 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6417]) ).
thf(6706,plain,
! [SV1086: $i,SV1701: $i,SV361: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1701 @ SV1086 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6418]) ).
thf(6707,plain,
! [SV1089: $i,SV364: $i,SV2053: $i,SV1704: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1704 @ SV2053 @ SV364 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV1704 @ SV364 ) @ ( c_HOL_Otimes__class_Otimes @ SV1089 @ SV2053 @ SV364 ) @ SV364 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV364 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6420]) ).
thf(6708,plain,
! [SV1705: $i,SV365: $i,SV2054: $i,SV1090: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1090 @ SV2054 @ SV365 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1090 @ SV1705 @ SV365 ) @ ( c_HOL_Otimes__class_Otimes @ SV2054 @ SV1705 @ SV365 ) @ SV365 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV365 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6421]) ).
thf(6709,plain,
! [SV379: $i,SV2056: $i,SV1710: $i,SV1104: $i] :
( ( ( c_lessequals @ SV1104 @ ( c_Orderings_Oord__class_Omin @ SV1710 @ SV2056 @ SV379 ) @ SV379 )
= $false )
| ( ( c_lessequals @ SV1104 @ SV1710 @ SV379 )
= $true )
| ( ( class_Orderings_Olinorder @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6422]) ).
thf(6710,plain,
! [SV380: $i,SV1711: $i,SV2057: $i,SV1105: $i] :
( ( ( c_lessequals @ SV1105 @ ( c_Orderings_Oord__class_Omin @ SV2057 @ SV1711 @ SV380 ) @ SV380 )
= $false )
| ( ( c_lessequals @ SV1105 @ SV1711 @ SV380 )
= $true )
| ( ( class_Orderings_Olinorder @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6423]) ).
thf(6711,plain,
! [SV1712: $i,SV381: $i,SV2058: $i,SV1106: $i] :
( ( ( c_lessequals @ SV1106 @ SV2058 @ SV381 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1106 @ SV1712 @ SV381 ) @ SV2058 @ SV381 )
= $true )
| ( ( class_Orderings_Olinorder @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6424]) ).
thf(6712,plain,
! [SV1107: $i,SV382: $i,SV2059: $i,SV1713: $i] :
( ( ( c_lessequals @ SV1713 @ SV2059 @ SV382 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1107 @ SV1713 @ SV382 ) @ SV2059 @ SV382 )
= $true )
| ( ( class_Orderings_Olinorder @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6425]) ).
thf(6713,plain,
! [SV1714: $i,SV383: $i,SV2060: $i,SV1108: $i] :
( ( ( c_lessequals @ SV1108 @ SV2060 @ SV383 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1108 @ SV1714 @ SV383 ) @ SV2060 @ SV383 )
= $true )
| ( ( class_Orderings_Olinorder @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6426]) ).
thf(6714,plain,
! [SV1109: $i,SV384: $i,SV2061: $i,SV1715: $i] :
( ( ( c_lessequals @ SV1715 @ SV2061 @ SV384 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV1109 @ SV1715 @ SV384 ) @ SV2061 @ SV384 )
= $true )
| ( ( class_Orderings_Olinorder @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6427]) ).
thf(6715,plain,
! [SV385: $i,SV2062: $i,SV1716: $i,SV1110: $i] :
( ( ( c_lessequals @ SV1110 @ ( c_Orderings_Oord__class_Omin @ SV1716 @ SV2062 @ SV385 ) @ SV385 )
= $false )
| ( ( c_lessequals @ SV1110 @ SV1716 @ SV385 )
= $true )
| ( ( class_Orderings_Olinorder @ SV385 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6428]) ).
thf(6716,plain,
! [SV386: $i,SV1717: $i,SV2063: $i,SV1111: $i] :
( ( ( c_lessequals @ SV1111 @ ( c_Orderings_Oord__class_Omin @ SV2063 @ SV1717 @ SV386 ) @ SV386 )
= $false )
| ( ( c_lessequals @ SV1111 @ SV1717 @ SV386 )
= $true )
| ( ( class_Orderings_Olinorder @ SV386 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6429]) ).
thf(6717,plain,
! [SV1113: $i,SV388: $i,SV1718: $i,SV2064: $i] :
( ( ( c_lessequals @ SV2064 @ SV1718 @ SV388 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2064 @ SV1113 @ SV388 ) @ SV1718 @ SV388 ) )
= $true )
| ( ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
= $true )
| ( ( class_Orderings_Olinorder @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6430]) ).
thf(6718,plain,
! [SV2179: $i,SV1117: $i,SV2066: $i,SV1722: $i,SV392: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SV2179 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1117 @ SV392 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ SV2179 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6431]) ).
thf(6719,plain,
! [SV2180: $i,SV1723: $i,SV1118: $i,SV2067: $i,SV393: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SV2067 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SV2180 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV2067 @ SV393 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2067 @ SV1118 @ tc_nat ) @ SV2180 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6432]) ).
thf(6720,plain,
! [SV2181: $i,SV1119: $i,SV394: $i,SV2068: $i,SV1724: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SV2068 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1724 @ SV1119 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6433]) ).
thf(6721,plain,
! [SV2182: $i,SV1120: $i,SV395: $i,SV2069: $i,SV1725: $i] :
( ( ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2069 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV395 @ SV2069 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2069 @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6434]) ).
thf(6722,plain,
! [SV2183: $i,SV2070: $i,SV412: $i,SV1728: $i,SV1134: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
= $true )
| ( ( ~ ( c_lessequals @ SV1728 @ SV2183 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6435]) ).
thf(6723,plain,
! [SV2184: $i,SV2071: $i,SV413: $i,SV1729: $i,SV1135: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 )
| ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6436]) ).
thf(6724,plain,
! [SV1136: $i,SV414: $i,SV1730: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6437]) ).
thf(6725,plain,
! [SV415: $i,SV1137: $i,SV1731: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6438]) ).
thf(6726,plain,
! [SV1732: $i,SV416: $i,SV2072: $i,SV1138: $i] :
( ( ( ~ ( c_lessequals @ SV1138 @ SV2072 @ SV416 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
= $true )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6439]) ).
thf(6727,plain,
! [SV1733: $i,SV417: $i,SV2073: $i,SV1139: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2073 @ SV1733 @ SV417 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
= $true )
| ( ( class_Orderings_Oorder @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6440]) ).
thf(6728,plain,
! [SV1140: $i,SV418: $i,SV1734: $i,SV2074: $i] :
( ( ( ~ ( c_lessequals @ SV2074 @ SV1734 @ SV418 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
= $true )
| ( ( class_Orderings_Opreorder @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6441]) ).
thf(6729,plain,
! [SV1141: $i,SV419: $i,SV1735: $i,SV2075: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1141 @ SV2075 @ SV419 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
= $true )
| ( ( class_Orderings_Opreorder @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6442]) ).
thf(6730,plain,
! [SV1736: $i,SV420: $i,SV2076: $i,SV1142: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1142 @ SV2076 @ SV420 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1142 @ SV1736 @ SV420 ) @ ( c_HOL_Oplus__class_Oplus @ SV2076 @ SV1736 @ SV420 ) @ SV420 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6443]) ).
thf(6731,plain,
! [SV1737: $i,SV421: $i,SV2077: $i,SV1143: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1143 @ SV2077 @ SV421 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1143 @ SV1737 @ SV421 ) @ ( c_HOL_Oplus__class_Oplus @ SV2077 @ SV1737 @ SV421 ) @ SV421 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6444]) ).
thf(6732,plain,
! [SV1738: $i,SV422: $i,SV2078: $i,SV1144: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1144 @ SV2078 @ SV422 ) @ ( c_HOL_Oplus__class_Oplus @ SV1738 @ SV2078 @ SV422 ) @ SV422 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1144 @ SV1738 @ SV422 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV422 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6445]) ).
thf(6733,plain,
! [SV1145: $i,SV423: $i,SV2079: $i,SV1739: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1739 @ SV2079 @ SV423 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV1739 @ SV423 ) @ ( c_HOL_Oplus__class_Oplus @ SV1145 @ SV2079 @ SV423 ) @ SV423 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6446]) ).
thf(6734,plain,
! [SV1146: $i,SV424: $i,SV2080: $i,SV1740: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1740 @ SV2080 @ SV424 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV1740 @ SV424 ) @ ( c_HOL_Oplus__class_Oplus @ SV1146 @ SV2080 @ SV424 ) @ SV424 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6447]) ).
thf(6735,plain,
! [SV1741: $i,SV425: $i,SV1147: $i,SV2081: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1147 @ SV425 ) @ ( c_HOL_Oplus__class_Oplus @ SV2081 @ SV1741 @ SV425 ) @ SV425 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1147 @ SV1741 @ SV425 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6448]) ).
thf(6736,plain,
! [SV2185: $i,SV2082: $i,SV428: $i,SV1744: $i,SV1150: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6451]) ).
thf(6737,plain,
! [SV429: $i,SV1745: $i,SV1151: $i] :
( ( ( c_lessequals @ SV1151 @ SV1745 @ SV429 )
= $false )
| ( ( c_lessequals @ SV1745 @ SV1151 @ SV429 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1745 @ SV429 )
= $true )
| ( ( class_Orderings_Opreorder @ SV429 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6452]) ).
thf(6738,plain,
! [SV1152: $i,SV430: $i,SV1746: $i,SV2083: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2083 @ SV1746 @ SV430 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2083 @ SV1152 @ SV430 ) @ SV1746 @ SV430 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
= $true )
| ( ( class_Orderings_Olinorder @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6453]) ).
thf(6739,plain,
! [SV2084: $i,SV432: $i,SV1154: $i,SV1748: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SV2084 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SV2084 @ SV432 ) @ SV432 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6455]) ).
thf(6740,plain,
! [SV2085: $i,SV433: $i,SV1155: $i,SV1749: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1155 @ SV433 ) @ SV433 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6456]) ).
thf(6741,plain,
! [SV434: $i,SV1750: $i,SV1156: $i] :
( ( ( c_lessequals @ SV1156 @ SV1750 @ SV434 )
= $false )
| ( ( SV1750 = SV1156 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1156 @ SV1750 @ SV434 )
= $true )
| ( ( class_Orderings_Oorder @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6457]) ).
thf(6742,plain,
! [SV435: $i,SV1751: $i,SV1157: $i] :
( ( ( c_lessequals @ SV1157 @ SV1751 @ SV435 )
= $false )
| ( ( SV1751 = SV1157 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1157 @ SV1751 @ SV435 )
= $true )
| ( ( class_Orderings_Oorder @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6458]) ).
thf(6743,plain,
! [SV436: $i,SV1752: $i,SV1158: $i] :
( ( ( c_lessequals @ SV1158 @ SV1752 @ SV436 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1158 @ SV1752 @ SV436 )
= $true )
| ( ( SV1158 = SV1752 )
= $true )
| ( ( class_Orderings_Olinorder @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6459]) ).
thf(6744,plain,
! [SV437: $i,SV1753: $i,SV1159: $i] :
( ( ( c_lessequals @ SV1159 @ SV1753 @ SV437 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1159 @ SV1753 @ SV437 )
= $true )
| ( ( SV1159 = SV1753 )
= $true )
| ( ( class_Orderings_Olinorder @ SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6460]) ).
thf(6745,plain,
! [SV438: $i,SV1754: $i,SV1160: $i] :
( ( ( c_lessequals @ SV1160 @ SV1754 @ SV438 )
= $false )
| ( ( SV1160 = SV1754 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1160 @ SV1754 @ SV438 )
= $true )
| ( ( class_Orderings_Oorder @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6461]) ).
thf(6746,plain,
! [SV439: $i,SV1755: $i,SV1161: $i] :
( ( ( c_lessequals @ SV1161 @ SV1755 @ SV439 )
= $false )
| ( ( SV1161 = SV1755 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1161 @ SV1755 @ SV439 )
= $true )
| ( ( class_Orderings_Oorder @ SV439 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6462]) ).
thf(6747,plain,
! [SV440: $i,SV1756: $i,SV1162: $i] :
( ( ( c_lessequals @ SV1162 @ SV1756 @ SV440 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1162 @ SV1756 @ SV440 )
= $true )
| ( ( SV1162 = SV1756 )
= $true )
| ( ( class_Orderings_Oorder @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6463]) ).
thf(6748,plain,
! [SV441: $i,SV1757: $i,SV1163: $i] :
( ( ( c_lessequals @ SV1163 @ SV1757 @ SV441 )
= $false )
| ( ( SV1163 = SV1757 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1163 @ SV1757 @ SV441 )
= $true )
| ( ( class_Orderings_Oorder @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6464]) ).
thf(6749,plain,
! [SV1758: $i,SV442: $i,SV2086: $i,SV1164: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
= $true )
| ( ( class_Orderings_Olinorder @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6465]) ).
thf(6750,plain,
! [SV443: $i,SV1165: $i,SV1759: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1759 @ SV1165 @ SV443 )
= $false )
| ( ( c_lessequals @ SV1165 @ SV1759 @ SV443 )
= $false )
| ( ( class_Orderings_Opreorder @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6466]) ).
thf(6751,plain,
! [SV447: $i,SV1169: $i,SV1761: $i] :
( ( ( c_lessequals @ SV1761 @ SV1169 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1169 @ SV1761 @ SV447 )
= $false )
| ( ( class_Orderings_Olinorder @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6468]) ).
thf(6752,plain,
! [SV450: $i,SV1172: $i,SV1764: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1764 @ SV1172 @ SV450 )
= $false )
| ( ( c_lessequals @ SV1172 @ SV1764 @ SV450 )
= $false )
| ( ( class_Orderings_Olinorder @ SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6469]) ).
thf(6753,plain,
! [SV1173: $i,SV451: $i,SV2087: $i,SV1765: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1765 @ SV2087 @ SV451 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1173 @ SV1765 @ SV451 ) @ SV2087 @ SV451 )
= $true )
| ( ( class_Orderings_Olinorder @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6470]) ).
thf(6754,plain,
! [SV1766: $i,SV452: $i,SV2088: $i,SV1174: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1174 @ SV2088 @ SV452 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1174 @ SV1766 @ SV452 ) @ SV2088 @ SV452 )
= $true )
| ( ( class_Orderings_Olinorder @ SV452 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6471]) ).
thf(6755,plain,
! [SV453: $i,SV1767: $i,SV2089: $i,SV1175: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1175 @ ( c_Orderings_Oord__class_Omin @ SV2089 @ SV1767 @ SV453 ) @ SV453 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1175 @ SV1767 @ SV453 )
= $true )
| ( ( class_Orderings_Olinorder @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(6756,plain,
! [SV454: $i,SV2090: $i,SV1768: $i,SV1176: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1176 @ ( c_Orderings_Oord__class_Omin @ SV1768 @ SV2090 @ SV454 ) @ SV454 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1176 @ SV1768 @ SV454 )
= $true )
| ( ( class_Orderings_Olinorder @ SV454 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6473]) ).
thf(6757,plain,
! [SV1177: $i,SV455: $i,SV2091: $i,SV1769: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1769 @ SV2091 @ SV455 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1177 @ SV1769 @ SV455 ) @ SV2091 @ SV455 )
= $true )
| ( ( class_Orderings_Olinorder @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6474]) ).
thf(6758,plain,
! [SV1770: $i,SV456: $i,SV2092: $i,SV1178: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1178 @ SV2092 @ SV456 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV1178 @ SV1770 @ SV456 ) @ SV2092 @ SV456 )
= $true )
| ( ( class_Orderings_Olinorder @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6475]) ).
thf(6759,plain,
! [SV2093: $i,SV457: $i,SV1771: $i,SV1179: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1771 @ SV457 ) @ SV457 ) @ SV2093 @ SV457 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1179 @ ( c_HOL_Oplus__class_Oplus @ SV1771 @ SV2093 @ SV457 ) @ SV457 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6476]) ).
thf(6760,plain,
! [SV2217: $i,SV2186: $i,SV2094: $i,SV1772: $i,SV1180: $i,SV458: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV458 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2186 @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 )
| ~ ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2186 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6477]) ).
thf(6761,plain,
! [SV2218: $i,SV2187: $i,SV2095: $i,SV1773: $i,SV1181: $i,SV459: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV459 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SV2187 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6478]) ).
thf(6762,plain,
! [SV2219: $i,SV2188: $i,SV2096: $i,SV1774: $i,SV1182: $i,SV460: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV460 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2188 @ SV1774 @ SV460 ) @ SV2219 @ SV460 ) @ SV460 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV2188 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SV2219 @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6479]) ).
thf(6763,plain,
! [SV2220: $i,SV2189: $i,SV2097: $i,SV1775: $i,SV1183: $i,SV461: $i] :
( ( ( class_Ring__and__Field_Opordered__ring @ SV461 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ SV2220 @ SV461 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SV2220 @ SV461 ) @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6480]) ).
thf(6764,plain,
! [SV462: $i,SV2098: $i,SV1776: $i,SV1184: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6481]) ).
thf(6765,plain,
! [SV1782: $i,SV468: $i,SV2103: $i,SV1190: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6482]) ).
thf(6766,plain,
! [SV2109: $i,SV1210: $i,SV1793: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV1793 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1210 @ SV2109 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV489 @ SV1210 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1793 @ SV2109 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6484]) ).
thf(6767,plain,
! [SV1234: $i,SV1800: $i,SV517: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6490]) ).
thf(6768,plain,
! [SV2191: $i,SV2110: $i,SV536: $i,SV1808: $i,SV1253: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6497]) ).
thf(6769,plain,
! [SV2192: $i,SV2111: $i,SV537: $i,SV1809: $i,SV1254: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6498]) ).
thf(6770,plain,
! [SV1260: $i,SV544: $i,SV1811: $i,SV2112: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV2112 @ SV1811 @ SV544 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1260 @ SV1811 @ SV544 ) @ SV2112 @ SV544 )
= ( c_Divides_Odiv__class_Omod @ SV1260 @ SV2112 @ SV544 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV544 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6499]) ).
thf(6771,plain,
! [SV2193: $i,SV2113: $i,SV549: $i,SV1812: $i,SV1265: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6501]) ).
thf(6772,plain,
! [SV2194: $i,SV559: $i,SV2114: $i,SV1815: $i,SV1272: $i] :
( ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
= $true )
| ( ( ~ ( c_lessequals @ SV2194 @ SV2114 @ SV559 )
| ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6503]) ).
thf(6773,plain,
! [SV1273: $i,SV560: $i,SV1816: $i,SV2115: $i] :
( ( ( ~ ( c_lessequals @ SV2115 @ SV1816 @ SV560 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1273 @ SV2115 @ SV560 ) )
= $true )
| ( ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
= $true )
| ( ( class_Orderings_Opreorder @ SV560 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6504]) ).
thf(6774,plain,
! [SV1274: $i,SV561: $i,SV1817: $i] :
( ( ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $false )
| ( ( ~ ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6505]) ).
thf(6775,plain,
! [SV1818: $i,SV562: $i,SV2116: $i,SV1275: $i] :
( ( ( ~ ( c_lessequals @ SV1275 @ SV2116 @ SV562 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2116 @ SV1818 @ SV562 ) )
= $true )
| ( ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
= $true )
| ( ( class_Orderings_Oorder @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6506]) ).
thf(6776,plain,
! [SV1281: $i,SV1821: $i,SV2117: $i,SV569: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV2117 @ SV569 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1281 @ SV569 ) @ SV569 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6507]) ).
thf(6777,plain,
! [SV1282: $i,SV570: $i,SV2118: $i,SV1822: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1822 @ SV2118 @ SV570 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV2118 @ SV570 ) @ SV570 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6508]) ).
thf(6778,plain,
! [SV1283: $i,SV1823: $i,SV2119: $i,SV571: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SV2119 @ SV571 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV2119 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SV2119 @ SV571 ) @ SV571 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6509]) ).
thf(6779,plain,
! [SV1284: $i,SV572: $i,SV2120: $i,SV1824: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1824 @ SV2120 @ SV572 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SV2120 @ SV1284 @ SV572 ) @ SV572 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6510]) ).
thf(6780,plain,
! [SV1292: $i,SV1828: $i,SV580: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1828 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV580 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1828 @ SV1292 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV580 @ SV1292 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6511]) ).
thf(6781,plain,
! [SV1293: $i,SV1829: $i,SV581: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1829 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1829 @ SV1293 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1293 @ SV1829 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV581 @ SV1293 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6512]) ).
thf(6782,plain,
! [SV621: $i,SV1325: $i,SV1844: $i] :
( ( ( c_lessequals @ SV1844 @ SV1325 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1844 @ SV621 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6516]) ).
thf(6783,plain,
! [SV622: $i,SV1845: $i,SV1326: $i] :
( ( ( c_lessequals @ SV1326 @ SV1845 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1326 @ SV622 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV622 @ SV1845 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6517]) ).
thf(6784,plain,
! [SV1854: $i,SV637: $i,SV1340: $i,SV2123: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV2123 @ SV1340 @ SV637 ) @ SV637 ) @ SV1854 @ SV637 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1340 @ SV1854 @ SV637 ) @ SV2123 @ SV637 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6521]) ).
thf(6785,plain,
! [SV646: $i,SV1349: $i,SV1859: $i] :
( ( ( c_lessequals @ SV1859 @ SV1349 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1859 @ SV646 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6526]) ).
thf(6786,plain,
! [SV647: $i,SV1860: $i,SV1350: $i] :
( ( ( c_lessequals @ SV1350 @ SV1860 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1350 @ SV647 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6527]) ).
thf(6787,plain,
! [SV654: $i,SV1357: $i,SV1862: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1862 @ SV1357 @ SV654 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV1862 @ SV654 )
= $false )
| ( ( class_Orderings_Oorder @ SV654 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6529]) ).
thf(6788,plain,
! [SV655: $i,SV1358: $i,SV1863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1863 @ SV1358 @ SV655 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1358 @ SV1863 @ SV655 )
= $false )
| ( ( class_Orderings_Olinorder @ SV655 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6530]) ).
thf(6789,plain,
! [SV656: $i,SV1359: $i,SV1864: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1864 @ SV1359 @ SV656 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1359 @ SV1864 @ SV656 )
= $false )
| ( ( class_Orderings_Opreorder @ SV656 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6531]) ).
thf(6790,plain,
! [SV657: $i,SV1360: $i,SV1865: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1865 @ SV1360 @ SV657 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1360 @ SV1865 @ SV657 )
= $false )
| ( ( class_Orderings_Opreorder @ SV657 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6532]) ).
thf(6791,plain,
! [SV1873: $i,SV672: $i,SV2124: $i,SV1373: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
= $true )
| ( ( class_Orderings_Oorder @ SV672 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6539]) ).
thf(6792,plain,
! [SV1374: $i,SV673: $i,SV1874: $i,SV2125: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
= $true )
| ( ( class_Orderings_Opreorder @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6540]) ).
thf(6793,plain,
! [SV2126: $i,SV1879: $i,SV1381: $i,SV682: $i] :
( ( ( class_Int_Onumber__ring @ SV682 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
| ( SV1879 = SV2126 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV682 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6542]) ).
thf(6794,plain,
! [SV2128: $i,SV685: $i,SV1882: $i,SV1384: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV1882 @ SV685 )
= ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV2128 @ SV685 ) )
= $false )
| ( ( SV1882 = SV2128 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV685 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6545]) ).
thf(6795,plain,
! [SV1385: $i,SV1883: $i,SV686: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6546]) ).
thf(6796,plain,
! [SV2196: $i,SV2129: $i,SV688: $i,SV1884: $i,SV1387: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
!= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
= $true )
| ( ( ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SV2196 @ SV2129 @ SV688 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6547]) ).
thf(6797,plain,
! [SV1388: $i,SV689: $i,SV1885: $i] :
( ( ( SV1885
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
= $true )
| ( ( SV1388
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1388 @ SV1885 @ SV689 )
= ( c_HOL_Ozero__class_Ozero @ SV689 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV689 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6548]) ).
thf(6798,plain,
! [SV2197: $i,SV2130: $i,SV690: $i,SV1886: $i,SV1389: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
!= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
= $true )
| ( ( ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6549]) ).
thf(6799,plain,
! [SV1888: $i,SV693: $i,SV1391: $i] :
( ( ( SV1391
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
= $true )
| ( ( SV1888
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1391 @ SV1888 @ SV693 )
= ( c_HOL_Ozero__class_Ozero @ SV693 ) )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV693 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6551]) ).
thf(6800,plain,
! [SV2131: $i,SV696: $i,SV1889: $i,SV1393: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1393 @ SV1889 @ SV696 )
= ( c_HOL_Ominus__class_Ominus @ SV2131 @ SV2131 @ SV696 ) )
= $false )
| ( ( SV1393 = SV1889 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV696 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6552]) ).
thf(6801,plain,
! [SV698: $i,SV1890: $i,SV1395: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
!= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
= $true )
| ( ( SV1395 = SV1890 )
= $true )
| ( ( class_Int_Onumber__ring @ SV698 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV698 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6553]) ).
thf(6802,plain,
! [SV2198: $i,SV702: $i,SV2132: $i,SV1891: $i,SV1397: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2132 @ SV702 ) @ SV702 )
!= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2198 @ SV702 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SV2132 @ SV702 )
= SV2198 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV702 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6554]) ).
thf(6803,plain,
! [SV1400: $i,SV1893: $i,SV705: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6556]) ).
thf(6804,plain,
! [SV2133: $i,SV1894: $i,SV708: $i,SV1402: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1402 @ SV708 )
= ( c_HOL_Ominus__class_Ominus @ SV1894 @ SV2133 @ SV708 ) )
= $false )
| ( ( SV1894 = SV2133 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV708 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6557]) ).
thf(6805,plain,
! [SV2199: $i,SV2134: $i,SV1895: $i,SV1403: $i,SV709: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV709 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV709 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6558]) ).
thf(6806,plain,
! [SV2200: $i,SV2135: $i,SV710: $i,SV1896: $i,SV1404: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
!= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6559]) ).
thf(6807,plain,
! [SV2136: $i,SV712: $i,SV1406: $i,SV1897: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1897 @ SV1406 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV712 @ SV2136 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV712 @ SV1406 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1897 @ SV2136 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6560]) ).
thf(6808,plain,
! [SV2221: $i,SV2201: $i,SV2137: $i,SV1898: $i,SV1407: $i,SV713: $i] :
( ( ( class_Divides_Oring__div @ SV713 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6561]) ).
thf(6809,plain,
! [SV722: $i,SV1902: $i,SV1416: $i] :
( ( ( SV1416
!= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
= $true )
| ( ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV722 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV722 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6563]) ).
thf(6810,plain,
! [SV1418: $i,SV724: $i,SV1903: $i] :
( ( ( SV1903
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
= $true )
| ( ( SV1418
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
= $true )
| ( ( ( c_HOL_Otimes__class_Otimes @ SV1418 @ SV1903 @ SV724 )
= ( c_HOL_Ozero__class_Ozero @ SV724 ) )
= $false )
| ( ( class_Ring__and__Field_Oring__no__zero__divisors @ SV724 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6564]) ).
thf(6811,plain,
! [SV2138: $i,SV725: $i,SV1904: $i,SV1419: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1419 @ SV1904 @ SV725 )
= ( c_HOL_Oplus__class_Oplus @ SV2138 @ SV1904 @ SV725 ) )
= $false )
| ( ( SV1419 = SV2138 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV725 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6565]) ).
thf(6812,plain,
! [SV2222: $i,SV2202: $i,SV2139: $i,SV1907: $i,SV1423: $i,SV729: $i] :
( ( ( class_Ring__and__Field_Oring @ SV729 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2202 @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
| ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2202 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6566]) ).
thf(6813,plain,
! [SV1910: $i,SV735: $i,SV1429: $i] :
( ( ( ~ ( c_lessequals @ SV1429 @ SV735 @ tc_nat ) )
= $true )
| ( ( SV735 = SV1910 )
= $true )
| ( ( c_lessequals @ SV1429 @ SV1910 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6569]) ).
thf(6814,plain,
! [SV2203: $i,SV1432: $i,SV1911: $i,SV2140: $i,SV738: $i] :
( ( ( ~ ( c_lessequals @ SV738 @ SV2140 @ tc_nat ) )
= $true )
| ( ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2140 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2140 @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6570]) ).
thf(6815,plain,
! [SV2204: $i,SV2141: $i,SV741: $i,SV1912: $i,SV1434: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
!= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6571]) ).
thf(6816,plain,
! [SV2223: $i,SV2205: $i,SV2142: $i,SV1913: $i,SV1435: $i,SV742: $i] :
( ( ( class_Divides_Osemiring__div @ SV742 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6572]) ).
thf(6817,plain,
! [SV2224: $i,SV2206: $i,SV2143: $i,SV1914: $i,SV1436: $i,SV743: $i] :
( ( ( class_Ring__and__Field_Oring @ SV743 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2206 @ SV1914 @ SV743 ) @ SV2224 @ SV743 ) )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SV2206 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SV2224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6573]) ).
thf(6818,plain,
! [SV2207: $i,SV2145: $i,SV1919: $i,SV1441: $i,SV748: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV748 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV748 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6577]) ).
thf(6819,plain,
! [SV2225: $i,SV2208: $i,SV2146: $i,SV1920: $i,SV1442: $i,SV749: $i] :
( ( ( class_Divides_Osemiring__div @ SV749 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6578]) ).
thf(6820,plain,
! [SV2148: $i,SV751: $i,SV1922: $i,SV1444: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV1922 @ SV751 )
= ( c_HOL_Oplus__class_Oplus @ SV1444 @ SV2148 @ SV751 ) )
= $false )
| ( ( SV1922 = SV2148 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV751 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6580]) ).
thf(6821,plain,
! [SV2209: $i,SV1924: $i,SV1446: $i,SV753: $i,SV2150: $i] :
( ( ( ~ ( c_lessequals @ SV2150 @ SV753 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV2150 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SV2209 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2150 @ SV1446 @ tc_nat ) @ SV2209 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6582]) ).
thf(6822,plain,
! [SV2210: $i,SV2151: $i,SV1925: $i,SV1447: $i,SV754: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV754 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
| ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV754 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6583]) ).
thf(6823,plain,
! [SV755: $i,SV1448: $i,SV1: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_HOL_Otimes__class_Otimes @ SV1448 @ SV755 @ SV1 ) @ SV1 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1448 @ SV1 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV755 @ SV1 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6584]) ).
thf(6824,plain,
! [SV1449: $i,SV756: $i,SV2: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_HOL_Otimes__class_Otimes @ SV756 @ SV1449 @ SV2 ) @ SV2 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV1449 @ SV2 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ SV756 @ SV2 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6585]) ).
thf(6825,plain,
! [SV1451: $i,SV6: $i,SV760: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $false )
| ( ( c_lessequals @ SV1451 @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV760 @ SV1451 @ SV6 ) @ ( c_HOL_Ozero__class_Ozero @ SV6 ) @ SV6 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6586]) ).
thf(6826,plain,
! [SV1452: $i,SV7: $i,SV761: $i] :
( ( ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV761 @ SV1452 @ SV7 ) @ ( c_HOL_Ozero__class_Ozero @ SV7 ) @ SV7 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6587]) ).
thf(6827,plain,
! [SV18: $i,SV1459: $i,SV770: $i] :
( ( ( c_lessequals @ SV770 @ SV1459 @ SV18 )
= $false )
| ( ( c_lessequals @ SV1459 @ SV770 @ SV18 )
= $false )
| ( ( SV770 = SV1459 )
= $true )
| ( ( class_Orderings_Oorder @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6589]) ).
thf(6828,plain,
! [SV19: $i,SV1460: $i,SV771: $i] :
( ( ( c_lessequals @ SV771 @ SV1460 @ SV19 )
= $false )
| ( ( c_lessequals @ SV1460 @ SV771 @ SV19 )
= $false )
| ( ( SV771 = SV1460 )
= $true )
| ( ( class_Orderings_Oorder @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6590]) ).
thf(6829,plain,
! [SV28: $i,SV780: $i,SV1461: $i] :
( ( ( c_lessequals @ SV1461 @ SV780 @ SV28 )
= $false )
| ( ( c_lessequals @ SV780 @ SV1461 @ SV28 )
= $false )
| ( ( SV780 = SV1461 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6591]) ).
thf(6830,plain,
! [SV783: $i,SV1463: $i,SV31: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV1463 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV31 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1463 @ SV783 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV783 @ SV1463 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV31 @ SV783 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6592]) ).
thf(6831,plain,
! [SV786: $i,SV35: $i,SV1464: $i,SV1930: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6593]) ).
thf(6832,plain,
! [SV1478: $i,SV801: $i,SV50: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV801 @ SV50 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1478 @ SV50 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV801 @ SV1478 @ SV50 ) @ SV50 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV801 @ SV50 ) @ ( c_HOL_Oabs__class_Oabs @ SV1478 @ SV50 ) @ SV50 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6600]) ).
thf(6833,plain,
! [SV1479: $i,SV802: $i,SV51: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV802 @ SV51 )
= $false )
| ( ( c_lessequals @ SV1479 @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV51 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV802 @ SV1479 @ SV51 ) @ SV51 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV802 @ SV51 ) @ ( c_HOL_Oabs__class_Oabs @ SV1479 @ SV51 ) @ SV51 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6601]) ).
thf(6834,plain,
! [SV1480: $i,SV52: $i,SV803: $i] :
( ( ( c_lessequals @ SV803 @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV52 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV1480 @ SV52 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV803 @ SV1480 @ SV52 ) @ SV52 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV803 @ SV52 ) @ ( c_HOL_Oabs__class_Oabs @ SV1480 @ SV52 ) @ SV52 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6602]) ).
thf(6835,plain,
! [SV1481: $i,SV53: $i,SV804: $i] :
( ( ( c_lessequals @ SV804 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= $false )
| ( ( c_lessequals @ SV1481 @ ( c_HOL_Ozero__class_Ozero @ SV53 ) @ SV53 )
= $false )
| ( ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ SV804 @ SV1481 @ SV53 ) @ SV53 )
= ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV804 @ SV53 ) @ ( c_HOL_Oabs__class_Oabs @ SV1481 @ SV53 ) @ SV53 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring__abs @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6603]) ).
thf(6836,plain,
! [SV1489: $i,SV62: $i,SV812: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV812 @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV1489 @ SV62 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV812 @ SV1489 @ SV62 ) @ ( c_HOL_Ozero__class_Ozero @ SV62 ) @ SV62 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6608]) ).
thf(6837,plain,
! [SV1490: $i,SV813: $i,SV63: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV813 @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1490 @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV813 @ SV1490 @ SV63 ) @ ( c_HOL_Ozero__class_Ozero @ SV63 ) @ SV63 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6609]) ).
thf(6838,plain,
! [SV814: $i,SV1491: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV1491 @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV814 @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV814 @ SV1491 @ SV64 ) @ ( c_HOL_Ozero__class_Ozero @ SV64 ) @ SV64 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6610]) ).
thf(6839,plain,
! [SV1492: $i,SV815: $i,SV65: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV815 @ SV65 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ SV1492 @ SV65 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV65 ) @ ( c_HOL_Otimes__class_Otimes @ SV815 @ SV1492 @ SV65 ) @ SV65 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6611]) ).
thf(6840,plain,
! [SV1493: $i,SV66: $i,SV816: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV816 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1493 @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ SV66 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV66 ) @ ( c_HOL_Otimes__class_Otimes @ SV816 @ SV1493 @ SV66 ) @ SV66 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6612]) ).
thf(6841,plain,
! [SV1495: $i,SV824: $i,SV1938: $i,SV77: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6613]) ).
thf(6842,plain,
! [SV1496: $i,SV825: $i,SV1939: $i,SV78: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6614]) ).
thf(6843,plain,
! [SV1497: $i,SV826: $i,SV1940: $i,SV79: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6615]) ).
thf(6844,plain,
! [SV1498: $i,SV827: $i,SV1941: $i,SV80: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6616]) ).
thf(6845,plain,
! [SV1500: $i,SV84: $i,SV1942: $i,SV831: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6617]) ).
thf(6846,plain,
! [SV1943: $i,SV85: $i,SV1501: $i,SV832: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6618]) ).
thf(6847,plain,
! [SV86: $i,SV1944: $i,SV1502: $i,SV833: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6619]) ).
thf(6848,plain,
! [SV1503: $i,SV87: $i,SV1945: $i,SV834: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6620]) ).
thf(6849,plain,
! [SV2211: $i,SV2155: $i,SV1946: $i,SV88: $i,SV1504: $i,SV835: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2155 @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 )
= $true )
| ( ( ~ ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2155 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6621]) ).
thf(6850,plain,
! [SV2212: $i,SV2156: $i,SV89: $i,SV1947: $i,SV1505: $i,SV836: $i] :
( ( ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SV2156 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6622]) ).
thf(6851,plain,
! [SV2213: $i,SV2157: $i,SV1948: $i,SV90: $i,SV1506: $i,SV837: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2157 @ SV1506 @ SV90 ) @ SV2213 @ SV90 ) @ SV90 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SV2157 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SV2213 @ SV90 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6623]) ).
thf(6852,plain,
! [SV2214: $i,SV2158: $i,SV1949: $i,SV91: $i,SV1507: $i,SV838: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ SV2214 @ SV91 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SV2214 @ SV91 ) @ SV91 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6624]) ).
thf(6853,plain,
! [SV96: $i,SV1950: $i,SV1508: $i,SV843: $i] :
( ( ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
= $true )
| ( ( ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6625]) ).
thf(6854,plain,
! [SV97: $i,SV1951: $i,SV1509: $i,SV844: $i] :
( ( ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
= $true )
| ( ( ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6626]) ).
thf(6855,plain,
! [SV2159: $i,SV850: $i,SV1512: $i,SV1952: $i,SV103: $i] :
( ( ( c_lessequals @ SV103 @ SV1952 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1512 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1952 @ SV103 @ tc_nat ) @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV103 @ SV850 @ tc_nat ) @ SV1512 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1952 @ SV850 @ tc_nat ) @ SV2159 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6627]) ).
thf(6856,plain,
! [SV2160: $i,SV104: $i,SV1953: $i,SV851: $i,SV1513: $i] :
( ( ( c_lessequals @ SV1513 @ SV851 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1513 @ SV1953 @ tc_nat ) @ SV104 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV851 @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV104 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1513 @ tc_nat ) @ SV1953 @ tc_nat ) @ SV2160 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6628]) ).
thf(6857,plain,
! [SV2161: $i,SV1514: $i,SV852: $i,SV105: $i,SV1954: $i] :
( ( ( c_lessequals @ SV1954 @ SV105 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV105 @ SV1954 @ tc_nat ) @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ SV2161 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV105 @ SV852 @ tc_nat ) @ SV1514 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1954 @ SV852 @ tc_nat ) @ SV2161 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6629]) ).
thf(6858,plain,
! [SV2162: $i,SV1955: $i,SV1515: $i,SV106: $i,SV853: $i] :
( ( ( c_lessequals @ SV853 @ SV106 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV106 @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV853 @ SV1515 @ tc_nat ) @ SV2162 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV106 @ SV853 @ tc_nat ) @ SV1515 @ tc_nat ) @ SV1955 @ tc_nat ) @ SV2162 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6630]) ).
thf(6859,plain,
! [SV857: $i,SV2164: $i,SV1957: $i,SV1519: $i,SV110: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6631]) ).
thf(6860,plain,
! [SV1521: $i,SV112: $i,SV1959: $i,SV859: $i] :
( ( ( c_lessequals @ SV859 @ SV1959 @ SV112 )
= $false )
| ( ( ~ ( c_lessequals @ SV859 @ SV1521 @ SV112 ) )
= $true )
| ( ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6632]) ).
thf(6861,plain,
! [SV1522: $i,SV113: $i,SV1960: $i,SV860: $i] :
( ( ( c_lessequals @ SV860 @ SV1960 @ SV113 )
= $false )
| ( ( ~ ( c_lessequals @ SV860 @ SV1522 @ SV113 ) )
= $true )
| ( ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Orderings_Olinorder @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6633]) ).
thf(6862,plain,
! [SV1523: $i,SV114: $i,SV1961: $i,SV861: $i] :
( ( ( c_lessequals @ SV861 @ SV1961 @ SV114 )
= $false )
| ( ( ~ ( c_lessequals @ SV861 @ SV1523 @ SV114 ) )
= $true )
| ( ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6634]) ).
thf(6863,plain,
! [SV1964: $i,SV877: $i,SV2165: $i,SV131: $i,SV1538: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6637]) ).
thf(6864,plain,
! [SV1550: $i,SV148: $i,SV1972: $i,SV891: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6642]) ).
thf(6865,plain,
! [SV1974: $i,SV1552: $i,SV895: $i,SV152: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
= $false )
| ( ( ~ ( c_lessequals @ SV1552 @ SV1974 @ SV152 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6644]) ).
thf(6866,plain,
! [SV1975: $i,SV1553: $i,SV896: $i,SV153: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
= $false )
| ( ( ~ ( c_lessequals @ SV1553 @ SV1975 @ SV153 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6645]) ).
thf(6867,plain,
! [SV1976: $i,SV897: $i,SV1554: $i,SV154: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
= $false )
| ( ( ~ ( c_lessequals @ SV897 @ SV1976 @ SV154 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6646]) ).
thf(6868,plain,
! [SV1555: $i,SV1977: $i,SV155: $i,SV898: $i] :
( ( ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
= $false )
| ( ( ~ ( c_lessequals @ SV1977 @ SV1555 @ SV155 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6647]) ).
thf(6869,plain,
! [SV899: $i,SV1978: $i,SV156: $i,SV1556: $i] :
( ( ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
= $false )
| ( ( ~ ( c_lessequals @ SV1978 @ SV899 @ SV156 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6648]) ).
thf(6870,plain,
! [SV1979: $i,SV2166: $i,SV901: $i,SV1557: $i,SV158: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6649]) ).
thf(6871,plain,
! [SV2215: $i,SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV166 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6650]) ).
thf(6872,plain,
! [SV2216: $i,SV2168: $i,SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring @ SV167 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6651]) ).
thf(6873,plain,
! [SV1567: $i,SV911: $i,SV168: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV911 @ SV168 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ SV1567 @ SV168 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV168 ) @ ( c_HOL_Otimes__class_Otimes @ SV911 @ SV1567 @ SV168 ) @ SV168 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6652]) ).
thf(6874,plain,
! [SV1568: $i,SV169: $i,SV912: $i] :
( ( ( c_lessequals @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
= $false )
| ( ( c_lessequals @ SV1568 @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ SV169 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV169 ) @ ( c_HOL_Otimes__class_Otimes @ SV912 @ SV1568 @ SV169 ) @ SV169 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6653]) ).
thf(6875,plain,
! [SV1569: $i,SV170: $i,SV913: $i] :
( ( ( c_lessequals @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
= $false )
| ( ( c_lessequals @ SV1569 @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ SV170 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV170 ) @ ( c_HOL_Otimes__class_Otimes @ SV913 @ SV1569 @ SV170 ) @ SV170 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6654]) ).
thf(6876,plain,
! [SV1570: $i,SV915: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV915 @ SV172 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ SV1570 @ SV172 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV172 ) @ ( c_HOL_Otimes__class_Otimes @ SV915 @ SV1570 @ SV172 ) @ SV172 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6655]) ).
thf(6877,plain,
! [SV1571: $i,SV173: $i,SV916: $i] :
( ( ( c_lessequals @ SV916 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
= $false )
| ( ( c_lessequals @ SV1571 @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ SV173 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV173 ) @ ( c_HOL_Otimes__class_Otimes @ SV916 @ SV1571 @ SV173 ) @ SV173 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6656]) ).
thf(6878,plain,
! [SV1572: $i,SV917: $i,SV174: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV917 @ SV174 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ SV1572 @ SV174 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV174 ) @ ( c_HOL_Otimes__class_Otimes @ SV917 @ SV1572 @ SV174 ) @ SV174 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6657]) ).
thf(6879,plain,
! [SV945: $i,SV2169: $i,SV1999: $i,SV1596: $i,SV204: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6663]) ).
thf(6880,plain,
! [SV2000: $i,SV2170: $i,SV946: $i,SV1597: $i,SV205: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6664]) ).
thf(6881,plain,
! [SV2001: $i,SV219: $i,SV1598: $i,SV960: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV1598 @ SV219 ) @ ( c_HOL_Otimes__class_Otimes @ SV960 @ SV2001 @ SV219 ) @ SV219 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV960 @ SV219 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV960 @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6665]) ).
thf(6882,plain,
! [SV2002: $i,SV220: $i,SV961: $i,SV1599: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1599 @ SV961 @ SV220 ) @ ( c_HOL_Otimes__class_Otimes @ SV2002 @ SV961 @ SV220 ) @ SV220 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV961 @ SV220 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV961 @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV220 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6666]) ).
thf(6883,plain,
! [SV1600: $i,SV221: $i,SV2003: $i,SV962: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6667]) ).
thf(6884,plain,
! [SV248: $i,SV2015: $i,SV1621: $i,SV986: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6668]) ).
thf(6885,plain,
! [SV1624: $i,SV990: $i,SV2016: $i,SV252: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 ) )
= $true )
| ( ( c_lessequals @ SV990 @ SV1624 @ SV252 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6669]) ).
thf(6886,plain,
! [SV1625: $i,SV991: $i,SV2017: $i,SV253: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 ) )
= $true )
| ( ( c_lessequals @ SV991 @ SV1625 @ SV253 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6670]) ).
thf(6887,plain,
! [SV992: $i,SV254: $i,SV2018: $i,SV1626: $i] :
( ( ( c_lessequals @ SV1626 @ SV2018 @ SV254 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6671]) ).
thf(6888,plain,
! [SV1627: $i,SV255: $i,SV993: $i,SV2019: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 ) )
= $true )
| ( ( c_lessequals @ SV993 @ SV1627 @ SV255 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6672]) ).
thf(6889,plain,
! [SV994: $i,SV256: $i,SV1628: $i,SV2020: $i] :
( ( ( c_lessequals @ SV2020 @ SV1628 @ SV256 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6673]) ).
thf(6890,plain,
! [SV995: $i,SV257: $i,SV1629: $i,SV2021: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 ) )
= $true )
| ( ( c_lessequals @ SV995 @ SV1629 @ SV257 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6674]) ).
thf(6891,plain,
! [SV1638: $i,SV271: $i,SV1006: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1638 @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1006 @ SV1638 @ SV271 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) @ SV271 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6675]) ).
thf(6892,plain,
! [SV2027: $i,SV1652: $i,SV1026: $i,SV298: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6676]) ).
thf(6893,plain,
! [SV1653: $i,SV299: $i,SV1027: $i,SV2028: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6677]) ).
thf(6894,plain,
! [SV1654: $i,SV300: $i,SV2029: $i,SV1028: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6678]) ).
thf(6895,plain,
! [SV2030: $i,SV1029: $i,SV1655: $i,SV301: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6679]) ).
thf(6896,plain,
! [SV1030: $i,SV2031: $i,SV302: $i,SV1656: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6680]) ).
thf(6897,plain,
! [SV1031: $i,SV303: $i,SV1657: $i,SV2032: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6681]) ).
thf(6898,plain,
! [SV1032: $i,SV304: $i,SV2033: $i,SV1658: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6682]) ).
thf(6899,plain,
! [SV2034: $i,SV1659: $i,SV1033: $i,SV305: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6683]) ).
thf(6900,plain,
! [SV1660: $i,SV2035: $i,SV306: $i,SV1034: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6684]) ).
thf(6901,plain,
! [SV1035: $i,SV307: $i,SV2036: $i,SV1661: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6685]) ).
thf(6902,plain,
! [SV1662: $i,SV308: $i,SV1036: $i,SV2037: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6686]) ).
thf(6903,plain,
! [SV1037: $i,SV309: $i,SV1663: $i,SV2038: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6687]) ).
thf(6904,plain,
! [SV1038: $i,SV310: $i,SV1664: $i,SV2039: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6688]) ).
thf(6905,plain,
! [SV1674: $i,SV320: $i,SV2042: $i,SV1048: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1048 @ SV2042 @ SV320 ) @ ( c_HOL_Otimes__class_Otimes @ SV1674 @ SV2042 @ SV320 ) @ SV320 )
= $false )
| ( ( SV2042
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1048 @ SV1674 @ SV320 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6689]) ).
thf(6906,plain,
! [SV1675: $i,SV321: $i,SV1049: $i,SV2043: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1049 @ SV321 ) @ ( c_HOL_Otimes__class_Otimes @ SV2043 @ SV1675 @ SV321 ) @ SV321 )
= $false )
| ( ( SV2043
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1049 @ SV1675 @ SV321 )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6690]) ).
thf(6907,plain,
! [SV1677: $i,SV1051: $i,SV323: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV1051 @ SV323 )
= $false )
| ( ( c_lessequals @ SV1677 @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1051 @ SV1677 @ SV323 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV323 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6691]) ).
thf(6908,plain,
! [SV1678: $i,SV324: $i,SV1052: $i] :
( ( ( c_lessequals @ SV1052 @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV1678 @ SV324 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1052 @ SV1678 @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) @ SV324 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6692]) ).
thf(6909,plain,
! [SV1679: $i,SV1053: $i,SV325: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV1053 @ SV325 )
= $false )
| ( ( c_lessequals @ SV1679 @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1053 @ SV1679 @ SV325 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) @ SV325 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6693]) ).
thf(6910,plain,
! [SV1680: $i,SV326: $i,SV1054: $i] :
( ( ( c_lessequals @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1680 @ SV326 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1054 @ SV1680 @ SV326 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV326 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6694]) ).
thf(6911,plain,
! [SV1681: $i,SV1055: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV1055 @ SV327 )
= $false )
| ( ( c_lessequals @ SV1681 @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1055 @ SV1681 @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) @ SV327 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV327 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6695]) ).
thf(6912,plain,
! [SV1682: $i,SV328: $i,SV1056: $i] :
( ( ( c_lessequals @ SV1056 @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV1682 @ SV328 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1056 @ SV1682 @ SV328 ) @ ( c_HOL_Ozero__class_Ozero @ SV328 ) @ SV328 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6696]) ).
thf(6913,plain,
! [SV1057: $i,SV1683: $i,SV329: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV1683 @ SV329 )
= $false )
| ( ( c_lessequals @ SV1057 @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV1057 @ SV1683 @ SV329 ) @ ( c_HOL_Ozero__class_Ozero @ SV329 ) @ SV329 )
= $true )
| ( ( class_Ring__and__Field_Opordered__cancel__semiring @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6697]) ).
thf(6914,plain,
! [SV1684: $i,SV1058: $i,SV331: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1058 @ SV331 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ SV1684 @ SV331 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV331 ) @ ( c_HOL_Oplus__class_Oplus @ SV1058 @ SV1684 @ SV331 ) @ SV331 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV331 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6698]) ).
thf(6915,plain,
! [SV1685: $i,SV1059: $i,SV332: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1059 @ SV332 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ SV1685 @ SV332 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV332 ) @ ( c_HOL_Oplus__class_Oplus @ SV1059 @ SV1685 @ SV332 ) @ SV332 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6699]) ).
thf(6916,plain,
! [SV340: $i,SV1066: $i,SV1689: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6700]) ).
thf(6917,plain,
! [SV1692: $i,SV1072: $i,SV346: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1072 @ SV346 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ SV1692 @ SV346 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV346 ) @ ( c_HOL_Oplus__class_Oplus @ SV1072 @ SV1692 @ SV346 ) @ SV346 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6701]) ).
thf(6918,plain,
! [SV2047: $i,SV1076: $i,SV351: $i,SV2174: $i,SV1694: $i] :
( ( ( ~ ( c_lessequals @ SV1694 @ SV2174 @ SV351 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6703]) ).
thf(6919,plain,
! [SV358: $i,SV2051: $i,SV1699: $i,SV1083: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
= $true )
| ( ( ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6704]) ).
thf(6920,plain,
! [SV1085: $i,SV1700: $i,SV360: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ ( c_HOL_Ominus__class_Ominus @ SV1700 @ SV1085 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1700 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1085 @ SV1700 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV360 @ SV1085 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6705]) ).
thf(6921,plain,
! [SV1701: $i,SV1086: $i,SV361: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ ( c_HOL_Ominus__class_Ominus @ SV1086 @ SV1701 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1701 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1701 @ SV1086 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV361 @ SV1086 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6706]) ).
thf(6922,plain,
! [SV1718: $i,SV388: $i,SV1113: $i,SV2064: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omin @ SV2064 @ SV1113 @ SV388 ) @ SV1718 @ SV388 )
= $false )
| ( ( c_lessequals @ SV2064 @ SV1718 @ SV388 )
= $true )
| ( ( c_lessequals @ SV1113 @ SV1718 @ SV388 )
= $true )
| ( ( class_Orderings_Olinorder @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6717]) ).
thf(6923,plain,
! [SV2179: $i,SV2066: $i,SV1722: $i,SV392: $i,SV1117: $i] :
( ( ( c_lessequals @ SV1117 @ SV392 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV392 @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1117 @ SV1722 @ tc_nat ) @ SV2179 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV392 @ SV1117 @ tc_nat ) @ SV1722 @ tc_nat ) @ SV2066 @ tc_nat ) @ SV2179 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6718]) ).
thf(6924,plain,
! [SV2180: $i,SV1723: $i,SV1118: $i,SV393: $i,SV2067: $i] :
( ( ( c_lessequals @ SV2067 @ SV393 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV393 @ SV2067 @ tc_nat ) @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ SV2180 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV393 @ SV1118 @ tc_nat ) @ SV1723 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2067 @ SV1118 @ tc_nat ) @ SV2180 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6719]) ).
thf(6925,plain,
! [SV2181: $i,SV394: $i,SV2068: $i,SV1119: $i,SV1724: $i] :
( ( ( c_lessequals @ SV1724 @ SV1119 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1724 @ SV2068 @ tc_nat ) @ SV394 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1119 @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV394 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1119 @ SV1724 @ tc_nat ) @ SV2068 @ tc_nat ) @ SV2181 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6720]) ).
thf(6926,plain,
! [SV2182: $i,SV1120: $i,SV1725: $i,SV2069: $i,SV395: $i] :
( ( ( c_lessequals @ SV395 @ SV2069 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1725 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2069 @ SV395 @ tc_nat ) @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV395 @ SV1120 @ tc_nat ) @ SV1725 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2069 @ SV1120 @ tc_nat ) @ SV2182 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6721]) ).
thf(6927,plain,
! [SV2070: $i,SV1134: $i,SV412: $i,SV2183: $i,SV1728: $i] :
( ( ( ~ ( c_lessequals @ SV1728 @ SV2183 @ SV412 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6722]) ).
thf(6928,plain,
! [SV2071: $i,SV1135: $i,SV413: $i,SV2184: $i,SV1729: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6723]) ).
thf(6929,plain,
! [SV414: $i,SV1730: $i,SV1136: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1136 @ SV1730 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1730 @ SV414 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1730 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV414 @ SV1136 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6724]) ).
thf(6930,plain,
! [SV415: $i,SV1731: $i,SV1137: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1137 @ SV1731 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV1137 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1731 @ SV415 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV415 @ SV1137 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6725]) ).
thf(6931,plain,
! [SV1732: $i,SV416: $i,SV2072: $i,SV1138: $i] :
( ( ( c_lessequals @ SV1138 @ SV2072 @ SV416 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
= $true )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6726]) ).
thf(6932,plain,
! [SV1733: $i,SV417: $i,SV2073: $i,SV1139: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 )
= $false )
| ( ( ~ ( c_lessequals @ SV2073 @ SV1733 @ SV417 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
= $true )
| ( ( class_Orderings_Oorder @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6727]) ).
thf(6933,plain,
! [SV1140: $i,SV418: $i,SV1734: $i,SV2074: $i] :
( ( ( c_lessequals @ SV2074 @ SV1734 @ SV418 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
= $true )
| ( ( class_Orderings_Opreorder @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6728]) ).
thf(6934,plain,
! [SV1141: $i,SV419: $i,SV1735: $i,SV2075: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 )
= $false )
| ( ( ~ ( c_lessequals @ SV1141 @ SV2075 @ SV419 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
= $true )
| ( ( class_Orderings_Opreorder @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6729]) ).
thf(6935,plain,
! [SV2082: $i,SV1150: $i,SV428: $i,SV2185: $i,SV1744: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6736]) ).
thf(6936,plain,
! [SV1746: $i,SV430: $i,SV1152: $i,SV2083: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omin @ SV2083 @ SV1152 @ SV430 ) @ SV1746 @ SV430 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2083 @ SV1746 @ SV430 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1152 @ SV1746 @ SV430 )
= $true )
| ( ( class_Orderings_Olinorder @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6738]) ).
thf(6937,plain,
! [SV1154: $i,SV432: $i,SV2084: $i,SV1748: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1748 @ SV2084 @ SV432 ) @ ( c_HOL_Otimes__class_Otimes @ SV1154 @ SV2084 @ SV432 ) @ SV432 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV1154 @ SV432 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1154 @ SV1748 @ SV432 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6739]) ).
thf(6938,plain,
! [SV1155: $i,SV433: $i,SV1749: $i,SV2085: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1749 @ SV433 ) @ ( c_HOL_Otimes__class_Otimes @ SV2085 @ SV1155 @ SV433 ) @ SV433 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1749 @ SV1155 @ SV433 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1155 @ SV1749 @ SV433 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6740]) ).
thf(6939,plain,
! [SV1758: $i,SV442: $i,SV2086: $i,SV1164: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
= $true )
| ( ( class_Orderings_Olinorder @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6749]) ).
thf(6940,plain,
! [SV2217: $i,SV2186: $i,SV2094: $i,SV458: $i,SV1772: $i,SV1180: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2186 @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2186 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6760]) ).
thf(6941,plain,
! [SV2218: $i,SV2187: $i,SV459: $i,SV2095: $i,SV1773: $i,SV1181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SV2187 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6761]) ).
thf(6942,plain,
! [SV2219: $i,SV2188: $i,SV2096: $i,SV460: $i,SV1774: $i,SV1182: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2188 @ SV1774 @ SV460 ) @ SV2219 @ SV460 ) @ SV460 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV2188 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SV2219 @ SV460 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6762]) ).
thf(6943,plain,
! [SV2220: $i,SV2189: $i,SV2097: $i,SV461: $i,SV1775: $i,SV1183: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ SV2220 @ SV461 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SV2220 @ SV461 ) @ SV461 ) )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6763]) ).
thf(6944,plain,
! [SV462: $i,SV2098: $i,SV1776: $i,SV1184: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6764]) ).
thf(6945,plain,
! [SV1782: $i,SV468: $i,SV2103: $i,SV1190: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6765]) ).
thf(6946,plain,
! [SV1800: $i,SV1234: $i,SV517: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1234 @ SV517 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV1800 @ SV517 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1800 @ SV517 ) @ SV517 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6767]) ).
thf(6947,plain,
! [SV2110: $i,SV2191: $i,SV1253: $i,SV1808: $i,SV536: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6768]) ).
thf(6948,plain,
! [SV2111: $i,SV2192: $i,SV1254: $i,SV1809: $i,SV537: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6769]) ).
thf(6949,plain,
! [SV2113: $i,SV1265: $i,SV549: $i,SV2193: $i,SV1812: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6771]) ).
thf(6950,plain,
! [SV1815: $i,SV1272: $i,SV559: $i,SV2114: $i,SV2194: $i] :
( ( ( ~ ( c_lessequals @ SV2194 @ SV2114 @ SV559 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 ) )
= $true )
| ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6772]) ).
thf(6951,plain,
! [SV1273: $i,SV560: $i,SV1816: $i,SV2115: $i] :
( ( ( c_lessequals @ SV2115 @ SV1816 @ SV560 )
= $false )
| ( ( ~ ( c_lessequals @ SV1273 @ SV2115 @ SV560 ) )
= $true )
| ( ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
= $true )
| ( ( class_Orderings_Opreorder @ SV560 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6773]) ).
thf(6952,plain,
! [SV1817: $i,SV561: $i,SV1274: $i] :
( ( ( c_lessequals @ SV1274 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $false )
| ( ( c_lessequals @ SV1817 @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1274 @ SV1817 @ SV561 ) @ ( c_HOL_Ozero__class_Ozero @ SV561 ) @ SV561 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6774]) ).
thf(6953,plain,
! [SV1818: $i,SV562: $i,SV2116: $i,SV1275: $i] :
( ( ( c_lessequals @ SV1275 @ SV2116 @ SV562 )
= $false )
| ( ( ~ ( c_lessequals @ SV2116 @ SV1818 @ SV562 ) )
= $true )
| ( ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
= $true )
| ( ( class_Orderings_Oorder @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6775]) ).
thf(6954,plain,
! [SV1281: $i,SV569: $i,SV1821: $i,SV2117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1821 @ SV569 ) @ ( c_HOL_Otimes__class_Otimes @ SV2117 @ SV1281 @ SV569 ) @ SV569 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV569 ) @ SV2117 @ SV569 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1281 @ SV1821 @ SV569 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6776]) ).
thf(6955,plain,
! [SV2118: $i,SV570: $i,SV1822: $i,SV1282: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV1822 @ SV570 ) @ ( c_HOL_Otimes__class_Otimes @ SV1282 @ SV2118 @ SV570 ) @ SV570 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1822 @ SV2118 @ SV570 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1282 @ ( c_HOL_Ozero__class_Ozero @ SV570 ) @ SV570 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6777]) ).
thf(6956,plain,
! [SV1283: $i,SV571: $i,SV2119: $i,SV1823: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1823 @ SV2119 @ SV571 ) @ ( c_HOL_Otimes__class_Otimes @ SV1283 @ SV2119 @ SV571 ) @ SV571 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV571 ) @ SV2119 @ SV571 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1823 @ SV571 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV571 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6778]) ).
thf(6957,plain,
! [SV2120: $i,SV572: $i,SV1284: $i,SV1824: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1824 @ SV1284 @ SV572 ) @ ( c_HOL_Otimes__class_Otimes @ SV2120 @ SV1284 @ SV572 ) @ SV572 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1824 @ SV2120 @ SV572 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1284 @ ( c_HOL_Ozero__class_Ozero @ SV572 ) @ SV572 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV572 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6779]) ).
thf(6958,plain,
! [SV1325: $i,SV621: $i,SV1844: $i] :
( ( ( c_lessequals @ SV1844 @ SV621 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1844 @ SV1325 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV621 @ SV1844 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV1844 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV621 @ SV1325 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6782]) ).
thf(6959,plain,
! [SV1845: $i,SV622: $i,SV1326: $i] :
( ( ( c_lessequals @ SV1326 @ SV622 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1326 @ SV1845 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV622 @ SV1845 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV622 @ SV1326 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1845 @ SV1326 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6783]) ).
thf(6960,plain,
! [SV1349: $i,SV646: $i,SV1859: $i] :
( ( ( c_lessequals @ SV1859 @ SV646 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1859 @ SV1349 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1859 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1349 @ SV1859 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV646 @ SV1349 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6785]) ).
thf(6961,plain,
! [SV1860: $i,SV647: $i,SV1350: $i] :
( ( ( c_lessequals @ SV1350 @ SV647 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1350 @ SV1860 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV647 @ SV1860 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1350 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1860 @ SV1350 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6786]) ).
thf(6962,plain,
! [SV1873: $i,SV672: $i,SV2124: $i,SV1373: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
= $true )
| ( ( class_Orderings_Oorder @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6791]) ).
thf(6963,plain,
! [SV1374: $i,SV673: $i,SV1874: $i,SV2125: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
= $true )
| ( ( class_Orderings_Opreorder @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6792]) ).
thf(6964,plain,
! [SV2126: $i,SV682: $i,SV1879: $i,SV1381: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
!= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
= $true )
| ( ( SV1879 = SV2126 )
= $true )
| ( ( class_Int_Onumber__ring @ SV682 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV682 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6793]) ).
thf(6965,plain,
! [SV1385: $i,SV1883: $i,SV686: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
| ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6795]) ).
thf(6966,plain,
! [SV2196: $i,SV2129: $i,SV688: $i,SV1884: $i,SV1387: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
= $false )
| ( ( ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
| ~ ( c_lessequals @ SV2196 @ SV2129 @ SV688 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6796]) ).
thf(6967,plain,
! [SV2197: $i,SV2130: $i,SV690: $i,SV1886: $i,SV1389: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
= $false )
| ( ( ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
| ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6798]) ).
thf(6968,plain,
! [SV698: $i,SV1890: $i,SV1395: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1395 @ SV1890 @ SV698 )
= ( c_HOL_Ozero__class_Ozero @ SV698 ) )
= $false )
| ( ( SV1395 = SV1890 )
= $true )
| ( ( class_Int_Onumber__ring @ SV698 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV698 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6801]) ).
thf(6969,plain,
! [SV2198: $i,SV702: $i,SV2132: $i,SV1891: $i,SV1397: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2132 @ SV702 ) @ SV702 )
= ( c_HOL_Oplus__class_Oplus @ SV1891 @ SV2198 @ SV702 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1397 @ SV2132 @ SV702 )
= SV2198 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV702 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6802]) ).
thf(6970,plain,
! [SV1400: $i,SV1893: $i,SV705: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
| ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6803]) ).
thf(6971,plain,
! [SV2199: $i,SV2134: $i,SV1895: $i,SV1403: $i,SV709: $i] :
( ( ( class_Int_Onumber__ring @ SV709 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
| ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV709 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6805]) ).
thf(6972,plain,
! [SV2200: $i,SV2135: $i,SV710: $i,SV1896: $i,SV1404: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
| ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6806]) ).
thf(6973,plain,
! [SV2221: $i,SV2201: $i,SV2137: $i,SV713: $i,SV1898: $i,SV1407: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) )
= $true )
| ( ( class_Divides_Oring__div @ SV713 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6808]) ).
thf(6974,plain,
! [SV722: $i,SV1902: $i,SV1416: $i] :
( ( ( SV1416
= ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1902 @ SV722 ) )
= $false )
| ( ( SV1902
= ( c_HOL_Ozero__class_Ozero @ SV722 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV722 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV722 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6809]) ).
thf(6975,plain,
! [SV2222: $i,SV2202: $i,SV2139: $i,SV729: $i,SV1907: $i,SV1423: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2202 @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
= $true )
| ( ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2202 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV729 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6812]) ).
thf(6976,plain,
! [SV1910: $i,SV735: $i,SV1429: $i] :
( ( ( c_lessequals @ SV1429 @ SV735 @ tc_nat )
= $false )
| ( ( SV735 = SV1910 )
= $true )
| ( ( c_lessequals @ SV1429 @ SV1910 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV735 @ SV1429 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1910 @ SV1429 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6813]) ).
thf(6977,plain,
! [SV2203: $i,SV1432: $i,SV1911: $i,SV2140: $i,SV738: $i] :
( ( ( c_lessequals @ SV738 @ SV2140 @ tc_nat )
= $false )
| ( ( SV1911
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2140 @ SV738 @ tc_nat ) @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV738 @ SV1432 @ tc_nat ) @ SV1911 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2140 @ SV1432 @ tc_nat ) @ SV2203 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6814]) ).
thf(6978,plain,
! [SV2204: $i,SV2141: $i,SV741: $i,SV1912: $i,SV1434: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6815]) ).
thf(6979,plain,
! [SV2223: $i,SV2205: $i,SV2142: $i,SV742: $i,SV1913: $i,SV1435: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6816]) ).
thf(6980,plain,
! [SV2224: $i,SV2206: $i,SV2143: $i,SV743: $i,SV1914: $i,SV1436: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2206 @ SV1914 @ SV743 ) @ SV2224 @ SV743 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SV2206 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SV2224 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV743 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6817]) ).
thf(6981,plain,
! [SV2207: $i,SV2145: $i,SV1919: $i,SV1441: $i,SV748: $i] :
( ( ( class_Int_Onumber__ring @ SV748 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
| ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV748 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6818]) ).
thf(6982,plain,
! [SV2225: $i,SV2208: $i,SV2146: $i,SV749: $i,SV1920: $i,SV1442: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV749 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6819]) ).
thf(6983,plain,
! [SV2209: $i,SV1924: $i,SV1446: $i,SV753: $i,SV2150: $i] :
( ( ( c_lessequals @ SV2150 @ SV753 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV2150 @ tc_nat ) @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= SV2209 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV753 @ SV1446 @ tc_nat ) @ SV1924 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2150 @ SV1446 @ tc_nat ) @ SV2209 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6821]) ).
thf(6984,plain,
! [SV2210: $i,SV2151: $i,SV1925: $i,SV1447: $i,SV754: $i] :
( ( ( class_Int_Onumber__ring @ SV754 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
| ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV754 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6822]) ).
thf(6985,plain,
! [SV1464: $i,SV35: $i,SV1930: $i,SV786: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1930 @ SV35 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1930 @ SV1464 @ SV35 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1464 @ SV35 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6831]) ).
thf(6986,plain,
! [SV1495: $i,SV77: $i,SV1938: $i,SV824: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV824 @ SV1938 @ SV77 ) @ ( c_HOL_Otimes__class_Otimes @ SV1495 @ SV1938 @ SV77 ) @ SV77 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV77 ) @ SV1938 @ SV77 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1495 @ SV77 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6841]) ).
thf(6987,plain,
! [SV1496: $i,SV78: $i,SV825: $i,SV1939: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV825 @ SV78 ) @ ( c_HOL_Otimes__class_Otimes @ SV1939 @ SV1496 @ SV78 ) @ SV78 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV78 ) @ SV1939 @ SV78 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV825 @ SV1496 @ SV78 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6842]) ).
thf(6988,plain,
! [SV1497: $i,SV79: $i,SV1940: $i,SV826: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV826 @ SV1940 @ SV79 ) @ ( c_HOL_Otimes__class_Otimes @ SV1497 @ SV1940 @ SV79 ) @ SV79 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV79 ) @ SV1940 @ SV79 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV826 @ SV1497 @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6843]) ).
thf(6989,plain,
! [SV1498: $i,SV80: $i,SV827: $i,SV1941: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV827 @ SV80 ) @ ( c_HOL_Otimes__class_Otimes @ SV1941 @ SV1498 @ SV80 ) @ SV80 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV80 ) @ SV1941 @ SV80 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1498 @ SV80 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6844]) ).
thf(6990,plain,
! [SV84: $i,SV1942: $i,SV1500: $i,SV831: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ ( c_Divides_Odiv__class_Omod @ SV1500 @ SV1942 @ SV84 ) @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1942 @ SV84 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV831 @ SV1500 @ SV84 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(6991,plain,
! [SV1501: $i,SV85: $i,SV1943: $i,SV832: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1943 @ SV85 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ SV1501 @ SV85 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV832 @ ( c_Divides_Odiv__class_Omod @ SV1501 @ SV1943 @ SV85 ) @ SV85 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6846]) ).
thf(6992,plain,
! [SV1502: $i,SV86: $i,SV1944: $i,SV833: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1944 @ SV86 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ ( c_Divides_Odiv__class_Omod @ SV1502 @ SV1944 @ SV86 ) @ SV86 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV833 @ SV1502 @ SV86 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6847]) ).
thf(6993,plain,
! [SV1945: $i,SV87: $i,SV1503: $i,SV834: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1503 @ SV87 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ SV1945 @ SV87 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV834 @ ( c_Divides_Odiv__class_Omod @ SV1503 @ SV1945 @ SV87 ) @ SV87 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6848]) ).
thf(6994,plain,
! [SV2211: $i,SV1504: $i,SV88: $i,SV835: $i,SV2155: $i,SV1946: $i] :
( ( ( c_lessequals @ SV1946 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2155 @ SV835 @ SV88 ) @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV835 @ SV1504 @ SV88 ) @ SV1946 @ SV88 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2155 @ SV1504 @ SV88 ) @ SV2211 @ SV88 ) @ SV88 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6849]) ).
thf(6995,plain,
! [SV2212: $i,SV1505: $i,SV836: $i,SV89: $i,SV2156: $i,SV1947: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1947 @ SV2156 @ SV89 ) @ SV836 @ SV89 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1505 @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 )
= $false )
| ( ( c_lessequals @ SV836 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1505 @ SV1947 @ SV89 ) @ SV2156 @ SV89 ) @ SV2212 @ SV89 ) @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6850]) ).
thf(6996,plain,
! [SV2213: $i,SV1948: $i,SV1506: $i,SV90: $i,SV2157: $i,SV837: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV837 @ SV2157 @ SV90 ) @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ SV2213 @ SV90 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV837 @ SV1506 @ SV90 ) @ SV1948 @ SV90 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2157 @ SV1506 @ SV90 ) @ SV2213 @ SV90 ) @ SV90 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(6997,plain,
! [SV2214: $i,SV1507: $i,SV2158: $i,SV91: $i,SV1949: $i,SV838: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV838 @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1507 @ SV1949 @ SV91 ) @ SV2214 @ SV91 ) @ SV91 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV838 @ SV1507 @ SV91 ) @ SV1949 @ SV91 ) @ SV2158 @ SV91 ) @ SV2214 @ SV91 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6852]) ).
thf(6998,plain,
! [SV1950: $i,SV96: $i,SV1508: $i,SV843: $i] :
( ( ( ~ ( c_lessequals @ SV843 @ SV1508 @ SV96 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true )
| ( ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6853]) ).
thf(6999,plain,
! [SV1509: $i,SV97: $i,SV1951: $i,SV844: $i] :
( ( ( ~ ( c_lessequals @ SV844 @ SV1951 @ SV97 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true )
| ( ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6854]) ).
thf(7000,plain,
! [SV857: $i,SV2164: $i,SV1957: $i,SV1519: $i,SV110: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6859]) ).
thf(7001,plain,
! [SV1959: $i,SV112: $i,SV1521: $i,SV859: $i] :
( ( ( c_lessequals @ SV859 @ SV1521 @ SV112 )
= $false )
| ( ( c_lessequals @ SV859 @ SV1959 @ SV112 )
= $false )
| ( ( c_lessequals @ SV859 @ ( c_Orderings_Oord__class_Omin @ SV1521 @ SV1959 @ SV112 ) @ SV112 )
= $true )
| ( ( class_Orderings_Olinorder @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6860]) ).
thf(7002,plain,
! [SV1960: $i,SV113: $i,SV1522: $i,SV860: $i] :
( ( ( c_lessequals @ SV860 @ SV1522 @ SV113 )
= $false )
| ( ( c_lessequals @ SV860 @ SV1960 @ SV113 )
= $false )
| ( ( c_lessequals @ SV860 @ ( c_Orderings_Oord__class_Omin @ SV1522 @ SV1960 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Orderings_Olinorder @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6861]) ).
thf(7003,plain,
! [SV1961: $i,SV114: $i,SV1523: $i,SV861: $i] :
( ( ( c_lessequals @ SV861 @ SV1523 @ SV114 )
= $false )
| ( ( c_lessequals @ SV861 @ SV1961 @ SV114 )
= $false )
| ( ( c_lessequals @ SV861 @ ( c_Orderings_Oord__class_Omin @ SV1523 @ SV1961 @ SV114 ) @ SV114 )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6862]) ).
thf(7004,plain,
! [SV1964: $i,SV877: $i,SV2165: $i,SV131: $i,SV1538: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6863]) ).
thf(7005,plain,
! [SV1972: $i,SV891: $i,SV1550: $i,SV148: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV148 ) @ SV1550 @ SV148 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ SV1972 @ SV148 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV891 @ ( c_HOL_Oplus__class_Oplus @ SV1550 @ SV1972 @ SV148 ) @ SV148 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6864]) ).
thf(7006,plain,
! [SV895: $i,SV152: $i,SV1974: $i,SV1552: $i] :
( ( ( c_lessequals @ SV1552 @ SV1974 @ SV152 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV152 ) @ SV895 @ SV152 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1552 @ SV152 ) @ ( c_HOL_Otimes__class_Otimes @ SV895 @ SV1974 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono1 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6865]) ).
thf(7007,plain,
! [SV896: $i,SV153: $i,SV1975: $i,SV1553: $i] :
( ( ( c_lessequals @ SV1553 @ SV1975 @ SV153 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV153 ) @ SV896 @ SV153 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1553 @ SV153 ) @ ( c_HOL_Otimes__class_Otimes @ SV896 @ SV1975 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6866]) ).
thf(7008,plain,
! [SV1554: $i,SV154: $i,SV1976: $i,SV897: $i] :
( ( ( c_lessequals @ SV897 @ SV1976 @ SV154 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV154 ) @ SV1554 @ SV154 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV897 @ SV1554 @ SV154 ) @ ( c_HOL_Otimes__class_Otimes @ SV1976 @ SV1554 @ SV154 ) @ SV154 )
= $true )
| ( ( class_Ring__and__Field_Omult__mono @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6867]) ).
thf(7009,plain,
! [SV898: $i,SV155: $i,SV1555: $i,SV1977: $i] :
( ( ( c_lessequals @ SV1977 @ SV1555 @ SV155 )
= $false )
| ( ( c_lessequals @ SV898 @ ( c_HOL_Ozero__class_Ozero @ SV155 ) @ SV155 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1555 @ SV155 ) @ ( c_HOL_Otimes__class_Otimes @ SV898 @ SV1977 @ SV155 ) @ SV155 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6868]) ).
thf(7010,plain,
! [SV1556: $i,SV156: $i,SV899: $i,SV1978: $i] :
( ( ( c_lessequals @ SV1978 @ SV899 @ SV156 )
= $false )
| ( ( c_lessequals @ SV1556 @ ( c_HOL_Ozero__class_Ozero @ SV156 ) @ SV156 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV899 @ SV1556 @ SV156 ) @ ( c_HOL_Otimes__class_Otimes @ SV1978 @ SV1556 @ SV156 ) @ SV156 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6869]) ).
thf(7011,plain,
! [SV1979: $i,SV2166: $i,SV901: $i,SV1557: $i,SV158: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6870]) ).
thf(7012,plain,
! [SV2215: $i,SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i,SV166: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV166 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6871]) ).
thf(7013,plain,
! [SV2216: $i,SV2168: $i,SV1983: $i,SV1566: $i,SV910: $i,SV167: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring @ SV167 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true )
| ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6872]) ).
thf(7014,plain,
! [SV945: $i,SV2169: $i,SV1999: $i,SV1596: $i,SV204: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
| ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6879]) ).
thf(7015,plain,
! [SV2000: $i,SV2170: $i,SV946: $i,SV1597: $i,SV205: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
| ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6880]) ).
thf(7016,plain,
! [SV2003: $i,SV221: $i,SV1600: $i,SV962: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV1600 @ SV221 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ SV2003 @ SV221 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV962 @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV2003 @ SV221 ) @ SV221 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6883]) ).
thf(7017,plain,
! [SV1621: $i,SV248: $i,SV2015: $i,SV986: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6884]) ).
thf(7018,plain,
! [SV1624: $i,SV252: $i,SV2016: $i,SV990: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV990 @ SV2016 @ SV252 ) @ ( c_HOL_Otimes__class_Otimes @ SV1624 @ SV2016 @ SV252 ) @ SV252 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV2016 @ SV252 )
= $false )
| ( ( c_lessequals @ SV990 @ SV1624 @ SV252 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6885]) ).
thf(7019,plain,
! [SV1625: $i,SV253: $i,SV991: $i,SV2017: $i] :
( ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV991 @ SV253 ) @ ( c_HOL_Otimes__class_Otimes @ SV2017 @ SV1625 @ SV253 ) @ SV253 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV2017 @ SV253 )
= $false )
| ( ( c_lessequals @ SV991 @ SV1625 @ SV253 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6886]) ).
thf(7020,plain,
! [SV2018: $i,SV1626: $i,SV992: $i,SV254: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV254 ) @ SV992 @ SV254 )
= $false )
| ( ( c_lessequals @ SV1626 @ SV2018 @ SV254 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV1626 @ SV254 ) @ ( c_HOL_Otimes__class_Otimes @ SV992 @ SV2018 @ SV254 ) @ SV254 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6887]) ).
thf(7021,plain,
! [SV1627: $i,SV993: $i,SV2019: $i,SV255: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV255 ) @ SV2019 @ SV255 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV993 @ SV255 ) @ ( c_HOL_Otimes__class_Otimes @ SV2019 @ SV1627 @ SV255 ) @ SV255 )
= $false )
| ( ( c_lessequals @ SV993 @ SV1627 @ SV255 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6888]) ).
thf(7022,plain,
! [SV1628: $i,SV2020: $i,SV256: $i,SV994: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
= $false )
| ( ( c_lessequals @ SV2020 @ SV1628 @ SV256 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV1628 @ SV256 ) @ ( c_HOL_Otimes__class_Otimes @ SV994 @ SV2020 @ SV256 ) @ SV256 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6889]) ).
thf(7023,plain,
! [SV995: $i,SV1629: $i,SV257: $i,SV2021: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2021 @ ( c_HOL_Ozero__class_Ozero @ SV257 ) @ SV257 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV1629 @ SV257 ) @ ( c_HOL_Otimes__class_Otimes @ SV2021 @ SV995 @ SV257 ) @ SV257 )
= $false )
| ( ( c_lessequals @ SV995 @ SV1629 @ SV257 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6890]) ).
thf(7024,plain,
! [SV1026: $i,SV298: $i,SV2027: $i,SV1652: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1652 @ SV2027 @ SV298 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV1026 @ SV298 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV1652 @ SV298 ) @ ( c_HOL_Otimes__class_Otimes @ SV1026 @ SV2027 @ SV298 ) @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Oordered__comm__semiring__strict @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6892]) ).
thf(7025,plain,
! [SV1027: $i,SV2028: $i,SV299: $i,SV1653: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1653 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2028 @ SV1027 @ SV299 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1027 @ SV1653 @ SV299 ) @ ( c_HOL_Otimes__class_Otimes @ SV2028 @ SV1653 @ SV299 ) @ SV299 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6893]) ).
thf(7026,plain,
! [SV2029: $i,SV1028: $i,SV1654: $i,SV300: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV1654 @ SV300 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1028 @ SV2029 @ SV300 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1028 @ SV1654 @ SV300 ) @ ( c_HOL_Otimes__class_Otimes @ SV2029 @ SV1654 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6894]) ).
thf(7027,plain,
! [SV1655: $i,SV301: $i,SV2030: $i,SV1029: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1029 @ SV2030 @ SV301 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV301 ) @ SV1655 @ SV301 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1029 @ SV1655 @ SV301 ) @ ( c_HOL_Otimes__class_Otimes @ SV2030 @ SV1655 @ SV301 ) @ SV301 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6895]) ).
thf(7028,plain,
! [SV1656: $i,SV302: $i,SV1030: $i,SV2031: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2031 @ SV1030 @ SV302 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1656 @ ( c_HOL_Ozero__class_Ozero @ SV302 ) @ SV302 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1030 @ SV1656 @ SV302 ) @ ( c_HOL_Otimes__class_Otimes @ SV2031 @ SV1656 @ SV302 ) @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6896]) ).
thf(7029,plain,
! [SV1657: $i,SV2032: $i,SV303: $i,SV1031: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1031 @ ( c_HOL_Ozero__class_Ozero @ SV303 ) @ SV303 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2032 @ SV1657 @ SV303 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV1657 @ SV303 ) @ ( c_HOL_Otimes__class_Otimes @ SV1031 @ SV2032 @ SV303 ) @ SV303 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6897]) ).
thf(7030,plain,
! [SV2033: $i,SV1658: $i,SV1032: $i,SV304: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV304 ) @ SV1032 @ SV304 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1658 @ SV2033 @ SV304 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV1658 @ SV304 ) @ ( c_HOL_Otimes__class_Otimes @ SV1032 @ SV2033 @ SV304 ) @ SV304 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV304 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6898]) ).
thf(7031,plain,
! [SV1033: $i,SV305: $i,SV2034: $i,SV1659: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1659 @ SV2034 @ SV305 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV305 ) @ SV1033 @ SV305 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV1659 @ SV305 ) @ ( c_HOL_Otimes__class_Otimes @ SV1033 @ SV2034 @ SV305 ) @ SV305 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6899]) ).
thf(7032,plain,
! [SV1034: $i,SV306: $i,SV1660: $i,SV2035: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2035 @ SV1660 @ SV306 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1034 @ ( c_HOL_Ozero__class_Ozero @ SV306 ) @ SV306 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV1660 @ SV306 ) @ ( c_HOL_Otimes__class_Otimes @ SV1034 @ SV2035 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6900]) ).
thf(7033,plain,
! [SV2036: $i,SV1661: $i,SV1035: $i,SV307: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV307 ) @ SV1035 @ SV307 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1661 @ SV2036 @ SV307 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV1661 @ SV307 ) @ ( c_HOL_Otimes__class_Otimes @ SV1035 @ SV2036 @ SV307 ) @ SV307 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV307 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6901]) ).
thf(7034,plain,
! [SV1662: $i,SV1036: $i,SV2037: $i,SV308: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV308 ) @ SV2037 @ SV308 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1036 @ SV308 ) @ ( c_HOL_Otimes__class_Otimes @ SV2037 @ SV1662 @ SV308 ) @ SV308 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1662 @ SV308 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6902]) ).
thf(7035,plain,
! [SV1663: $i,SV2038: $i,SV309: $i,SV1037: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1037 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2038 @ SV1663 @ SV309 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV1663 @ SV309 ) @ ( c_HOL_Otimes__class_Otimes @ SV1037 @ SV2038 @ SV309 ) @ SV309 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV309 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6903]) ).
thf(7036,plain,
! [SV1038: $i,SV1664: $i,SV310: $i,SV2039: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2039 @ ( c_HOL_Ozero__class_Ozero @ SV310 ) @ SV310 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1664 @ SV310 ) @ ( c_HOL_Otimes__class_Otimes @ SV2039 @ SV1038 @ SV310 ) @ SV310 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1664 @ SV310 )
= $true )
| ( ( class_Ring__and__Field_Oordered__ring__strict @ SV310 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6904]) ).
thf(7037,plain,
! [SV340: $i,SV1689: $i,SV1066: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1066 @ SV1689 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV1066 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1689 @ SV340 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1689 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV340 @ SV1066 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6916]) ).
thf(7038,plain,
! [SV2047: $i,SV1076: $i,SV351: $i,SV2174: $i,SV1694: $i] :
( ( ( c_lessequals @ SV1694 @ SV2174 @ SV351 )
= $false )
| ( ( ~ ( c_lessequals @ SV1076 @ SV2047 @ SV351 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6918]) ).
thf(7039,plain,
! [SV1699: $i,SV358: $i,SV2051: $i,SV1083: $i] :
( ( ( ~ ( c_lessequals @ SV1083 @ SV2051 @ SV358 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6919]) ).
thf(7040,plain,
! [SV2070: $i,SV1134: $i,SV412: $i,SV2183: $i,SV1728: $i] :
( ( ( c_lessequals @ SV1728 @ SV2183 @ SV412 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6927]) ).
thf(7041,plain,
! [SV2071: $i,SV1135: $i,SV413: $i,SV2184: $i,SV1729: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 )
= $false )
| ( ( ~ ( c_lessequals @ SV1135 @ SV2071 @ SV413 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6928]) ).
thf(7042,plain,
! [SV1138: $i,SV416: $i,SV1732: $i,SV2072: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2072 @ SV1732 @ SV416 )
= $false )
| ( ( c_lessequals @ SV1138 @ SV2072 @ SV416 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1138 @ SV1732 @ SV416 )
= $true )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6931]) ).
thf(7043,plain,
! [SV1139: $i,SV417: $i,SV1733: $i,SV2073: $i] :
( ( ( c_lessequals @ SV2073 @ SV1733 @ SV417 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV2073 @ SV417 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1139 @ SV1733 @ SV417 )
= $true )
| ( ( class_Orderings_Oorder @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6932]) ).
thf(7044,plain,
! [SV1734: $i,SV418: $i,SV2074: $i,SV1140: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV2074 @ SV418 )
= $false )
| ( ( c_lessequals @ SV2074 @ SV1734 @ SV418 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1140 @ SV1734 @ SV418 )
= $true )
| ( ( class_Orderings_Opreorder @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6933]) ).
thf(7045,plain,
! [SV1735: $i,SV419: $i,SV2075: $i,SV1141: $i] :
( ( ( c_lessequals @ SV1141 @ SV2075 @ SV419 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2075 @ SV1735 @ SV419 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1141 @ SV1735 @ SV419 )
= $true )
| ( ( class_Orderings_Opreorder @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6934]) ).
thf(7046,plain,
! [SV2082: $i,SV1150: $i,SV428: $i,SV2185: $i,SV1744: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6935]) ).
thf(7047,plain,
! [SV2086: $i,SV442: $i,SV1758: $i,SV1164: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1164 @ SV1758 @ SV442 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1164 @ SV2086 @ SV442 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1164 @ ( c_Orderings_Oord__class_Omin @ SV1758 @ SV2086 @ SV442 ) @ SV442 )
= $true )
| ( ( class_Orderings_Olinorder @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6939]) ).
thf(7048,plain,
! [SV2217: $i,SV1772: $i,SV458: $i,SV1180: $i,SV2186: $i,SV2094: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2094 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2186 @ SV1180 @ SV458 ) @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1180 @ SV1772 @ SV458 ) @ SV2094 @ SV458 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2186 @ SV1772 @ SV458 ) @ SV2217 @ SV458 ) @ SV458 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6940]) ).
thf(7049,plain,
! [SV2218: $i,SV1773: $i,SV1181: $i,SV459: $i,SV2187: $i,SV2095: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2095 @ SV2187 @ SV459 ) @ SV1181 @ SV459 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1773 @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1181 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1773 @ SV2095 @ SV459 ) @ SV2187 @ SV459 ) @ SV2218 @ SV459 ) @ SV459 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6941]) ).
thf(7050,plain,
! [SV2219: $i,SV2096: $i,SV1774: $i,SV460: $i,SV2188: $i,SV1182: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV2188 @ SV460 ) @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ SV2219 @ SV460 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1182 @ SV1774 @ SV460 ) @ SV2096 @ SV460 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2188 @ SV1774 @ SV460 ) @ SV2219 @ SV460 ) @ SV460 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6942]) ).
thf(7051,plain,
! [SV2220: $i,SV1775: $i,SV2189: $i,SV461: $i,SV2097: $i,SV1183: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1183 @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1775 @ SV2097 @ SV461 ) @ SV2220 @ SV461 ) @ SV461 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1775 @ SV461 ) @ SV2097 @ SV461 ) @ SV2189 @ SV461 ) @ SV2220 @ SV461 )
= $true )
| ( ( class_Ring__and__Field_Opordered__ring @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6943]) ).
thf(7052,plain,
! [SV1184: $i,SV462: $i,SV2098: $i,SV1776: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1776 @ SV2098 @ SV462 ) @ SV1184 @ SV462 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1184 @ ( c_HOL_Oplus__class_Oplus @ SV1776 @ SV2098 @ SV462 ) @ SV462 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV1776 @ SV462 ) @ SV462 ) @ SV2098 @ SV462 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6944]) ).
thf(7053,plain,
! [SV2103: $i,SV468: $i,SV1782: $i,SV1190: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV1782 @ SV468 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ SV2103 @ SV468 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1190 @ ( c_HOL_Ominus__class_Ominus @ SV1782 @ SV2103 @ SV468 ) @ SV468 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6945]) ).
thf(7054,plain,
! [SV2110: $i,SV2191: $i,SV1253: $i,SV1808: $i,SV536: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
| ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6947]) ).
thf(7055,plain,
! [SV2111: $i,SV2192: $i,SV1254: $i,SV1809: $i,SV537: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
| ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6948]) ).
thf(7056,plain,
! [SV2113: $i,SV1265: $i,SV549: $i,SV2193: $i,SV1812: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6949]) ).
thf(7057,plain,
! [SV1815: $i,SV1272: $i,SV559: $i,SV2114: $i,SV2194: $i] :
( ( ( c_lessequals @ SV2194 @ SV2114 @ SV559 )
= $false )
| ( ( ~ ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 ) )
= $true )
| ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6950]) ).
thf(7058,plain,
! [SV1816: $i,SV560: $i,SV2115: $i,SV1273: $i] :
( ( ( c_lessequals @ SV1273 @ SV2115 @ SV560 )
= $false )
| ( ( c_lessequals @ SV2115 @ SV1816 @ SV560 )
= $false )
| ( ( c_lessequals @ SV1273 @ SV1816 @ SV560 )
= $true )
| ( ( class_Orderings_Opreorder @ SV560 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6951]) ).
thf(7059,plain,
! [SV1275: $i,SV562: $i,SV1818: $i,SV2116: $i] :
( ( ( c_lessequals @ SV2116 @ SV1818 @ SV562 )
= $false )
| ( ( c_lessequals @ SV1275 @ SV2116 @ SV562 )
= $false )
| ( ( c_lessequals @ SV1275 @ SV1818 @ SV562 )
= $true )
| ( ( class_Orderings_Oorder @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6953]) ).
thf(7060,plain,
! [SV1373: $i,SV672: $i,SV1873: $i,SV2124: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2124 @ SV1873 @ SV672 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV2124 @ SV672 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1873 @ SV672 )
= $true )
| ( ( class_Orderings_Oorder @ SV672 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6962]) ).
thf(7061,plain,
! [SV1874: $i,SV673: $i,SV2125: $i,SV1374: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV2125 @ SV673 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2125 @ SV1874 @ SV673 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1374 @ SV1874 @ SV673 )
= $true )
| ( ( class_Orderings_Opreorder @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6963]) ).
thf(7062,plain,
! [SV2126: $i,SV682: $i,SV1879: $i,SV1381: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV1879 @ SV682 )
= ( c_HOL_Oplus__class_Oplus @ SV1381 @ SV2126 @ SV682 ) )
= $false )
| ( ( SV1879 = SV2126 )
= $true )
| ( ( class_Int_Onumber__ring @ SV682 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV682 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6964]) ).
thf(7063,plain,
! [SV1883: $i,SV1385: $i,SV686: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 ) )
= $true )
| ( ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6965]) ).
thf(7064,plain,
! [SV2129: $i,SV2196: $i,SV688: $i,SV1387: $i,SV1884: $i] :
( ( ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
= $true )
| ( ( ~ ( c_lessequals @ SV2196 @ SV2129 @ SV688 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6966]) ).
thf(7065,plain,
! [SV1389: $i,SV1886: $i,SV690: $i,SV2130: $i,SV2197: $i] :
( ( ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
= $true )
| ( ( ~ ( c_lessequals @ SV1886 @ SV1389 @ SV690 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6967]) ).
thf(7066,plain,
! [SV1893: $i,SV1400: $i,SV705: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 ) )
= $true )
| ( ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6970]) ).
thf(7067,plain,
! [SV2199: $i,SV2134: $i,SV709: $i,SV1895: $i,SV1403: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
= $true )
| ( ( ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV709 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV709 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6971]) ).
thf(7068,plain,
! [SV2200: $i,SV2135: $i,SV710: $i,SV1896: $i,SV1404: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6972]) ).
thf(7069,plain,
! [SV2221: $i,SV2201: $i,SV2137: $i,SV713: $i,SV1898: $i,SV1407: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) ) )
= $true )
| ( ( class_Divides_Oring__div @ SV713 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6973]) ).
thf(7070,plain,
! [SV2222: $i,SV2202: $i,SV2139: $i,SV729: $i,SV1907: $i,SV1423: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1423 @ SV1907 @ SV729 ) @ SV2139 @ SV729 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2202 @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
= $false )
| ( ( SV2139
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV2202 @ SV1423 @ SV729 ) @ SV1907 @ SV729 ) @ SV2222 @ SV729 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV729 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6975]) ).
thf(7071,plain,
! [SV1912: $i,SV1434: $i,SV741: $i,SV2204: $i,SV2141: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6978]) ).
thf(7072,plain,
! [SV2223: $i,SV2205: $i,SV2142: $i,SV742: $i,SV1913: $i,SV1435: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6979]) ).
thf(7073,plain,
! [SV2224: $i,SV2206: $i,SV2143: $i,SV743: $i,SV1914: $i,SV1436: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1436 @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV2206 @ SV1914 @ SV743 ) @ SV2224 @ SV743 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ SV1436 @ SV2206 @ SV743 ) @ SV1914 @ SV743 ) @ SV2143 @ SV743 )
= SV2224 )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV743 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6980]) ).
thf(7074,plain,
! [SV2207: $i,SV2145: $i,SV748: $i,SV1919: $i,SV1441: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
!= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
= $true )
| ( ( ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV748 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV748 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6981]) ).
thf(7075,plain,
! [SV2225: $i,SV2208: $i,SV2146: $i,SV749: $i,SV1920: $i,SV1442: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV749 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6982]) ).
thf(7076,plain,
! [SV2210: $i,SV754: $i,SV2151: $i,SV1925: $i,SV1447: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
!= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
= $true )
| ( ( ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV754 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV754 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6984]) ).
thf(7077,plain,
! [SV1950: $i,SV96: $i,SV1508: $i,SV843: $i] :
( ( ( c_lessequals @ SV843 @ SV1508 @ SV96 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 ) )
= $true )
| ( ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6998]) ).
thf(7078,plain,
! [SV1509: $i,SV97: $i,SV1951: $i,SV844: $i] :
( ( ( c_lessequals @ SV844 @ SV1951 @ SV97 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 ) )
= $true )
| ( ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6999]) ).
thf(7079,plain,
! [SV857: $i,SV2164: $i,SV1519: $i,SV1957: $i,SV110: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7000]) ).
thf(7080,plain,
! [SV2165: $i,SV1538: $i,SV1964: $i,SV131: $i,SV877: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ SV1964 @ SV131 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV2165 @ SV131 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ SV877 @ SV131 ) @ ( c_HOL_Oabs__class_Oabs @ SV1538 @ SV131 ) @ SV131 ) @ ( c_HOL_Otimes__class_Otimes @ SV1964 @ SV2165 @ SV131 ) @ SV131 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7004]) ).
thf(7081,plain,
! [SV1979: $i,SV2166: $i,SV1557: $i,SV901: $i,SV158: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7011]) ).
thf(7082,plain,
! [SV2215: $i,SV166: $i,SV2167: $i,SV1982: $i,SV1565: $i,SV909: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV166 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7012]) ).
thf(7083,plain,
! [SV2216: $i,SV2168: $i,SV167: $i,SV1983: $i,SV1566: $i,SV910: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV167 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7013]) ).
thf(7084,plain,
! [SV945: $i,SV2169: $i,SV1596: $i,SV1999: $i,SV204: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7014]) ).
thf(7085,plain,
! [SV2000: $i,SV2170: $i,SV1597: $i,SV946: $i,SV205: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7015]) ).
thf(7086,plain,
! [SV1621: $i,SV248: $i,SV2015: $i,SV986: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7017]) ).
thf(7087,plain,
! [SV2174: $i,SV1694: $i,SV351: $i,SV2047: $i,SV1076: $i] :
( ( ( c_lessequals @ SV1076 @ SV2047 @ SV351 )
= $false )
| ( ( c_lessequals @ SV1694 @ SV2174 @ SV351 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1076 @ SV1694 @ SV351 ) @ ( c_HOL_Oplus__class_Oplus @ SV2047 @ SV2174 @ SV351 ) @ SV351 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7038]) ).
thf(7088,plain,
! [SV1699: $i,SV358: $i,SV2051: $i,SV1083: $i] :
( ( ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7039]) ).
thf(7089,plain,
! [SV2183: $i,SV1728: $i,SV412: $i,SV2070: $i,SV1134: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1134 @ SV2070 @ SV412 )
= $false )
| ( ( c_lessequals @ SV1728 @ SV2183 @ SV412 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1134 @ SV1728 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV2070 @ SV2183 @ SV412 ) @ SV412 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7040]) ).
thf(7090,plain,
! [SV2184: $i,SV1729: $i,SV413: $i,SV2071: $i,SV1135: $i] :
( ( ( c_lessequals @ SV1135 @ SV2071 @ SV413 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1729 @ SV2184 @ SV413 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1135 @ SV1729 @ SV413 ) @ ( c_HOL_Oplus__class_Oplus @ SV2071 @ SV2184 @ SV413 ) @ SV413 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7041]) ).
thf(7091,plain,
! [SV2185: $i,SV1744: $i,SV428: $i,SV2082: $i,SV1150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1150 @ SV2082 @ SV428 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1744 @ SV2185 @ SV428 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1150 @ SV1744 @ SV428 ) @ ( c_HOL_Oplus__class_Oplus @ SV2082 @ SV2185 @ SV428 ) @ SV428 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7046]) ).
thf(7092,plain,
! [SV2110: $i,SV2191: $i,SV1808: $i,SV1253: $i,SV536: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7054]) ).
thf(7093,plain,
! [SV2111: $i,SV2192: $i,SV1809: $i,SV1254: $i,SV537: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7055]) ).
thf(7094,plain,
! [SV2193: $i,SV1812: $i,SV549: $i,SV2113: $i,SV1265: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1265 @ SV2113 @ SV549 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1812 @ SV2193 @ SV549 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Otimes__class_Otimes @ SV1265 @ SV1812 @ SV549 ) @ ( c_HOL_Otimes__class_Otimes @ SV2113 @ SV2193 @ SV549 ) @ SV549 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV549 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7056]) ).
thf(7095,plain,
! [SV2114: $i,SV559: $i,SV2194: $i,SV1815: $i,SV1272: $i] :
( ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2194 @ SV559 ) @ SV559 )
= $false )
| ( ( c_lessequals @ SV2194 @ SV2114 @ SV559 )
= $false )
| ( ( c_lessequals @ SV1272 @ ( c_HOL_Oplus__class_Oplus @ SV1815 @ SV2114 @ SV559 ) @ SV559 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7057]) ).
thf(7096,plain,
! [SV1883: $i,SV1385: $i,SV686: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1385 @ SV686 )
= $false )
| ( ( SV1385
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV686 ) @ SV1883 @ SV686 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV1883 @ SV686 )
= ( c_HOL_Ozero__class_Ozero @ SV686 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV686 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7063]) ).
thf(7097,plain,
! [SV1387: $i,SV1884: $i,SV688: $i,SV2129: $i,SV2196: $i] :
( ( ( c_lessequals @ SV2196 @ SV2129 @ SV688 )
= $false )
| ( ( c_lessequals @ SV1884 @ SV1387 @ SV688 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1387 @ SV1884 @ SV688 )
= ( c_HOL_Ominus__class_Ominus @ SV2129 @ SV2196 @ SV688 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV688 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7064]) ).
thf(7098,plain,
! [SV2130: $i,SV2197: $i,SV690: $i,SV1389: $i,SV1886: $i] :
( ( ( c_lessequals @ SV1886 @ SV1389 @ SV690 )
= $false )
| ( ( c_lessequals @ SV2197 @ SV2130 @ SV690 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1389 @ SV1886 @ SV690 )
= ( c_HOL_Ominus__class_Ominus @ SV2130 @ SV2197 @ SV690 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV690 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7065]) ).
thf(7099,plain,
! [SV1893: $i,SV1400: $i,SV705: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1400 @ SV705 )
= $false )
| ( ( SV1893
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV705 ) @ SV1893 @ SV705 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1400 @ SV1893 @ SV705 )
= ( c_HOL_Ozero__class_Ozero @ SV705 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7066]) ).
thf(7100,plain,
! [SV2199: $i,SV2134: $i,SV709: $i,SV1895: $i,SV1403: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
= $false )
| ( ( ( SV1895 = SV2199 )
| ( SV1403 = SV2134 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV709 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV709 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7067]) ).
thf(7101,plain,
! [SV1896: $i,SV1404: $i,SV710: $i,SV2200: $i,SV2135: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2135 @ SV2200 @ SV710 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1404 @ SV1896 @ SV710 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1404 @ SV1896 @ SV710 )
= ( c_HOL_Ominus__class_Ominus @ SV2135 @ SV2200 @ SV710 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV710 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7068]) ).
thf(7102,plain,
! [SV2137: $i,SV1407: $i,SV2221: $i,SV713: $i,SV1898: $i,SV2201: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
!= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
= $false )
| ( ( class_Divides_Oring__div @ SV713 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7069]) ).
thf(7103,plain,
! [SV2204: $i,SV2141: $i,SV741: $i,SV1912: $i,SV1434: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1434 @ SV1912 @ SV741 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2141 @ SV2204 @ SV741 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1434 @ SV1912 @ SV741 )
= ( c_HOL_Ominus__class_Ominus @ SV2141 @ SV2204 @ SV741 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV741 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7071]) ).
thf(7104,plain,
! [SV2142: $i,SV1435: $i,SV2223: $i,SV742: $i,SV1913: $i,SV2205: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
!= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV742 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7072]) ).
thf(7105,plain,
! [SV2207: $i,SV2145: $i,SV748: $i,SV1919: $i,SV1441: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
= $false )
| ( ( ( SV1919 = SV2207 )
| ( SV1441 = SV2145 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV748 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV748 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7074]) ).
thf(7106,plain,
! [SV2146: $i,SV1442: $i,SV2225: $i,SV749: $i,SV1920: $i,SV2208: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
!= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV749 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7075]) ).
thf(7107,plain,
! [SV2210: $i,SV754: $i,SV2151: $i,SV1925: $i,SV1447: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
= $false )
| ( ( ( SV2151 = SV2210 )
| ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV754 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV754 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7076]) ).
thf(7108,plain,
! [SV1508: $i,SV843: $i,SV1950: $i,SV96: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1950 @ SV96 )
= $false )
| ( ( c_lessequals @ SV843 @ SV1508 @ SV96 )
= $false )
| ( ( c_lessequals @ SV843 @ ( c_HOL_Oplus__class_Oplus @ SV1508 @ SV1950 @ SV96 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7077]) ).
thf(7109,plain,
! [SV1951: $i,SV844: $i,SV1509: $i,SV97: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1509 @ SV97 )
= $false )
| ( ( c_lessequals @ SV844 @ SV1951 @ SV97 )
= $false )
| ( ( c_lessequals @ SV844 @ ( c_HOL_Oplus__class_Oplus @ SV1509 @ SV1951 @ SV97 ) @ SV97 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV97 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7078]) ).
thf(7110,plain,
! [SV857: $i,SV2164: $i,SV1519: $i,SV1957: $i,SV110: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7079]) ).
thf(7111,plain,
! [SV1979: $i,SV2166: $i,SV1557: $i,SV901: $i,SV158: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7081]) ).
thf(7112,plain,
! [SV1982: $i,SV2167: $i,SV166: $i,SV2215: $i,SV1565: $i,SV909: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV166 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7082]) ).
thf(7113,plain,
! [SV1983: $i,SV167: $i,SV2216: $i,SV2168: $i,SV1566: $i,SV910: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV167 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7083]) ).
thf(7114,plain,
! [SV945: $i,SV2169: $i,SV1596: $i,SV1999: $i,SV204: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
= $false )
| ( ( ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
| ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7084]) ).
thf(7115,plain,
! [SV2000: $i,SV2170: $i,SV1597: $i,SV946: $i,SV205: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
= $false )
| ( ( ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
| ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7085]) ).
thf(7116,plain,
! [SV2015: $i,SV986: $i,SV1621: $i,SV248: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV1621 @ SV248 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV986 @ SV2015 @ SV248 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV986 @ ( c_HOL_Oplus__class_Oplus @ SV1621 @ SV2015 @ SV248 ) @ SV248 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV248 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7086]) ).
thf(7117,plain,
! [SV2051: $i,SV1083: $i,SV1699: $i,SV358: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV358 ) @ SV1699 @ SV358 )
= $false )
| ( ( c_lessequals @ SV1083 @ SV2051 @ SV358 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1083 @ ( c_HOL_Oplus__class_Oplus @ SV1699 @ SV2051 @ SV358 ) @ SV358 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV358 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7088]) ).
thf(7118,plain,
! [SV2110: $i,SV2191: $i,SV1808: $i,SV1253: $i,SV536: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
| ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7092]) ).
thf(7119,plain,
! [SV2111: $i,SV2192: $i,SV1809: $i,SV1254: $i,SV537: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
= $false )
| ( ( ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
| ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7093]) ).
thf(7120,plain,
! [SV709: $i,SV2134: $i,SV1403: $i,SV2199: $i,SV1895: $i] :
( ( ( SV1895 = SV2199 )
= $true )
| ( ( SV1403 = SV2134 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV1895 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV2199 @ SV709 ) @ SV709 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1403 @ SV2199 @ SV709 ) @ ( c_HOL_Otimes__class_Otimes @ SV2134 @ SV1895 @ SV709 ) @ SV709 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV709 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV709 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7100]) ).
thf(7121,plain,
! [SV2137: $i,SV1407: $i,SV2221: $i,SV713: $i,SV1898: $i,SV2201: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV2201 @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ SV2221 @ SV1898 @ SV713 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2201 @ SV1407 @ SV713 ) @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV2221 @ SV2137 @ SV713 ) @ SV1898 @ SV713 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1407 @ SV1898 @ SV713 )
= ( c_Divides_Odiv__class_Omod @ SV2137 @ SV1898 @ SV713 ) )
= $false )
| ( ( class_Divides_Oring__div @ SV713 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7102]) ).
thf(7122,plain,
! [SV2142: $i,SV1435: $i,SV2223: $i,SV742: $i,SV1913: $i,SV2205: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV2205 @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ SV2223 @ SV1913 @ SV742 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2205 @ SV1435 @ SV742 ) @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV2223 @ SV2142 @ SV742 ) @ SV1913 @ SV742 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1435 @ SV1913 @ SV742 )
= ( c_Divides_Odiv__class_Omod @ SV2142 @ SV1913 @ SV742 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV742 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7104]) ).
thf(7123,plain,
! [SV748: $i,SV2145: $i,SV1441: $i,SV2207: $i,SV1919: $i] :
( ( ( SV1919 = SV2207 )
= $true )
| ( ( SV1441 = SV2145 )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV1919 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV2207 @ SV748 ) @ SV748 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ SV1441 @ SV2207 @ SV748 ) @ ( c_HOL_Otimes__class_Otimes @ SV2145 @ SV1919 @ SV748 ) @ SV748 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV748 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV748 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7105]) ).
thf(7124,plain,
! [SV2146: $i,SV1442: $i,SV2225: $i,SV749: $i,SV1920: $i,SV2208: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV2208 @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ SV2225 @ SV1920 @ SV749 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2208 @ SV1442 @ SV749 ) @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Otimes__class_Otimes @ SV2225 @ SV2146 @ SV749 ) @ SV1920 @ SV749 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1442 @ SV1920 @ SV749 )
= ( c_Divides_Odiv__class_Omod @ SV2146 @ SV1920 @ SV749 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV749 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7106]) ).
thf(7125,plain,
! [SV1447: $i,SV754: $i,SV1925: $i,SV2210: $i,SV2151: $i] :
( ( ( SV2151 = SV2210 )
= $true )
| ( ( SV1925
= ( c_HOL_Ozero__class_Ozero @ SV754 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2151 @ SV754 ) @ SV754 )
= ( c_HOL_Oplus__class_Oplus @ SV1447 @ ( c_HOL_Otimes__class_Otimes @ SV1925 @ SV2210 @ SV754 ) @ SV754 ) )
= $false )
| ( ( class_Int_Onumber__ring @ SV754 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV754 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7107]) ).
thf(7126,plain,
! [SV1957: $i,SV857: $i,SV110: $i,SV2164: $i,SV1519: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7110]) ).
thf(7127,plain,
! [SV1979: $i,SV901: $i,SV158: $i,SV2166: $i,SV1557: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7111]) ).
thf(7128,plain,
! [SV1982: $i,SV2167: $i,SV166: $i,SV2215: $i,SV1565: $i,SV909: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV166 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7112]) ).
thf(7129,plain,
! [SV1983: $i,SV167: $i,SV2216: $i,SV2168: $i,SV1566: $i,SV910: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV167 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7113]) ).
thf(7130,plain,
! [SV1999: $i,SV945: $i,SV204: $i,SV2169: $i,SV1596: $i] :
( ( ( ~ ( c_lessequals @ SV1596 @ SV2169 @ SV204 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7114]) ).
thf(7131,plain,
! [SV2000: $i,SV946: $i,SV205: $i,SV2170: $i,SV1597: $i] :
( ( ( ~ ( c_lessequals @ SV1597 @ SV2170 @ SV205 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7115]) ).
thf(7132,plain,
! [SV2110: $i,SV1253: $i,SV536: $i,SV2191: $i,SV1808: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7118]) ).
thf(7133,plain,
! [SV2111: $i,SV1254: $i,SV537: $i,SV2192: $i,SV1809: $i] :
( ( ( ~ ( c_lessequals @ SV1809 @ SV2192 @ SV537 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[7119]) ).
thf(7134,plain,
! [SV1957: $i,SV857: $i,SV110: $i,SV2164: $i,SV1519: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7126]) ).
thf(7135,plain,
! [SV1979: $i,SV901: $i,SV158: $i,SV2166: $i,SV1557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7127]) ).
thf(7136,plain,
! [SV1982: $i,SV2215: $i,SV1565: $i,SV166: $i,SV2167: $i,SV909: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ SV2167 @ SV166 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ SV1565 @ SV2215 @ SV166 ) @ SV166 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV909 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1565 @ ( c_HOL_Otimes__class_Otimes @ SV1982 @ SV2167 @ SV166 ) @ SV166 ) @ SV2215 @ SV166 ) @ SV166 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV166 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7128]) ).
thf(7137,plain,
! [SV1983: $i,SV2168: $i,SV1566: $i,SV167: $i,SV2216: $i,SV910: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ SV2216 @ SV167 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1566 @ ( c_HOL_Otimes__class_Otimes @ SV2168 @ SV2216 @ SV167 ) @ SV167 ) @ SV1983 @ SV167 ) @ SV167 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV910 @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1983 @ SV167 ) @ SV167 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring @ SV167 )
= $false )
| ( ( class_Ring__and__Field_Odvd @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7129]) ).
thf(7138,plain,
! [SV1999: $i,SV945: $i,SV204: $i,SV2169: $i,SV1596: $i] :
( ( ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
= $false )
| ( ( ~ ( c_lessequals @ SV945 @ SV1999 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7130]) ).
thf(7139,plain,
! [SV2000: $i,SV946: $i,SV205: $i,SV2170: $i,SV1597: $i] :
( ( ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
= $false )
| ( ( ~ ( c_lessequals @ SV946 @ SV2000 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7131]) ).
thf(7140,plain,
! [SV2110: $i,SV1253: $i,SV536: $i,SV2191: $i,SV1808: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
= $false )
| ( ( ~ ( c_lessequals @ SV1253 @ SV2110 @ SV536 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7132]) ).
thf(7141,plain,
! [SV2111: $i,SV1254: $i,SV537: $i,SV2192: $i,SV1809: $i] :
( ( ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7133]) ).
thf(7142,plain,
! [SV2164: $i,SV1519: $i,SV110: $i,SV1957: $i,SV857: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1957 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1519 @ SV2164 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1957 @ SV110 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV1519 @ SV110 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV857 @ SV1519 @ SV110 ) @ ( c_HOL_Otimes__class_Otimes @ SV1957 @ SV2164 @ SV110 ) @ SV110 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7134]) ).
thf(7143,plain,
! [SV2166: $i,SV1557: $i,SV158: $i,SV1979: $i,SV901: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV901 @ SV1979 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1557 @ SV2166 @ SV158 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV901 @ SV158 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV158 ) @ SV1557 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV901 @ SV1557 @ SV158 ) @ ( c_HOL_Otimes__class_Otimes @ SV1979 @ SV2166 @ SV158 ) @ SV158 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7135]) ).
thf(7144,plain,
! [SV2169: $i,SV1596: $i,SV204: $i,SV1999: $i,SV945: $i] :
( ( ( c_lessequals @ SV945 @ SV1999 @ SV204 )
= $false )
| ( ( c_lessequals @ SV1596 @ SV2169 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1999 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1596 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV945 @ SV1596 @ SV204 ) @ ( c_HOL_Otimes__class_Otimes @ SV1999 @ SV2169 @ SV204 ) @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7138]) ).
thf(7145,plain,
! [SV2170: $i,SV1597: $i,SV205: $i,SV2000: $i,SV946: $i] :
( ( ( c_lessequals @ SV946 @ SV2000 @ SV205 )
= $false )
| ( ( c_lessequals @ SV1597 @ SV2170 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV946 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV205 ) @ SV1597 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ SV946 @ SV1597 @ SV205 ) @ ( c_HOL_Otimes__class_Otimes @ SV2000 @ SV2170 @ SV205 ) @ SV205 )
= $true )
| ( ( class_Ring__and__Field_Opordered__semiring @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7139]) ).
thf(7146,plain,
! [SV2191: $i,SV1808: $i,SV536: $i,SV2110: $i,SV1253: $i] :
( ( ( c_lessequals @ SV1253 @ SV2110 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1808 @ SV2191 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1253 @ SV536 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV536 ) @ SV1808 @ SV536 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1253 @ SV1808 @ SV536 ) @ ( c_HOL_Otimes__class_Otimes @ SV2110 @ SV2191 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV536 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7140]) ).
thf(7147,plain,
! [SV2192: $i,SV1809: $i,SV537: $i,SV2111: $i,SV1254: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1254 @ SV2111 @ SV537 )
= $false )
| ( ( c_lessequals @ SV1809 @ SV2192 @ SV537 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1254 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV537 ) @ SV1809 @ SV537 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ SV1254 @ SV1809 @ SV537 ) @ ( c_HOL_Otimes__class_Otimes @ SV2111 @ SV2192 @ SV537 ) @ SV537 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semiring__strict @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[7141]) ).
thf(7148,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1607,7147,7146,7145,7144,7143,7142,7137,7136,7125,7124,7123,7122,7121,7120,7117,7116,7109,7108,7103,7101,7099,7098,7097,7096,7095,7094,7091,7090,7089,7087,7080,7073,7070,7062,7061,7060,7059,7058,7053,7052,7051,7050,7049,7048,7047,7045,7044,7043,7042,7037,7036,7035,7034,7033,7032,7031,7030,7029,7028,7027,7026,7025,7024,7023,7022,7021,7020,7019,7018,7016,7010,7009,7008,7007,7006,7005,7003,7002,7001,6997,6996,6995,6994,6993,6992,6991,6990,6989,6988,6987,6986,6985,6983,6977,6976,6974,6969,6968,6961,6960,6959,6958,6957,6956,6955,6954,6952,6946,6938,6937,6936,6930,6929,6926,6925,6924,6923,6922,6921,6920,6917,6915,6914,6913,6912,6911,6910,6909,6908,6907,6906,6905,6891,6882,6881,6878,6877,6876,6875,6874,6873,6858,6857,6856,6855,6840,6839,6838,6837,6836,6835,6834,6833,6832,6830,6829,6828,6827,6826,6825,6824,6823,6820,6811,6810,6807,6804,6800,6799,6797,6794,6790,6789,6788,6787,6784,6781,6780,6770,6766,6759,6758,6757,6756,6755,6754,6753,6752,6751,6750,6748,6747,6746,6745,6744,6743,6742,6741,6737,6735,6734,6733,6732,6731,6730,6716,6715,6714,6713,6712,6711,6710,6709,6708,6707,6702,6662,6661,6660,6659,6658,6643,6641,6640,6639,6638,6636,6635,6607,6606,6605,6604,6599,6598,6597,6596,6595,6594,6588,6581,6579,6576,6575,6574,6568,6567,6562,6555,6550,6544,6543,6541,6538,6537,6536,6535,6534,6533,6528,6525,6524,6523,6522,6520,6519,6518,6515,6514,6513,6502,6500,6496,6495,6494,6493,6492,6491,6489,6488,6487,6486,6485,6483,6467,6454,6450,6449,6419,6415,6414,6413,6409,6408,6406,6394,6393,6392,6391,6390,6389,6375,6374,6372,6371,6370,6369,6368,6367,6359,6328,6324,6323,6318,6317,6312,6311,6275,6270,6269,6268,6253,6245,6243,6239,6235,6215,6197,6190,6182,6181,6180,6179,6174,6168,6165,6164,6162,6161,6158,6157,6142,6141,6140,6139,6138,6136,6135,6134,6133,6119,6118,6115,6082,6077,6067,6059,6058,6049,6048,6047,6046,6035,6032,6031,6011,6010,6009,6008,6007,5990,5989,5988,5987,5986,5985,5984,5983,5982,5981,5976,5975,5974,5973,5972,5971,5970,5969,5968,5964,5959,5958,5957,5956,5955,5954,5953,5952,5951,5950,5949,5948,5947,5946,5945,5936,5935,5922,5921,5920,5910,5886,5885,5884,5883,5882,5881,5860,5857,5855,5854,5853,5852,5851,5850,5849,5848,5844,5838,5818,5814,5810,5808,5805,5798,5795,5792,5790,5784,5777,5775,5774,5765,5764,5763,5762,5754,5753,5742,5741,5736,5735,5734,5733,5732,5731,5729,5728,5727,5726,5725,5724,5723,5711,5710,5709,5702,5700,5693,5688,5687,5683,5673,5672,5671,5669,5668,5667,5666,5660,5657,5636,5600,5595,5594,5582,5581,5580,5579,5576,5570,5521,5518,5517,5513,5512,5511,5510,5505,5493,5492,5488,5487,5486,5485,5484,5483,5482,5481,5473,5467,5434,5423,5422,5421,5420,5419,5403,5402,5399,5398,5393,5392,5391,5390,5389,5388,5381,5363,5343,5342,5341,5336,5329,5328,5327,5326,5325,5324,5302,5301,5281,5279,5278,5273,5268,5261,5260,5259,5258,5244,5225,5219,5218,5204,5202,5201,5186,5180,5179,5177,5176,5175,5168,5164,5163,5154,5153,5152,5135,5134,5132,5122,5121,5110,5109,5108,5102,5097,5096,5093,5092,5091,5090,5089,5088,5087,5086,5085,5084,5083,5082,5078,5077,5065,5064,5063,5062,5004,5003,5002,5001,4999,4998,4997,4996,4995,4994,4984,4971,4970,4969,4968,4966,4959,4949,4948,4946,4945,4942,4902,4886,4885,4884,4880,4847,4840,4835,4830,4825,4818,4817,4799,4785,4767,4766,4760,4735,4734,4733,4732,4723,4721,4715,4679,4662,4599,4576,4555,4545,4538,4537,4534,4528,4526,4525,4524,4523,4501,4499,4485,4416,4415,4331,4286,4273,4268,4257,4235,4234,4233,4221,4180,4179,4141,4140,4133,4095,4092,4087,4083,4082,4081,4016,3980,3971,3951,3918,3911,3905,3903,3887,3872,3871,3859,3845,3844,3840,3826,3804,3801,3800,3780,3769,3761,3739,3738,3737,3736,3708,3600,3593,3592,3562,3520,3518,3507,3506,3479,3475,3453,3382,3381,3370,3334,3333,3332,3272,3240,3239,3156,3107,3101,3100,3078,3077,3039,3037,2989,2980,2979,2973,2966,2889,2888,2887,2774,2770,2754,2745,2744,2717,2683,2555,2554,2552,2513,2480,2398,2397,2396,2395,2394,2393,2392,2391,2390,2389,2388,2387,2386,2385,2384,2383,2382,2381,2380,2379,2378,2377,2376,2375,2374,2373,2372,2371,2370,2369,2368,2362,2247,2231,2193,2170,2055,2050,1986,1760,1743]) ).
thf(7149,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[7148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV689-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.19 % Computer : n018.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 16:44:07 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 237.51/39.90 ......
% 237.51/39.90
% 237.51/39.90 No.of.Axioms: 798
% 237.51/39.90
% 237.51/39.90 Length.of.Defs: 0
% 237.51/39.90
% 237.51/39.90 Contains.Choice.Funs: false
% 237.51/39.90 ................................................................................................................................................................................................................................
% 237.51/39.90
% 237.51/39.90 ********************************
% 237.51/39.90 * All subproblems solved! *
% 237.51/39.90 ********************************
% 237.51/39.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:798,ps:0,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:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7148,loop_count:0,foatp_calls:1,translation:fof_full)
% 237.51/39.90
% 237.51/39.90 %**** Beginning of derivation protocol ****
% 237.51/39.90 % SZS output start CNFRefutation
% See solution above
% 39.85/39.94
% 39.85/39.94 %**** End of derivation protocol ****
% 39.85/39.94 %**** no. of clauses in derivation: 7149 ****
% 39.85/39.94 %**** clause counter: 7148 ****
% 39.85/39.94
% 39.85/39.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:798,ps:0,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:295,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:7148,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------