%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV678-1 : 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 : n014.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 10:58:28 AM UTC 2026
% Result : Unsatisfiable 153.86s 26.04s
% Output : CNFRefutation 25.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 688
% Syntax : Number of formulae : 6134 (3264 unt; 0 typ; 0 def)
% Number of atoms : 38700 (12941 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 91031 (9605 ~;13184 |; 0 &;68242 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 7 con; 0-3 aty)
% Number of variables : 16946 ( 0 ^;16946 !; 0 ?;16946 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Divides_Odiv__class_Omod,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(tp_c_GCD_Ogcd__class_Ogcd,type,
c_GCD_Ogcd__class_Ogcd: $i > $i > $i > $i ).
thf(tp_c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: $i > $i > $i > $i ).
thf(tp_c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: $i > $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $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_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_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Transcendental_Oexp,type,
c_Transcendental_Oexp: $i > $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_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_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $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__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_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_RealVector_Oreal__normed__field,type,
class_RealVector_Oreal__normed__field: $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__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
thf(tp_class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $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__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_class_SEQ_Obanach,type,
class_SEQ_Obanach: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_a,type,
v_a: $i ).
thf(tp_v_m,type,
v_m: $i ).
thf(tp_v_n,type,
v_n: $i ).
thf(1,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(2,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(3,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(4,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
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_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(9,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(10,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(11,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(12,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
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_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(15,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(16,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(17,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(18,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(19,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(20,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(21,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(22,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(23,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(24,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Power_Opower @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Power_Opower) ).
thf(25,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oidom @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oidom) ).
thf(26,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1) ).
thf(27,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ogroup__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Ogroup__add) ).
thf(28,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__add) ).
thf(29,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Omonoid__mult) ).
thf(30,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Omult__zero @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Omult__zero) ).
thf(31,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Oab__group__add) ).
thf(32,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Osemiring__0) ).
thf(33,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Osemiring__1) ).
thf(34,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__ring__1) ).
thf(35,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ozero__neq__one @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ozero__neq__one) ).
thf(36,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocomm__monoid__add) ).
thf(37,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Odivision__ring @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Odivision__ring) ).
thf(38,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Oab__semigroup__add) ).
thf(39,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1) ).
thf(40,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ono__zero__divisors @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ono__zero__divisors) ).
thf(41,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocancel__semigroup__add) ).
thf(42,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(43,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(44,axiom,
( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(45,axiom,
c_lessequals @ v_n @ v_m @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(46,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(47,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(48,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(49,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(50,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(51,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(52,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(53,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(54,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(55,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(56,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one__over_0) ).
thf(57,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_ya @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_ya @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
thf(58,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
thf(59,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__divide_0) ).
thf(60,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(61,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(62,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(63,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(64,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(65,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(66,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(67,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
thf(68,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(69,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(70,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(71,axiom,
c_lessequals @ v_n @ v_m @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(72,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(73,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(74,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(75,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(76,axiom,
! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(77,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(78,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(79,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(80,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(81,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff_0) ).
thf(82,axiom,
! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(83,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(84,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(85,axiom,
! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(86,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(87,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).
thf(88,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).
thf(89,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).
thf(90,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).
thf(91,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(92,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(93,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(94,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(95,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(96,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(97,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(98,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(99,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__diff2__nat_0) ).
thf(100,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__diff1__nat_0) ).
thf(101,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(102,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(103,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(104,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(105,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(106,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(107,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(108,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(109,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(110,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(111,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(112,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(113,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(114,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(115,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(116,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__diff__inverse_0) ).
thf(117,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__power__dvd_0) ).
thf(118,axiom,
! [T_a: $i,V_x: $i,V_n: $i,V_y: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_m @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__le_0) ).
thf(119,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__dvd_0) ).
thf(120,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
thf(121,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ V_x @ T_a ) @ ( c_Transcendental_Oexp @ V_y @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__diff_0) ).
thf(122,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(123,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(124,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).
thf(125,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).
thf(126,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_x @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
thf(127,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).
thf(128,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
thf(129,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
thf(130,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power_1) ).
thf(131,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(132,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(133,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(134,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).
thf(135,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).
thf(136,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).
thf(137,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).
thf(138,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__le__0__iff_4) ).
thf(139,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__le__0__iff_5) ).
thf(140,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__right__mono_0) ).
thf(141,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( 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_divide__right__mono__neg_0) ).
thf(142,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).
thf(143,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).
thf(144,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).
thf(145,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).
thf(146,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(147,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(148,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(149,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(150,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(151,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(152,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_0) ).
thf(153,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_0) ).
thf(154,axiom,
! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq2_0) ).
thf(155,axiom,
! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_Oinf__eq__top__eq1_0) ).
thf(156,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_0) ).
thf(157,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_1) ).
thf(158,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(159,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__left__idem_0) ).
thf(160,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(161,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(162,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(163,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__nat_Osimps_1) ).
thf(164,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(165,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__commute_0) ).
thf(166,axiom,
! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__commute__nat_0) ).
thf(167,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(168,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
thf(169,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(170,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(171,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(172,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(173,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(174,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(175,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(176,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(177,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(178,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(179,axiom,
! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ 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_dvd__power_0) ).
thf(180,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__less__0__iff_5) ).
thf(181,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__less__0__iff_4) ).
thf(182,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
thf(183,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
thf(184,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(185,axiom,
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__zero__nat_2) ).
thf(186,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
!= V_x )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__iff__inf_1) ).
thf(187,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__proj1__if__dvd__nat_0) ).
thf(188,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__proj2__if__dvd__nat_0) ).
thf(189,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(190,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(191,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(192,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(193,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(194,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(195,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(196,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__pos__nat_0) ).
thf(197,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(198,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(199,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
thf(200,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).
thf(201,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(202,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(203,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(204,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(205,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(206,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(207,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(208,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(209,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(210,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
thf(211,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(212,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(213,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(214,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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_negative__imp__inverse__negative_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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_inverse__negative__iff__negative_1) ).
thf(216,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
thf(217,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(218,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(219,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(220,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(221,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(222,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(223,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(224,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(225,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(226,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
thf(227,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(228,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(229,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(230,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(231,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(232,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(233,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__assoc_0) ).
thf(234,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__assoc__nat_0) ).
thf(235,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__left__commute__nat_0) ).
thf(236,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
thf(237,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__pos__nat_1) ).
thf(238,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__pos__nat_2) ).
thf(239,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(240,axiom,
! [T_a: $i,V_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_Power_Opower__class_Opower @ V_a @ V_n @ 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__power_0) ).
thf(241,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(242,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(243,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(244,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(245,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(246,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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__divide__iff_4) ).
thf(247,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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__divide__iff_5) ).
thf(248,axiom,
! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).
thf(249,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(250,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ 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__power__iff_1) ).
thf(251,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ 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__power_0) ).
thf(252,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(253,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(254,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).
thf(255,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(256,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).
thf(257,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(258,axiom,
( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nz_0) ).
thf(259,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(260,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(261,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(262,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(263,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(264,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(265,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(266,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(267,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(268,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(269,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(270,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(271,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(272,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(273,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(274,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(275,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(276,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(277,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(278,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(279,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(280,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(281,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(282,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(283,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(284,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(285,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(286,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(287,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(288,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(289,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(290,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(291,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(292,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(293,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(294,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(295,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(296,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(297,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(298,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(299,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(300,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(301,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(302,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(303,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(304,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(305,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(306,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(307,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_ya @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_ya @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
thf(308,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
thf(309,axiom,
! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
thf(310,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
thf(311,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
thf(312,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
thf(313,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
thf(314,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).
thf(315,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
thf(316,axiom,
! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
thf(317,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(318,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(319,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inverse_0) ).
thf(320,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(321,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(322,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(323,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(324,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(325,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(326,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(327,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(328,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(329,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(330,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(331,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(332,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(333,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(334,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(335,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(336,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(337,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(338,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).
thf(339,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
thf(340,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
thf(341,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
thf(342,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
thf(343,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
thf(344,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
thf(345,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(346,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(347,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( 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__imp__inverse__le__neg_0) ).
thf(348,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).
thf(349,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).
thf(350,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).
thf(351,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(352,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(353,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(354,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(355,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(356,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(357,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(358,axiom,
! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(359,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(360,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(361,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_x @ tc_nat )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__idem__nat_0) ).
thf(362,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(363,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(364,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__0__nat_0) ).
thf(365,axiom,
! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__0__left__nat_0) ).
thf(366,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(367,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(368,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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_inverse__nonnegative__iff__nonnegative_1) ).
thf(369,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).
thf(370,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(371,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(372,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(373,axiom,
! [T_a: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__zero_0) ).
thf(374,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(375,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(376,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ 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 @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
thf(377,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_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_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
thf(378,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
thf(379,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ 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_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
thf(380,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ 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_power__Suc__less__one_0) ).
thf(381,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(382,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(383,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(384,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
thf(385,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(386,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(387,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(388,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(389,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(390,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(391,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(392,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(393,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
thf(394,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(395,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(396,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(397,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(398,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(399,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(400,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(401,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(402,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(403,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(404,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(405,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(406,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__strict__right__mono__neg_0) ).
thf(407,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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_divide__strict__right__mono_0) ).
thf(408,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(409,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(410,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
thf(411,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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_zero__less__divide__iff_5) ).
thf(412,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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_zero__less__divide__iff_4) ).
thf(413,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
thf(414,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
thf(415,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(416,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(417,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(418,axiom,
! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__le1__nat_0) ).
thf(419,axiom,
! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__le2__nat_0) ).
thf(420,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
thf(421,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
thf(422,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ 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 @ ( 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
thf(423,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 @ ( 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_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
thf(424,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(425,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
thf(426,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).
thf(427,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(428,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(429,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(430,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(431,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(432,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(433,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(434,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(435,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(436,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(437,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
thf(438,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
thf(439,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
thf(440,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
thf(441,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(442,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(443,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(444,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(445,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
thf(446,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(447,axiom,
! [T_a: $i,V_m: $i,V_n: $i,V_a: $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_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(448,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(449,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(450,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(451,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
thf(452,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(453,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
thf(454,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(455,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
thf(456,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
thf(457,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ 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_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).
thf(458,axiom,
! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ 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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).
thf(459,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).
thf(460,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).
thf(461,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).
thf(462,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ 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_divide__nonneg__neg_0) ).
thf(463,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).
thf(464,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).
thf(465,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).
thf(466,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).
thf(467,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).
thf(468,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(469,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( 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_power__inject__base_0) ).
thf(470,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).
thf(471,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(472,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).
thf(473,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).
thf(474,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(475,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(476,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(477,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(478,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(479,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(480,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(481,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(482,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(483,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(484,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(485,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(486,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(487,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(488,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(489,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(490,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(491,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(492,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(493,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(494,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(495,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(496,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(497,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(498,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(499,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(500,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(501,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(502,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(503,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(504,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(505,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(506,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(507,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(508,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(509,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(510,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(511,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(512,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__greatest__iff__nat_2) ).
thf(513,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__greatest__nat_0) ).
thf(514,axiom,
! [V_e: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_5) ).
thf(515,axiom,
! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_4) ).
thf(516,axiom,
! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__unique__nat_3) ).
thf(517,axiom,
! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd2__nat_0) ).
thf(518,axiom,
! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__dvd1__nat_0) ).
thf(519,axiom,
! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le1_0) ).
thf(520,axiom,
! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_y @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__le2_0) ).
thf(521,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI_0) ).
thf(522,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_2) ).
thf(523,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI1_1) ).
thf(524,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oless__infI2_1) ).
thf(525,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Oinf__greatest_0) ).
thf(526,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(527,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(528,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(529,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(530,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(531,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(532,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(533,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(534,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(535,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(536,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(537,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(538,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(539,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ V_x @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
thf(540,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(541,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( 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_power__eq__imp__eq__base_0) ).
thf(542,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
thf(543,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
thf(544,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
thf(545,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
thf(546,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
thf(547,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
thf(548,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
thf(549,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(550,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(551,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(552,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
thf(553,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(554,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(555,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(556,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(557,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(558,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
thf(559,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(560,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(561,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(562,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(563,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(564,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(565,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(566,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(567,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(568,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(569,axiom,
! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_1) ).
thf(570,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__inf__iff_0) ).
thf(571,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI2_0) ).
thf(572,axiom,
! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infI1_0) ).
thf(573,axiom,
! [V_x: $i,V_b: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infE_1) ).
thf(574,axiom,
! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__semilattice__nat_Ole__infE_0) ).
thf(575,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__gcd__D1__nat_0) ).
thf(576,axiom,
! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__gcd__D2__nat_0) ).
thf(577,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(578,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(579,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(580,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(581,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(582,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(583,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(584,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(585,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(586,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(587,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(588,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(589,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(590,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(591,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(592,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).
thf(593,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(594,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(595,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(596,axiom,
! [V_m: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( 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_gcd__Suc__0_0) ).
thf(597,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(598,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(599,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(600,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(601,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(602,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(603,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(604,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(605,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(606,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(607,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(608,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(609,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(610,axiom,
! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__red__nat_0) ).
thf(611,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(612,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(613,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(614,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(615,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(616,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(617,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(618,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(619,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(620,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(621,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(622,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(623,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(624,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(625,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(626,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(627,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(628,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(629,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(630,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(631,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(632,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(633,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(634,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(635,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(636,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(637,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
thf(638,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(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] :
( ~ ( 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(641,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(642,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
thf(643,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(644,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(645,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(646,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(647,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(648,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(649,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_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_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
thf(650,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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_inverse__positive__iff__positive_1) ).
thf(651,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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_positive__imp__inverse__positive_0) ).
thf(652,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(653,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).
thf(654,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(655,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).
thf(656,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ 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_inverse__nonpositive__iff__nonpositive_1) ).
thf(657,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(658,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(659,axiom,
! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__add2__nat_0) ).
thf(660,axiom,
! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gcd__add1__nat_0) ).
thf(661,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ 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_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(662,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).
thf(663,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(664,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(665,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(666,axiom,
! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
thf(667,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(668,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(669,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(670,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(671,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(672,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(673,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(674,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(675,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(676,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(677,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(678,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(679,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(680,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(681,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(682,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(683,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(684,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(685,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[684]) ).
thf(686,negated_conjecture,
( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(687,negated_conjecture,
( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
| ~ ( c_lessequals @ v_n @ v_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(688,negated_conjecture,
( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( c_lessequals @ v_n @ v_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(689,negated_conjecture,
class_Ring__and__Field_Ofield @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(690,plain,
$false = $false,
inference(unfold_def,[status(thm)],[685]) ).
thf(691,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(692,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(693,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(694,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(695,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(696,plain,
( ( class_Divides_Osemiring__div @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(697,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(698,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(699,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(700,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(701,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(702,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(703,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(704,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(705,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(706,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(707,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(708,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(709,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(710,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(711,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(712,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(713,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(714,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Power_Opower @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(715,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(716,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(717,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ogroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(718,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(719,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(720,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Omult__zero @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(721,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(722,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(723,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(724,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(725,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ozero__neq__one @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(726,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(727,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Odivision__ring @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(728,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(729,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(730,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ono__zero__divisors @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(731,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(732,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(733,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(734,plain,
( ( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(735,plain,
( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(736,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)],[46]) ).
thf(737,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)],[47]) ).
thf(738,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)],[48]) ).
thf(739,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)],[49]) ).
thf(740,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)],[50]) ).
thf(741,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)],[51]) ).
thf(742,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)],[52]) ).
thf(743,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)],[53]) ).
thf(744,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)],[54]) ).
thf(745,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)],[55]) ).
thf(746,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(747,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_ya @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(748,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(749,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(750,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)],[60]) ).
thf(751,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)],[61]) ).
thf(752,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)],[62]) ).
thf(753,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)],[63]) ).
thf(754,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)],[64]) ).
thf(755,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)],[65]) ).
thf(756,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)],[66]) ).
thf(757,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(758,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(759,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(760,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(761,plain,
( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(762,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)],[72]) ).
thf(763,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)],[73]) ).
thf(764,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(765,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)],[75]) ).
thf(766,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(767,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)],[77]) ).
thf(768,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)],[78]) ).
thf(769,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)],[79]) ).
thf(770,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)],[80]) ).
thf(771,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(772,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(773,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(774,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(775,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(776,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)],[86]) ).
thf(777,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(778,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(779,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(780,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(781,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)],[91]) ).
thf(782,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)],[92]) ).
thf(783,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)],[93]) ).
thf(784,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)],[94]) ).
thf(785,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)],[95]) ).
thf(786,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)],[96]) ).
thf(787,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)],[97]) ).
thf(788,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)],[98]) ).
thf(789,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(790,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(791,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)],[101]) ).
thf(792,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)],[102]) ).
thf(793,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)],[103]) ).
thf(794,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)],[104]) ).
thf(795,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)],[105]) ).
thf(796,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)],[106]) ).
thf(797,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)],[107]) ).
thf(798,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)],[108]) ).
thf(799,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)],[109]) ).
thf(800,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)],[110]) ).
thf(801,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)],[111]) ).
thf(802,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)],[112]) ).
thf(803,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)],[113]) ).
thf(804,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)],[114]) ).
thf(805,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)],[115]) ).
thf(806,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(807,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(808,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_m @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(809,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(810,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(811,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ V_x @ T_a ) @ ( c_Transcendental_Oexp @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(812,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)],[122]) ).
thf(813,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)],[123]) ).
thf(814,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(815,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(816,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_x @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(817,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(818,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(819,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(820,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(821,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(822,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(823,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(824,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(825,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(826,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(827,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(828,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ 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)],[138]) ).
thf(829,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ 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)],[139]) ).
thf(830,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[140]) ).
thf(831,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(832,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(833,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(834,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(835,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(836,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)],[146]) ).
thf(837,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)],[147]) ).
thf(838,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)],[148]) ).
thf(839,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)],[149]) ).
thf(840,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)],[150]) ).
thf(841,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)],[151]) ).
thf(842,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(843,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(844,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(845,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(846,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(847,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(848,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)],[158]) ).
thf(849,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(850,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)],[160]) ).
thf(851,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)],[161]) ).
thf(852,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)],[162]) ).
thf(853,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(854,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)],[164]) ).
thf(855,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(856,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(857,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)],[167]) ).
thf(858,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(859,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)],[169]) ).
thf(860,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)],[170]) ).
thf(861,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)],[171]) ).
thf(862,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)],[172]) ).
thf(863,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)],[173]) ).
thf(864,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)],[174]) ).
thf(865,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)],[175]) ).
thf(866,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)],[176]) ).
thf(867,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)],[177]) ).
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 ) @ ( 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)],[178]) ).
thf(869,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ 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)],[179]) ).
thf(870,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ 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)],[180]) ).
thf(871,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ 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)],[181]) ).
thf(872,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(873,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(874,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)],[184]) ).
thf(875,plain,
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(876,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
!= V_x )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(877,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(878,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(879,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)],[189]) ).
thf(880,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)],[190]) ).
thf(881,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)],[191]) ).
thf(882,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)],[192]) ).
thf(883,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)],[193]) ).
thf(884,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)],[194]) ).
thf(885,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)],[195]) ).
thf(886,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(887,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)],[197]) ).
thf(888,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)],[198]) ).
thf(889,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(890,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(891,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)],[201]) ).
thf(892,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)],[202]) ).
thf(893,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(894,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)],[204]) ).
thf(895,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)],[205]) ).
thf(896,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)],[206]) ).
thf(897,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)],[207]) ).
thf(898,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(899,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(900,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(901,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)],[211]) ).
thf(902,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)],[212]) ).
thf(903,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)],[213]) ).
thf(904,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[214]) ).
thf(905,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[215]) ).
thf(906,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(907,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)],[217]) ).
thf(908,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)],[218]) ).
thf(909,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)],[219]) ).
thf(910,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(911,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(912,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)],[222]) ).
thf(913,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)],[223]) ).
thf(914,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)],[224]) ).
thf(915,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)],[225]) ).
thf(916,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(917,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)],[227]) ).
thf(918,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)],[228]) ).
thf(919,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)],[229]) ).
thf(920,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)],[230]) ).
thf(921,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)],[231]) ).
thf(922,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)],[232]) ).
thf(923,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(924,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(925,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(926,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(927,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(928,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(929,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(930,plain,
( ( ! [T_a: $i,V_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_Power_Opower__class_Opower @ V_a @ V_n @ 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)],[240]) ).
thf(931,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)],[241]) ).
thf(932,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)],[242]) ).
thf(933,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)],[243]) ).
thf(934,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)],[244]) ).
thf(935,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)],[245]) ).
thf(936,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[246]) ).
thf(937,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[247]) ).
thf(938,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(939,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(940,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(941,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(942,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)],[252]) ).
thf(943,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)],[253]) ).
thf(944,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(945,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(946,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(947,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(948,plain,
( ( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(949,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)],[259]) ).
thf(950,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)],[260]) ).
thf(951,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)],[261]) ).
thf(952,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)],[262]) ).
thf(953,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)],[263]) ).
thf(954,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)],[264]) ).
thf(955,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)],[265]) ).
thf(956,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)],[266]) ).
thf(957,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)],[267]) ).
thf(958,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)],[268]) ).
thf(959,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)],[269]) ).
thf(960,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)],[270]) ).
thf(961,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)],[271]) ).
thf(962,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)],[272]) ).
thf(963,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)],[273]) ).
thf(964,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)],[274]) ).
thf(965,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(966,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)],[276]) ).
thf(967,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)],[277]) ).
thf(968,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)],[278]) ).
thf(969,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(970,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)],[280]) ).
thf(971,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)],[281]) ).
thf(972,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)],[282]) ).
thf(973,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)],[283]) ).
thf(974,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)],[284]) ).
thf(975,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)],[285]) ).
thf(976,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)],[286]) ).
thf(977,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)],[287]) ).
thf(978,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)],[288]) ).
thf(979,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)],[289]) ).
thf(980,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)],[290]) ).
thf(981,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)],[291]) ).
thf(982,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)],[292]) ).
thf(983,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)],[293]) ).
thf(984,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)],[294]) ).
thf(985,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)],[295]) ).
thf(986,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)],[296]) ).
thf(987,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)],[297]) ).
thf(988,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)],[298]) ).
thf(989,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)],[299]) ).
thf(990,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)],[300]) ).
thf(991,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)],[301]) ).
thf(992,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)],[302]) ).
thf(993,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(994,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)],[304]) ).
thf(995,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)],[305]) ).
thf(996,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)],[306]) ).
thf(997,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_ya @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(998,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(999,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(1000,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(1001,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1003,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(1004,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1005,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(1007,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(1008,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(1009,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(1010,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)],[320]) ).
thf(1011,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)],[321]) ).
thf(1012,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)],[322]) ).
thf(1013,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)],[323]) ).
thf(1014,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)],[324]) ).
thf(1015,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)],[325]) ).
thf(1016,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)],[326]) ).
thf(1017,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)],[327]) ).
thf(1018,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)],[328]) ).
thf(1019,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)],[329]) ).
thf(1020,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)],[330]) ).
thf(1021,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)],[331]) ).
thf(1022,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)],[332]) ).
thf(1023,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)],[333]) ).
thf(1024,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)],[334]) ).
thf(1025,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)],[335]) ).
thf(1026,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)],[336]) ).
thf(1027,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)],[337]) ).
thf(1028,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1029,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1030,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1031,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(1032,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1033,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1034,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(1035,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1036,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)],[346]) ).
thf(1037,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1038,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1039,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1040,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1041,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)],[351]) ).
thf(1042,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)],[352]) ).
thf(1043,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)],[353]) ).
thf(1044,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)],[354]) ).
thf(1045,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)],[355]) ).
thf(1046,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)],[356]) ).
thf(1047,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)],[357]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1049,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)],[359]) ).
thf(1050,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)],[360]) ).
thf(1051,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1052,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)],[362]) ).
thf(1053,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)],[363]) ).
thf(1054,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1055,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(1056,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)],[366]) ).
thf(1057,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)],[367]) ).
thf(1058,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[368]) ).
thf(1059,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(1060,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)],[370]) ).
thf(1061,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)],[371]) ).
thf(1062,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)],[372]) ).
thf(1063,plain,
( ( ! [T_a: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(1064,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)],[374]) ).
thf(1065,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)],[375]) ).
thf(1066,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ 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 @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(1067,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_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_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1068,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(1069,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ 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_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ 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)],[380]) ).
thf(1071,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)],[381]) ).
thf(1072,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)],[382]) ).
thf(1073,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)],[383]) ).
thf(1074,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1075,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)],[385]) ).
thf(1076,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)],[386]) ).
thf(1077,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)],[387]) ).
thf(1078,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)],[388]) ).
thf(1079,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)],[389]) ).
thf(1080,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1081,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)],[391]) ).
thf(1082,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)],[392]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1084,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)],[394]) ).
thf(1085,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)],[395]) ).
thf(1086,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)],[396]) ).
thf(1087,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)],[397]) ).
thf(1088,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)],[398]) ).
thf(1089,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)],[399]) ).
thf(1090,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)],[400]) ).
thf(1091,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)],[401]) ).
thf(1092,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)],[402]) ).
thf(1093,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)],[403]) ).
thf(1094,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)],[404]) ).
thf(1095,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)],[405]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[406]) ).
thf(1097,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[407]) ).
thf(1098,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)],[408]) ).
thf(1099,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)],[409]) ).
thf(1100,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1101,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[411]) ).
thf(1102,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[412]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1104,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1105,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)],[415]) ).
thf(1106,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)],[416]) ).
thf(1107,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)],[417]) ).
thf(1108,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1109,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1110,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1111,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ 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 @ ( 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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1113,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 @ ( 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_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1114,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1116,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1117,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)],[427]) ).
thf(1118,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)],[428]) ).
thf(1119,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)],[429]) ).
thf(1120,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)],[430]) ).
thf(1121,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)],[431]) ).
thf(1122,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)],[432]) ).
thf(1123,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)],[433]) ).
thf(1124,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)],[434]) ).
thf(1125,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)],[435]) ).
thf(1126,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)],[436]) ).
thf(1127,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1128,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1131,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)],[441]) ).
thf(1132,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)],[442]) ).
thf(1133,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)],[443]) ).
thf(1134,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)],[444]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1137,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $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_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1138,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1139,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1140,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1142,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1144,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1145,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1146,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1147,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ 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_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1148,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ 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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1149,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1150,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1151,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1152,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1155,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1156,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1159,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( 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)],[469]) ).
thf(1160,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1163,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1164,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)],[474]) ).
thf(1165,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)],[475]) ).
thf(1166,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)],[476]) ).
thf(1167,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)],[477]) ).
thf(1168,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)],[478]) ).
thf(1169,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)],[479]) ).
thf(1170,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)],[480]) ).
thf(1171,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)],[481]) ).
thf(1172,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)],[482]) ).
thf(1173,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)],[483]) ).
thf(1174,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)],[484]) ).
thf(1175,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)],[485]) ).
thf(1176,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)],[486]) ).
thf(1177,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)],[487]) ).
thf(1178,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)],[488]) ).
thf(1179,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)],[489]) ).
thf(1180,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)],[490]) ).
thf(1181,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)],[491]) ).
thf(1182,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)],[492]) ).
thf(1183,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)],[493]) ).
thf(1184,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)],[494]) ).
thf(1185,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)],[495]) ).
thf(1186,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)],[496]) ).
thf(1187,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)],[497]) ).
thf(1188,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)],[498]) ).
thf(1189,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)],[499]) ).
thf(1190,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)],[500]) ).
thf(1191,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)],[501]) ).
thf(1192,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)],[502]) ).
thf(1193,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)],[503]) ).
thf(1194,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)],[504]) ).
thf(1195,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)],[505]) ).
thf(1196,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)],[506]) ).
thf(1197,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)],[507]) ).
thf(1198,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)],[508]) ).
thf(1199,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)],[509]) ).
thf(1200,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)],[510]) ).
thf(1201,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)],[511]) ).
thf(1202,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1203,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1204,plain,
( ( ! [V_e: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1205,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1206,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1207,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1208,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1209,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1210,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_y @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1211,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1212,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1213,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1214,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1215,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1216,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)],[526]) ).
thf(1217,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)],[527]) ).
thf(1218,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)],[528]) ).
thf(1219,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)],[529]) ).
thf(1220,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)],[530]) ).
thf(1221,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)],[531]) ).
thf(1222,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)],[532]) ).
thf(1223,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)],[533]) ).
thf(1224,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)],[534]) ).
thf(1225,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)],[535]) ).
thf(1226,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)],[536]) ).
thf(1227,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)],[537]) ).
thf(1228,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)],[538]) ).
thf(1229,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ V_x @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1230,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)],[540]) ).
thf(1231,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( 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)],[541]) ).
thf(1232,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1233,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1234,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1235,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1236,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1237,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1238,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1239,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1240,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1241,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)],[551]) ).
thf(1242,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1243,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)],[553]) ).
thf(1244,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)],[554]) ).
thf(1245,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)],[555]) ).
thf(1246,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1247,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1248,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1249,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1250,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1251,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1252,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)],[562]) ).
thf(1253,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)],[563]) ).
thf(1254,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)],[564]) ).
thf(1255,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1256,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)],[566]) ).
thf(1257,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)],[567]) ).
thf(1258,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)],[568]) ).
thf(1259,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1260,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1261,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1262,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1263,plain,
( ( ! [V_x: $i,V_b: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1264,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1265,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1266,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1267,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)],[577]) ).
thf(1268,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)],[578]) ).
thf(1269,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)],[579]) ).
thf(1270,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)],[580]) ).
thf(1271,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)],[581]) ).
thf(1272,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)],[582]) ).
thf(1273,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)],[583]) ).
thf(1274,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)],[584]) ).
thf(1275,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)],[585]) ).
thf(1276,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)],[586]) ).
thf(1277,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)],[587]) ).
thf(1278,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)],[588]) ).
thf(1279,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)],[589]) ).
thf(1280,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)],[590]) ).
thf(1281,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)],[591]) ).
thf(1282,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1283,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)],[593]) ).
thf(1284,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)],[594]) ).
thf(1285,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)],[595]) ).
thf(1286,plain,
( ( ! [V_m: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( 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)],[596]) ).
thf(1287,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)],[597]) ).
thf(1288,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)],[598]) ).
thf(1289,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)],[599]) ).
thf(1290,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)],[600]) ).
thf(1291,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)],[601]) ).
thf(1292,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)],[602]) ).
thf(1293,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)],[603]) ).
thf(1294,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)],[604]) ).
thf(1295,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)],[605]) ).
thf(1296,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)],[606]) ).
thf(1297,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)],[607]) ).
thf(1298,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)],[608]) ).
thf(1299,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)],[609]) ).
thf(1300,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1301,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)],[611]) ).
thf(1302,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)],[612]) ).
thf(1303,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)],[613]) ).
thf(1304,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)],[614]) ).
thf(1305,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)],[615]) ).
thf(1306,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)],[616]) ).
thf(1307,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)],[617]) ).
thf(1308,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)],[618]) ).
thf(1309,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)],[619]) ).
thf(1310,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)],[620]) ).
thf(1311,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)],[621]) ).
thf(1312,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)],[622]) ).
thf(1313,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)],[623]) ).
thf(1314,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)],[624]) ).
thf(1315,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)],[625]) ).
thf(1316,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)],[626]) ).
thf(1317,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)],[627]) ).
thf(1318,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)],[628]) ).
thf(1319,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)],[629]) ).
thf(1320,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1321,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(1322,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1323,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)],[633]) ).
thf(1324,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)],[634]) ).
thf(1325,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)],[635]) ).
thf(1326,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)],[636]) ).
thf(1327,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1328,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)],[638]) ).
thf(1329,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(1330,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)],[640]) ).
thf(1331,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)],[641]) ).
thf(1332,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1333,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)],[643]) ).
thf(1334,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)],[644]) ).
thf(1335,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)],[645]) ).
thf(1336,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)],[646]) ).
thf(1337,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)],[647]) ).
thf(1338,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)],[648]) ).
thf(1339,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_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_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1340,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[650]) ).
thf(1341,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[651]) ).
thf(1342,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)],[652]) ).
thf(1343,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1344,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)],[654]) ).
thf(1345,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1346,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[656]) ).
thf(1347,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(1348,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)],[658]) ).
thf(1349,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(1350,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1351,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ 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_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(1352,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1353,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)],[663]) ).
thf(1354,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)],[664]) ).
thf(1355,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)],[665]) ).
thf(1356,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(1357,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)],[667]) ).
thf(1358,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)],[668]) ).
thf(1359,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)],[669]) ).
thf(1360,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)],[670]) ).
thf(1361,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)],[671]) ).
thf(1362,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1363,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)],[673]) ).
thf(1364,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)],[674]) ).
thf(1365,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)],[675]) ).
thf(1366,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)],[676]) ).
thf(1367,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)],[677]) ).
thf(1368,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)],[678]) ).
thf(1369,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)],[679]) ).
thf(1370,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)],[680]) ).
thf(1371,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)],[681]) ).
thf(1372,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)],[682]) ).
thf(1373,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)],[683]) ).
thf(1374,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(1375,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
| ~ ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(1376,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(1377,plain,
( ( class_Ring__and__Field_Ofield @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1378,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[690]) ).
thf(1379,plain,
( ( class_Ring__and__Field_Ofield @ t_a )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(1380,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1376]) ).
thf(1381,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
| ~ ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(1382,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(1383,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)],[1373]) ).
thf(1384,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)],[1372]) ).
thf(1385,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)],[1371]) ).
thf(1386,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)],[1370]) ).
thf(1387,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)],[1369]) ).
thf(1388,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)],[1368]) ).
thf(1389,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)],[1367]) ).
thf(1390,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)],[1366]) ).
thf(1391,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)],[1365]) ).
thf(1392,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)],[1364]) ).
thf(1393,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)],[1363]) ).
thf(1394,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(1395,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)],[1361]) ).
thf(1396,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)],[1360]) ).
thf(1397,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)],[1359]) ).
thf(1398,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)],[1358]) ).
thf(1399,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)],[1357]) ).
thf(1400,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1401,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)],[1355]) ).
thf(1402,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)],[1354]) ).
thf(1403,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)],[1353]) ).
thf(1404,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(1405,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ 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_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(1406,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1407,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( c_HOL_Oplus__class_Oplus @ V_m @ V_n @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1408,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)],[1348]) ).
thf(1409,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1347]) ).
thf(1410,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[1346]) ).
thf(1411,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1345]) ).
thf(1412,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)],[1344]) ).
thf(1413,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1414,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)],[1342]) ).
thf(1415,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[1341]) ).
thf(1416,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[1340]) ).
thf(1417,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_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_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1418,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)],[1338]) ).
thf(1419,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)],[1337]) ).
thf(1420,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)],[1336]) ).
thf(1421,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)],[1335]) ).
thf(1422,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)],[1334]) ).
thf(1423,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)],[1333]) ).
thf(1424,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1425,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)],[1331]) ).
thf(1426,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)],[1330]) ).
thf(1427,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)],[1329]) ).
thf(1428,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)],[1328]) ).
thf(1429,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(1430,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)],[1326]) ).
thf(1431,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)],[1325]) ).
thf(1432,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)],[1324]) ).
thf(1433,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)],[1323]) ).
thf(1434,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(1435,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(1436,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(1437,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)],[1319]) ).
thf(1438,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)],[1318]) ).
thf(1439,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)],[1317]) ).
thf(1440,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)],[1316]) ).
thf(1441,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)],[1315]) ).
thf(1442,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)],[1314]) ).
thf(1443,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)],[1313]) ).
thf(1444,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)],[1312]) ).
thf(1445,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)],[1311]) ).
thf(1446,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)],[1310]) ).
thf(1447,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)],[1309]) ).
thf(1448,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)],[1308]) ).
thf(1449,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)],[1307]) ).
thf(1450,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)],[1306]) ).
thf(1451,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)],[1305]) ).
thf(1452,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)],[1304]) ).
thf(1453,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)],[1303]) ).
thf(1454,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)],[1302]) ).
thf(1455,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)],[1301]) ).
thf(1456,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(1457,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)],[1299]) ).
thf(1458,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)],[1298]) ).
thf(1459,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)],[1297]) ).
thf(1460,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)],[1296]) ).
thf(1461,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)],[1295]) ).
thf(1462,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)],[1294]) ).
thf(1463,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)],[1293]) ).
thf(1464,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)],[1292]) ).
thf(1465,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)],[1291]) ).
thf(1466,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)],[1290]) ).
thf(1467,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)],[1289]) ).
thf(1468,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)],[1288]) ).
thf(1469,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)],[1287]) ).
thf(1470,plain,
( ( ! [V_m: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ ( 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)],[1286]) ).
thf(1471,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)],[1285]) ).
thf(1472,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)],[1284]) ).
thf(1473,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)],[1283]) ).
thf(1474,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(1475,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)],[1281]) ).
thf(1476,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)],[1280]) ).
thf(1477,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)],[1279]) ).
thf(1478,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)],[1278]) ).
thf(1479,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)],[1277]) ).
thf(1480,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)],[1276]) ).
thf(1481,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)],[1275]) ).
thf(1482,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)],[1274]) ).
thf(1483,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)],[1273]) ).
thf(1484,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)],[1272]) ).
thf(1485,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)],[1271]) ).
thf(1486,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)],[1270]) ).
thf(1487,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)],[1269]) ).
thf(1488,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)],[1268]) ).
thf(1489,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)],[1267]) ).
thf(1490,plain,
( ( ! [V_k: $i,V_n: $i,V_m: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(1491,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(1492,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(1493,plain,
( ( ! [V_x: $i,V_b: $i,V_a: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1494,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1495,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1496,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1497,plain,
( ( ! [V_x: $i,V_z: $i,V_y: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(1498,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)],[1258]) ).
thf(1499,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)],[1257]) ).
thf(1500,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)],[1256]) ).
thf(1501,plain,
( ( ! [V_x: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1502,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)],[1254]) ).
thf(1503,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)],[1253]) ).
thf(1504,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)],[1252]) ).
thf(1505,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1506,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(1507,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oplus__class_Oplus @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1508,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1509,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1510,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1511,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)],[1245]) ).
thf(1512,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)],[1244]) ).
thf(1513,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)],[1243]) ).
thf(1514,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1515,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)],[1241]) ).
thf(1516,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(1517,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1239]) ).
thf(1518,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(1519,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1520,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1521,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1522,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(1523,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(1524,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( 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 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1525,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( 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)],[1231]) ).
thf(1526,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)],[1230]) ).
thf(1527,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ V_x @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1229]) ).
thf(1528,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)],[1228]) ).
thf(1529,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)],[1227]) ).
thf(1530,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)],[1226]) ).
thf(1531,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)],[1225]) ).
thf(1532,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)],[1224]) ).
thf(1533,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)],[1223]) ).
thf(1534,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)],[1222]) ).
thf(1535,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)],[1221]) ).
thf(1536,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)],[1220]) ).
thf(1537,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)],[1219]) ).
thf(1538,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)],[1218]) ).
thf(1539,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)],[1217]) ).
thf(1540,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)],[1216]) ).
thf(1541,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1542,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1543,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1544,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_z @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1545,plain,
( ( ! [V_x: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1546,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_y @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1547,plain,
( ( ! [V_x: $i,V_y: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1548,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1549,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1550,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1551,plain,
( ( ! [V_a: $i,V_b: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1552,plain,
( ( ! [V_e: $i,V_a: $i,V_b: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_e @ V_a @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1553,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1554,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1555,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)],[1201]) ).
thf(1556,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)],[1200]) ).
thf(1557,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)],[1199]) ).
thf(1558,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)],[1198]) ).
thf(1559,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)],[1197]) ).
thf(1560,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)],[1196]) ).
thf(1561,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)],[1195]) ).
thf(1562,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)],[1194]) ).
thf(1563,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)],[1193]) ).
thf(1564,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)],[1192]) ).
thf(1565,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)],[1191]) ).
thf(1566,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)],[1190]) ).
thf(1567,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)],[1189]) ).
thf(1568,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)],[1188]) ).
thf(1569,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)],[1187]) ).
thf(1570,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)],[1186]) ).
thf(1571,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)],[1185]) ).
thf(1572,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)],[1184]) ).
thf(1573,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)],[1183]) ).
thf(1574,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)],[1182]) ).
thf(1575,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)],[1181]) ).
thf(1576,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)],[1180]) ).
thf(1577,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)],[1179]) ).
thf(1578,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)],[1178]) ).
thf(1579,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)],[1177]) ).
thf(1580,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)],[1176]) ).
thf(1581,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)],[1175]) ).
thf(1582,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)],[1174]) ).
thf(1583,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)],[1173]) ).
thf(1584,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)],[1172]) ).
thf(1585,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)],[1171]) ).
thf(1586,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)],[1170]) ).
thf(1587,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)],[1169]) ).
thf(1588,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)],[1168]) ).
thf(1589,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)],[1167]) ).
thf(1590,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)],[1166]) ).
thf(1591,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)],[1165]) ).
thf(1592,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)],[1164]) ).
thf(1593,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(1594,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1595,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1596,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( 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)],[1159]) ).
thf(1598,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1599,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(1600,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1601,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1602,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1603,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(1604,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(1605,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i,V_w: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_z @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_w @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_w @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_w @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(1606,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(1607,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(1608,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ 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 ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1609,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ 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_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1610,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1611,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(1612,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(1613,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(1614,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(1615,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_x
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(1616,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(1617,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(1618,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(1619,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $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_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(1620,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(1621,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(1622,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)],[1134]) ).
thf(1623,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)],[1133]) ).
thf(1624,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)],[1132]) ).
thf(1625,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)],[1131]) ).
thf(1626,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(1627,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) )
| ( V_a = V_b )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(1628,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1128]) ).
thf(1629,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(1630,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)],[1126]) ).
thf(1631,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)],[1125]) ).
thf(1632,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)],[1124]) ).
thf(1633,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)],[1123]) ).
thf(1634,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)],[1122]) ).
thf(1635,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)],[1121]) ).
thf(1636,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)],[1120]) ).
thf(1637,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)],[1119]) ).
thf(1638,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)],[1118]) ).
thf(1639,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)],[1117]) ).
thf(1640,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(1641,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(1642,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1114]) ).
thf(1643,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 @ ( 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_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(1644,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ V_a @ 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 @ ( 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 ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(1645,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1646,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ 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 @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(1647,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_b @ tc_nat )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(1648,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_a @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(1649,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)],[1107]) ).
thf(1650,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)],[1106]) ).
thf(1651,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)],[1105]) ).
thf(1652,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(1653,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(1654,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[1102]) ).
thf(1655,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[1101]) ).
thf(1656,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1657,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)],[1099]) ).
thf(1658,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)],[1098]) ).
thf(1659,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[1097]) ).
thf(1660,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[1096]) ).
thf(1661,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)],[1095]) ).
thf(1662,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)],[1094]) ).
thf(1663,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)],[1093]) ).
thf(1664,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)],[1092]) ).
thf(1665,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)],[1091]) ).
thf(1666,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)],[1090]) ).
thf(1667,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)],[1089]) ).
thf(1668,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)],[1088]) ).
thf(1669,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)],[1087]) ).
thf(1670,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)],[1086]) ).
thf(1671,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)],[1085]) ).
thf(1672,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)],[1084]) ).
thf(1673,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
= V_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1674,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)],[1082]) ).
thf(1675,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)],[1081]) ).
thf(1676,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1677,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)],[1079]) ).
thf(1678,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)],[1078]) ).
thf(1679,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)],[1077]) ).
thf(1680,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)],[1076]) ).
thf(1681,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)],[1075]) ).
thf(1682,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(1683,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)],[1073]) ).
thf(1684,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)],[1072]) ).
thf(1685,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)],[1071]) ).
thf(1686,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ 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)],[1070]) ).
thf(1687,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ 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_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(1688,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(1689,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_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_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1690,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ 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 @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1691,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)],[1065]) ).
thf(1692,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)],[1064]) ).
thf(1693,plain,
( ( ! [T_a: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1694,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)],[1062]) ).
thf(1695,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)],[1061]) ).
thf(1696,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)],[1060]) ).
thf(1697,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(1698,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(1699,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)],[1057]) ).
thf(1700,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)],[1056]) ).
thf(1701,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(1702,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(1703,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)],[1053]) ).
thf(1704,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)],[1052]) ).
thf(1705,plain,
( ( ! [V_x: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_x @ tc_nat )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1706,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)],[1050]) ).
thf(1707,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)],[1049]) ).
thf(1708,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1709,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)],[1047]) ).
thf(1710,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)],[1046]) ).
thf(1711,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)],[1045]) ).
thf(1712,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)],[1044]) ).
thf(1713,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)],[1043]) ).
thf(1714,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)],[1042]) ).
thf(1715,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)],[1041]) ).
thf(1716,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(1717,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(1718,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(1719,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(1720,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)],[1036]) ).
thf(1721,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1722,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1723,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1724,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_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 ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1725,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1726,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1727,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1728,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1729,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)],[1027]) ).
thf(1730,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)],[1026]) ).
thf(1731,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)],[1025]) ).
thf(1732,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)],[1024]) ).
thf(1733,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)],[1023]) ).
thf(1734,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)],[1022]) ).
thf(1735,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)],[1021]) ).
thf(1736,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)],[1020]) ).
thf(1737,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)],[1019]) ).
thf(1738,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)],[1018]) ).
thf(1739,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)],[1017]) ).
thf(1740,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)],[1016]) ).
thf(1741,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)],[1015]) ).
thf(1742,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)],[1014]) ).
thf(1743,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)],[1013]) ).
thf(1744,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)],[1012]) ).
thf(1745,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)],[1011]) ).
thf(1746,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)],[1010]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1748,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(1749,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(1750,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_n @ T_a ) @ T_a )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1751,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1752,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1753,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(1754,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1755,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1756,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1757,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1758,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1759,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_ya @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(1760,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)],[996]) ).
thf(1761,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)],[995]) ).
thf(1762,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(1763,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1764,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)],[992]) ).
thf(1765,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)],[991]) ).
thf(1766,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)],[990]) ).
thf(1767,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)],[989]) ).
thf(1768,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)],[988]) ).
thf(1769,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)],[987]) ).
thf(1770,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)],[986]) ).
thf(1771,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)],[985]) ).
thf(1772,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)],[984]) ).
thf(1773,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)],[983]) ).
thf(1774,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)],[982]) ).
thf(1775,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)],[981]) ).
thf(1776,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)],[980]) ).
thf(1777,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)],[979]) ).
thf(1778,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)],[978]) ).
thf(1779,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)],[977]) ).
thf(1780,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)],[976]) ).
thf(1781,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)],[975]) ).
thf(1782,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)],[974]) ).
thf(1783,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)],[973]) ).
thf(1784,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)],[972]) ).
thf(1785,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)],[971]) ).
thf(1786,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)],[970]) ).
thf(1787,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1788,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)],[968]) ).
thf(1789,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)],[967]) ).
thf(1790,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)],[966]) ).
thf(1791,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(1792,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)],[964]) ).
thf(1793,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)],[963]) ).
thf(1794,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)],[962]) ).
thf(1795,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)],[961]) ).
thf(1796,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)],[960]) ).
thf(1797,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)],[959]) ).
thf(1798,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)],[958]) ).
thf(1799,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)],[957]) ).
thf(1800,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)],[956]) ).
thf(1801,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)],[955]) ).
thf(1802,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)],[954]) ).
thf(1803,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)],[953]) ).
thf(1804,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)],[952]) ).
thf(1805,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)],[951]) ).
thf(1806,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)],[950]) ).
thf(1807,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)],[949]) ).
thf(1808,plain,
( ( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1809,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1810,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1811,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1812,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1813,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)],[943]) ).
thf(1814,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)],[942]) ).
thf(1815,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1816,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1817,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(1818,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( c_lessequals @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1819,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[937]) ).
thf(1820,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[936]) ).
thf(1821,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1822,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)],[934]) ).
thf(1823,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)],[933]) ).
thf(1824,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)],[932]) ).
thf(1825,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)],[931]) ).
thf(1826,plain,
( ( ! [T_a: $i,V_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_Power_Opower__class_Opower @ V_a @ V_n @ 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)],[930]) ).
thf(1827,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1828,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(1829,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1830,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ V_n @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(1831,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(1832,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_k @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_k @ ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(1833,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ V_z @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_z @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(1834,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)],[922]) ).
thf(1835,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)],[921]) ).
thf(1836,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)],[920]) ).
thf(1837,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)],[919]) ).
thf(1838,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)],[918]) ).
thf(1839,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)],[917]) ).
thf(1840,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Divides_Osemiring__div @ T_a )
| ( ( c_Divides_Odiv__class_Omod @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1841,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)],[915]) ).
thf(1842,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)],[914]) ).
thf(1843,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)],[913]) ).
thf(1844,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)],[912]) ).
thf(1845,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1846,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1847,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)],[909]) ).
thf(1848,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)],[908]) ).
thf(1849,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)],[907]) ).
thf(1850,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1851,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[905]) ).
thf(1852,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[904]) ).
thf(1853,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)],[903]) ).
thf(1854,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)],[902]) ).
thf(1855,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)],[901]) ).
thf(1856,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1857,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(1858,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(1859,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)],[897]) ).
thf(1860,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)],[896]) ).
thf(1861,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)],[895]) ).
thf(1862,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)],[894]) ).
thf(1863,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(1864,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)],[892]) ).
thf(1865,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)],[891]) ).
thf(1866,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1867,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1868,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)],[888]) ).
thf(1869,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)],[887]) ).
thf(1870,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1871,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)],[885]) ).
thf(1872,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)],[884]) ).
thf(1873,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)],[883]) ).
thf(1874,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)],[882]) ).
thf(1875,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)],[881]) ).
thf(1876,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)],[880]) ).
thf(1877,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)],[879]) ).
thf(1878,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_y )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(1879,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= V_x )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(1880,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
!= V_x )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1881,plain,
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1882,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)],[874]) ).
thf(1883,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(1884,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_y @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1885,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ 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)],[871]) ).
thf(1886,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ 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)],[870]) ).
thf(1887,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ ( c_Power_Opower__class_Opower @ V_x @ 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)],[869]) ).
thf(1888,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)],[868]) ).
thf(1889,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)],[867]) ).
thf(1890,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)],[866]) ).
thf(1891,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)],[865]) ).
thf(1892,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)],[864]) ).
thf(1893,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)],[863]) ).
thf(1894,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)],[862]) ).
thf(1895,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)],[861]) ).
thf(1896,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)],[860]) ).
thf(1897,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)],[859]) ).
thf(1898,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1899,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)],[857]) ).
thf(1900,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1901,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1902,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)],[854]) ).
thf(1903,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_y @ ( c_Divides_Odiv__class_Omod @ V_x @ V_y @ tc_nat ) @ tc_nat ) )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1904,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)],[852]) ).
thf(1905,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)],[851]) ).
thf(1906,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)],[850]) ).
thf(1907,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ V_x @ ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1908,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)],[848]) ).
thf(1909,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1910,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1911,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1912,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ V_A @ V_B @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_B
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1913,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_a @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_a @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1914,plain,
( ( ! [V_a: $i,V_b: $i,V_x: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ V_a @ V_b @ tc_nat ) @ V_x @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_b @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_b @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1915,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)],[841]) ).
thf(1916,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)],[840]) ).
thf(1917,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)],[839]) ).
thf(1918,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)],[838]) ).
thf(1919,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)],[837]) ).
thf(1920,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)],[836]) ).
thf(1921,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1922,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1923,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(1924,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1925,plain,
( ( ! [T_a: $i,V_b: $i,V_c: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_c @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(1926,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ 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)],[830]) ).
thf(1927,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ 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)],[829]) ).
thf(1928,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ 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)],[828]) ).
thf(1929,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(1930,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1931,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1932,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_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_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1933,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1934,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1935,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1936,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1937,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1938,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(1939,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Oinverse__class_Oinverse @ V_x @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1940,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ V_x @ V_x @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1941,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1942,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_a @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1943,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)],[813]) ).
thf(1944,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)],[812]) ).
thf(1945,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_SEQ_Obanach @ T_a )
| ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ V_x @ T_a ) @ ( c_Transcendental_Oexp @ V_y @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(1946,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) )
| ( V_b
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1947,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1948,plain,
( ( ! [T_a: $i,V_x: $i,V_n: $i,V_y: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_x @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_y @ V_m @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1949,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1950,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1951,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)],[805]) ).
thf(1952,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)],[804]) ).
thf(1953,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)],[803]) ).
thf(1954,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)],[802]) ).
thf(1955,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)],[801]) ).
thf(1956,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)],[800]) ).
thf(1957,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)],[799]) ).
thf(1958,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)],[798]) ).
thf(1959,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)],[797]) ).
thf(1960,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)],[796]) ).
thf(1961,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)],[795]) ).
thf(1962,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)],[794]) ).
thf(1963,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)],[793]) ).
thf(1964,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)],[792]) ).
thf(1965,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)],[791]) ).
thf(1966,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1967,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ V_n @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1968,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)],[788]) ).
thf(1969,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)],[787]) ).
thf(1970,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)],[786]) ).
thf(1971,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)],[785]) ).
thf(1972,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)],[784]) ).
thf(1973,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)],[783]) ).
thf(1974,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)],[782]) ).
thf(1975,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)],[781]) ).
thf(1976,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_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 ) ) )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(1977,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1978,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1979,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ 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_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1980,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)],[776]) ).
thf(1981,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(1982,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(1983,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1984,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1985,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1986,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)],[770]) ).
thf(1987,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)],[769]) ).
thf(1988,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)],[768]) ).
thf(1989,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)],[767]) ).
thf(1990,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1991,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)],[765]) ).
thf(1992,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1993,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)],[763]) ).
thf(1994,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)],[762]) ).
thf(1995,plain,
( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(1996,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(1997,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1998,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1999,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(2000,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)],[756]) ).
thf(2001,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)],[755]) ).
thf(2002,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)],[754]) ).
thf(2003,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)],[753]) ).
thf(2004,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)],[752]) ).
thf(2005,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)],[751]) ).
thf(2006,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)],[750]) ).
thf(2007,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(2008,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ V_c @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ V_a @ V_c @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_b @ V_c @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(2009,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_ya: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a ) @ V_ya @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ V_x @ V_ya @ T_a ) @ ( c_HOL_Oinverse__class_Odivide @ V_y @ V_ya @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(2010,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ T_a )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) @ V_n @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(2011,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)],[745]) ).
thf(2012,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)],[744]) ).
thf(2013,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)],[743]) ).
thf(2014,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)],[742]) ).
thf(2015,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)],[741]) ).
thf(2016,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)],[740]) ).
thf(2017,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)],[739]) ).
thf(2018,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)],[738]) ).
thf(2019,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)],[737]) ).
thf(2020,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)],[736]) ).
thf(2021,plain,
( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(2022,plain,
( ( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(2023,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(2024,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(2025,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocancel__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(2026,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ono__zero__divisors @ T ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(2027,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(2028,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__semigroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(2029,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Odivision__ring @ T ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(2030,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ocomm__monoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(2031,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ozero__neq__one @ T ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(2032,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Ocomm__ring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(2033,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(2034,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Osemiring__0 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(2035,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Oab__group__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(2036,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Omult__zero @ T ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(2037,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__mult @ T ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(2038,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Omonoid__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(2039,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_OrderedGroup_Ogroup__add @ T ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(2040,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oring__1 @ T ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(2041,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Ring__and__Field_Oidom @ T ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(2042,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T )
| ( class_Power_Opower @ T ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(2043,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(2044,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(2045,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(2046,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(2047,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(2048,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(2049,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(2050,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[706]) ).
thf(2051,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(2052,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(2053,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(2054,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(2055,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(2056,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(2057,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(2058,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(2059,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(2060,plain,
( ( class_Divides_Osemiring__div @ tc_nat )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(2061,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(2062,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(2063,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(2064,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(2065,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(2066,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1378]) ).
thf(2067,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1910]) ).
thf(2068,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)],[1665]) ).
thf(2069,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1748]) ).
thf(2070,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)],[1743]) ).
thf(2071,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1821]) ).
thf(2072,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1436]) ).
thf(2073,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)],[1418]) ).
thf(2074,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)],[1414]) ).
thf(2075,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)],[1419]) ).
thf(2076,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1516]) ).
thf(2077,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1912]) ).
thf(2078,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_SEQ_Obanach @ SX0 )
| ~ ( class_RealVector_Oreal__normed__field @ SX0 )
| ( ( c_Transcendental_Oexp @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1527]) ).
thf(2079,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)],[1822]) ).
thf(2080,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1435]) ).
thf(2081,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)],[2001]) ).
thf(2082,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)],[1459]) ).
thf(2083,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1909]) ).
thf(2084,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Oinverse__class_Oinverse @ SX2 @ SX0 ) )
| ( SX1 = SX2 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1627]) ).
thf(2085,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)],[1677]) ).
thf(2086,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)],[1667]) ).
thf(2087,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)],[1729]) ).
thf(2088,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)],[1458]) ).
thf(2089,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX2 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1525]) ).
thf(2090,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)],[2002]) ).
thf(2091,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1911]) ).
thf(2092,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)],[1712]) ).
thf(2093,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) )
| ( SX1
= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1615]) ).
thf(2094,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)],[2016]) ).
thf(2095,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)],[1683]) ).
thf(2096,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1382]) ).
thf(2097,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)],[1678]) ).
thf(2098,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)],[1671]) ).
thf(2099,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)],[1662]) ).
thf(2100,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)],[1666]) ).
thf(2101,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Oone__class_Oone @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1614]) ).
thf(2102,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)],[1733]) ).
thf(2103,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Oinverse__class_Oinverse @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1626]) ).
thf(2104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1867]) ).
thf(2105,plain,
( ( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1808]) ).
thf(2106,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)],[1800]) ).
thf(2107,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX1 @ SX3 @ SX0 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SX0 ) @ SX1 @ SX0 )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1933]) ).
thf(2108,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1612]) ).
thf(2109,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)],[1964]) ).
thf(2110,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)],[1460]) ).
thf(2111,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)],[1825]) ).
thf(2112,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)],[1634]) ).
thf(2113,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)],[1744]) ).
thf(2114,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1858]) ).
thf(2115,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)],[1461]) ).
thf(2116,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)],[1635]) ).
thf(2117,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SX0 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SX0 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SX1 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1866]) ).
thf(2118,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)],[1661]) ).
thf(2119,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1517]) ).
thf(2120,plain,
( ( ~ ( class_Ring__and__Field_Ofield @ t_a )
| ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2022]) ).
thf(2121,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)],[1463]) ).
thf(2122,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)],[1734]) ).
thf(2123,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
| ~ ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1381]) ).
thf(2124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1720]) ).
thf(2125,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
| ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[1380]) ).
thf(2126,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)],[1742]) ).
thf(2127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SX0 @ SX1 @ tc_nat )
!= SX0 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1880]) ).
thf(2128,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)],[1465]) ).
thf(2129,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1394]) ).
thf(2130,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)],[1664]) ).
thf(2131,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)],[2015]) ).
thf(2132,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)],[1663]) ).
thf(2133,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)],[2017]) ).
thf(2134,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)],[1464]) ).
thf(2135,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_Suc @ SX2 ) @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ ( c_Suc @ SX2 ) @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1597]) ).
thf(2136,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)],[1824]) ).
thf(2137,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1749]) ).
thf(2138,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1857]) ).
thf(2139,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)],[1462]) ).
thf(2140,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SX0 )
| ( ( c_HOL_Oinverse__class_Odivide @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1937]) ).
thf(2141,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)],[1457]) ).
thf(2142,plain,
! [SV1: $i] :
( ( ! [SY1679: $i,SY1680: $i,SY1681: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV1 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1679 @ SY1680 @ SV1 ) @ SY1681 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SY1679 @ ( c_HOL_Oplus__class_Oplus @ SY1680 @ SY1681 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(2143,plain,
! [SV2: $i] :
( ( ! [SY1682: $i,SY1683: $i,SY1684: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1682 @ ( c_HOL_Oplus__class_Oplus @ SY1683 @ SY1684 @ SV2 ) @ SV2 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1682 @ SY1683 @ SV2 ) @ SY1684 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(2144,plain,
! [SV3: $i] :
( ( ! [SY1685: $i,SY1686: $i,SY1687: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV3 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1685 @ ( c_HOL_Oplus__class_Oplus @ SY1686 @ SY1687 @ SV3 ) @ SV3 )
= ( c_HOL_Oplus__class_Oplus @ SY1686 @ ( c_HOL_Oplus__class_Oplus @ SY1685 @ SY1687 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(2145,plain,
! [SV4: $i] :
( ( ! [SY1688: $i,SY1689: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV4 @ SY1688 @ tc_nat ) @ SY1689 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV4 @ ( c_HOL_Oplus__class_Oplus @ SY1688 @ SY1689 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(2146,plain,
! [SV5: $i] :
( ( ! [SY1690: $i,SY1691: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV5 @ ( c_HOL_Oplus__class_Oplus @ SY1690 @ SY1691 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY1690 @ ( c_HOL_Oplus__class_Oplus @ SV5 @ SY1691 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(2147,plain,
! [SV6: $i] :
( ( ! [SY1692: $i,SY1693: $i,SY1694: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV6 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1692 @ SY1693 @ SV6 ) @ SY1694 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ SY1692 @ ( c_HOL_Oplus__class_Oplus @ SY1693 @ SY1694 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(2148,plain,
! [SV7: $i] :
( ( ! [SY1695: $i,SY1696: $i,SY1697: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1695 @ ( c_HOL_Oplus__class_Oplus @ SY1696 @ SY1697 @ SV7 ) @ SV7 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1695 @ SY1696 @ SV7 ) @ SY1697 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(2149,plain,
! [SV8: $i] :
( ( ! [SY1698: $i,SY1699: $i,SY1700: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV8 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1698 @ SY1699 @ SV8 ) @ SY1700 @ SV8 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1698 @ SY1700 @ SV8 ) @ SY1699 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(2150,plain,
! [SV9: $i] :
( ( ! [SY1701: $i,SY1702: $i,SY1703: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1701 @ ( c_HOL_Oplus__class_Oplus @ SY1702 @ SY1703 @ SV9 ) @ SV9 )
= ( c_HOL_Oplus__class_Oplus @ SY1702 @ ( c_HOL_Oplus__class_Oplus @ SY1701 @ SY1703 @ SV9 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(2151,plain,
! [SV10: $i] :
( ( ! [SY1704: $i,SY1705: $i,SY1706: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV10 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY1704 @ SY1705 @ SV10 ) @ SY1706 @ SV10 )
= ( c_HOL_Oplus__class_Oplus @ SY1704 @ ( c_HOL_Oplus__class_Oplus @ SY1705 @ SY1706 @ SV10 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(2152,plain,
! [SV11: $i] :
( ( ! [SY1707: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV11 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1707 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY1707 @ SV11 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(2153,plain,
! [SV12: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV12 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(2154,plain,
! [SV13: $i] :
( ( ! [SY1708: $i,SY1709: $i,SY1710: $i] :
( ~ ( class_Divides_Osemiring__div @ SV13 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1708 @ SY1709 @ SV13 ) @ SY1710 @ SV13 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1708 @ ( c_Divides_Odiv__class_Omod @ SY1709 @ SY1710 @ SV13 ) @ SV13 ) @ SY1710 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(2155,plain,
! [SV14: $i] :
( ( ! [SY1711: $i,SY1712: $i,SY1713: $i] :
( ~ ( class_Divides_Osemiring__div @ SV14 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1711 @ SY1712 @ SV14 ) @ SY1713 @ SV14 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY1711 @ SY1713 @ SV14 ) @ SY1712 @ SV14 ) @ SY1713 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(2156,plain,
! [SV15: $i] :
( ( ! [SY1714: $i,SY1715: $i,SY1716: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ SY1714 @ ( c_HOL_Oplus__class_Oplus @ SY1715 @ SY1716 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY1714 @ SY1716 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SY1715 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(2157,plain,
! [SV16: $i] :
( ( ! [SY1717: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV16 @ ( c_HOL_Oplus__class_Oplus @ SV16 @ SY1717 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(2158,plain,
! [SV17: $i] :
( ( ! [SY1718: $i,SY1719: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 )
| ( c_HOL_Oord__class_Oless @ SY1718 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY1718 @ SY1719 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(2159,plain,
! [SV18: $i] :
( ( ( SV18
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV18
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV18 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(2160,plain,
! [SV19: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV19 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(2161,plain,
! [SV20: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV20 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(2162,plain,
! [SV21: $i] :
( ( ! [SY1720: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV21 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SY1720 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY1720 @ SV21 ) @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(2163,plain,
! [SV22: $i] :
( ( ! [SY1721: $i,SY1722: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV22 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SY1721 @ SY1722 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1722 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SY1721 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(2164,plain,
! [SV23: $i] :
( ( ! [SY1723: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oplus__class_Oplus @ SV23 @ SY1723 @ tc_nat ) @ SY1723 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV23 @ SY1723 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(2165,plain,
! [SV24: $i] :
( ( ! [SY1724: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV24 @ ( c_HOL_Oplus__class_Oplus @ SV24 @ SY1724 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV24 @ SY1724 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(2166,plain,
! [SV25: $i] :
( ( ! [SY1725: $i,SY1726: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1725 @ SY1726 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY1726 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY1725 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(2167,plain,
! [SV26: $i] :
( ( ! [SY1727: $i,SY1728: $i,SY1729: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY1727 @ SY1728 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SY1729 @ SY1728 @ SV26 ) @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1728 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SY1727 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY1727 @ SY1729 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(2168,plain,
! [SV27: $i] :
( ( ! [SY1730: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV27 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY1730 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
| ~ ( c_lessequals @ SY1730 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(2169,plain,
! [SV28: $i] :
( ( ! [SY1731: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( c_lessequals @ SY1731 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY1731 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(2170,plain,
! [SV29: $i] :
( ( ! [SY1732: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV29 ) @ SY1732 @ tc_nat )
| ( ( c_Suc @ SV29 )
= SY1732 )
| ~ ( c_HOL_Oord__class_Oless @ SV29 @ SY1732 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(2171,plain,
! [SV30: $i] :
( ( ! [SY1733: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV30 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SY1733 @ SV30 )
| ( c_lessequals @ SY1733 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY1733 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(2172,plain,
! [SV31: $i] :
( ( ! [SY1734: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV31 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY1734 @ SV31 ) @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SY1734 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(2173,plain,
! [SV32: $i] :
( ( ! [SY1735: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV32 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY1735 @ SV32 ) @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SY1735 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(2174,plain,
! [SV33: $i] :
( ( ! [SY1736: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV33 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SY1736 @ SV33 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY1736 @ SV33 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(2175,plain,
! [SV34: $i] :
( ( ! [SY1737: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV34 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1737 @ SV34 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(2176,plain,
! [SV35: $i] :
( ( ! [SY1738: $i,SY1739: $i,SY1740: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1738 @ ( c_HOL_Oplus__class_Oplus @ SY1739 @ SY1740 @ SV35 ) @ SV35 )
= ( c_HOL_Oplus__class_Oplus @ SY1739 @ ( c_HOL_Oplus__class_Oplus @ SY1738 @ SY1740 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(2177,plain,
! [SV36: $i] :
( ( ! [SY1741: $i,SY1742: $i,SY1743: $i] :
( ~ ( class_Orderings_Opreorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SY1741 @ SY1742 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY1743 @ SY1742 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY1741 @ SY1743 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(2178,plain,
! [SV37: $i] :
( ( ! [SY1744: $i,SY1745: $i,SY1746: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SY1744 @ SY1745 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SY1744 @ SY1746 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SY1746 @ SY1745 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(2179,plain,
! [SV38: $i] :
( ( ! [SY1747: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV38 )
| ( SY1747
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SY1747 @ SV38 ) @ SV38 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(2180,plain,
! [SV39: $i] :
( ( ! [SY1748: $i,SY1749: $i,SY1750: $i] :
( ~ ( class_Divides_Osemiring__div @ SV39 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1748 @ SY1749 @ SV39 ) @ SY1750 @ SV39 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY1748 @ SY1750 @ SV39 ) @ ( c_Divides_Odiv__class_Omod @ SY1749 @ SY1750 @ SV39 ) @ SV39 ) @ SY1750 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(2181,plain,
! [SV40: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV40 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(2182,plain,
! [SV41: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(2183,plain,
! [SV42: $i] :
( ( ! [SY1751: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV42 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV42 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SY1751 @ SV42 ) @ SV42 )
= SY1751 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(2184,plain,
! [SV43: $i] :
( ( ! [SY1752: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV43 ) @ SY1752 @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV43 @ SY1752 @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV43 @ SY1752 @ tc_nat ) )
= SY1752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(2185,plain,
! [SV44: $i] :
( ( ( SV44
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV44 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(2186,plain,
! [SV45: $i] :
( ( ! [SY1753: $i] :
( ~ ( class_Divides_Osemiring__div @ SV45 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ SY1753 @ SV45 )
= ( c_HOL_Ozero__class_Ozero @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(2187,plain,
! [SV46: $i] :
( ( ! [SY1754: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV46 )
| ~ ( class_Power_Opower @ SV46 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Suc @ SY1754 ) @ SV46 )
= ( c_HOL_Ozero__class_Ozero @ SV46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(2188,plain,
! [SV47: $i] :
( ( ! [SY1755: $i] : ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV47 @ SY1755 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(2189,plain,
! [SV48: $i] :
( ( ! [SY1756: $i] : ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SY1756 @ SV48 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(2190,plain,
! [SV49: $i] :
( ( ! [SY1757: $i] : ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV49 @ SY1757 @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(2191,plain,
! [SV50: $i] :
( ( ! [SY1758: $i,SY1759: $i,SY1760: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SY1758 @ ( c_HOL_Oplus__class_Oplus @ SY1759 @ SY1760 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SY1758 @ SY1760 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY1759 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(2192,plain,
! [SV51: $i] :
( ( ! [SY1761: $i,SY1762: $i,SY1763: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
| ( c_lessequals @ SY1761 @ ( c_HOL_Oplus__class_Oplus @ SY1762 @ SY1763 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SY1761 @ SY1762 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SY1763 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(2193,plain,
! [SV52: $i] :
( ( ! [SY1764: $i] :
( ( c_HOL_Oord__class_Oless @ SV52 @ SY1764 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV52 ) @ SY1764 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(2194,plain,
! [SV53: $i] :
( ( ! [SY1765: $i] :
( ( c_lessequals @ ( c_Suc @ SV53 ) @ SY1765 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV53 @ SY1765 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(2195,plain,
! [SV54: $i] :
( ( ! [SY1766: $i] :
( ( c_HOL_Oord__class_Oless @ SV54 @ SY1766 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV54 ) @ SY1766 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(2196,plain,
! [SV55: $i] :
( ( ! [SY1767: $i] :
( ( c_lessequals @ ( c_Suc @ SV55 ) @ SY1767 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV55 @ SY1767 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(2197,plain,
! [SV56: $i] :
( ( ! [SY1768: $i,SY1769: $i] :
( ( c_HOL_Oord__class_Oless @ SV56 @ ( c_HOL_Oplus__class_Oplus @ SY1768 @ SY1769 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SY1769 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(2198,plain,
! [SV57: $i] :
( ( ! [SY1770: $i,SY1771: $i] :
( ( c_HOL_Oord__class_Oless @ SV57 @ ( c_HOL_Oplus__class_Oplus @ SY1770 @ SY1771 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SY1770 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(2199,plain,
! [SV58: $i] :
( ( ! [SY1772: $i,SY1773: $i] :
( ( c_HOL_Oord__class_Oless @ SV58 @ SY1772 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV58 @ SY1773 @ tc_nat ) @ SY1772 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(2200,plain,
! [SV59: $i] :
( ( ! [SY1774: $i,SY1775: $i] :
( ( c_HOL_Oord__class_Oless @ SV59 @ ( c_HOL_Oplus__class_Oplus @ SY1774 @ SY1775 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SY1775 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(2201,plain,
! [SV60: $i] :
( ( ! [SY1776: $i,SY1777: $i] :
( ( c_HOL_Oord__class_Oless @ SV60 @ ( c_HOL_Oplus__class_Oplus @ SY1776 @ SY1777 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV60 @ SY1776 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(2202,plain,
! [SV61: $i] :
( ( ! [SY1778: $i,SY1779: $i,SY1780: $i] :
( ~ ( class_Divides_Osemiring__div @ SV61 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1778 @ ( c_Divides_Odiv__class_Omod @ SY1779 @ SY1780 @ SV61 ) @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1778 @ SY1780 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1778 @ SY1779 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(2203,plain,
! [SV62: $i] :
( ( ! [SY1781: $i,SY1782: $i,SY1783: $i] :
( ~ ( class_Divides_Osemiring__div @ SV62 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1781 @ SY1782 @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1781 @ ( c_Divides_Odiv__class_Omod @ SY1782 @ SY1783 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1781 @ SY1783 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(2204,plain,
! [SV63: $i] :
( ( ! [SY1784: $i,SY1785: $i,SY1786: $i] :
( ~ ( class_Divides_Osemiring__div @ SV63 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1784 @ ( c_Divides_Odiv__class_Omod @ SY1785 @ SY1786 @ SV63 ) @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1784 @ SY1785 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1784 @ SY1786 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(2205,plain,
! [SV64: $i] :
( ( ! [SY1787: $i,SY1788: $i,SY1789: $i] :
( ~ ( class_Divides_Osemiring__div @ SV64 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1787 @ SY1788 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1787 @ SY1789 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1787 @ ( c_Divides_Odiv__class_Omod @ SY1788 @ SY1789 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(2206,plain,
! [SV65: $i] :
( ( ! [SY1790: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV65 @ SY1790 @ tc_nat ) @ SY1790 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1790 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(2207,plain,
! [SV66: $i] :
( ( ! [SY1791: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV66 @ SY1791 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY1791 @ ( c_Divides_Odiv__class_Omod @ SV66 @ SY1791 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(2208,plain,
! [SV67: $i] :
( ( ! [SY1792: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV67 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1792 @ SY1792 @ SV67 ) @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
| ~ ( c_HOL_Oord__class_Oless @ SY1792 @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(2209,plain,
! [SV68: $i] :
( ( ! [SY1793: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV68 )
| ( c_HOL_Oord__class_Oless @ SY1793 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1793 @ SY1793 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(2210,plain,
! [SV69: $i] :
( ( ! [SY1794: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
| ( c_HOL_Oord__class_Oless @ SY1794 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1794 @ SY1794 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(2211,plain,
! [SV70: $i] :
( ( ! [SY1795: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV70 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1795 @ SY1795 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ SY1795 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(2212,plain,
! [SV71: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV71 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(2213,plain,
! [SV72: $i] :
( ( ! [SY1796: $i,SY1797: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1796 @ SY1797 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_lessequals @ SY1797 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SY1796 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(2214,plain,
! [SV73: $i] :
( ( ! [SY1798: $i,SY1799: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1798 @ SY1799 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_HOL_Oord__class_Oless @ SY1799 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_lessequals @ SY1798 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(2215,plain,
! [SV74: $i] :
( ( ! [SY1800: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV74 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY1800 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
| ~ ( c_lessequals @ SY1800 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(2216,plain,
! [SV75: $i] :
( ( ! [SY1801: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV75 @ SY1801 @ tc_nat )
= SV75 )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SY1801 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(2217,plain,
! [SV76: $i] :
( ( ! [SY1802: $i,SY1803: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY1802 @ SY1803 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY1803 @ SY1802 @ SV76 )
| ( SY1803 = SY1802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(2218,plain,
! [SV77: $i] :
( ( ! [SY1804: $i] :
( ( c_HOL_Oord__class_Oless @ SV77 @ SY1804 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1804 @ SV77 @ tc_nat )
| ( SY1804 = SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(2219,plain,
! [SV78: $i] :
( ( ! [SY1805: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV78 @ SY1805 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1805 @ SV78 @ tc_nat )
| ( SY1805 = SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(2220,plain,
! [SV79: $i] :
( ( ! [SY1806: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV79 @ SY1806 @ tc_nat )
| ( SY1806 = SV79 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1806 @ SV79 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(2221,plain,
! [SV80: $i] :
( ( ! [SY1807: $i] :
( ( SV80 = SY1807 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV80 @ SY1807 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1807 @ SV80 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(2222,plain,
! [SV81: $i] :
( ( ! [SY1808: $i] :
( ( c_HOL_Oord__class_Oless @ SV81 @ SY1808 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY1808 @ SV81 @ tc_nat )
| ( SY1808 = SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(2223,plain,
! [SV82: $i] :
( ( ! [SY1809: $i] :
( ( SV82 = SY1809 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1809 @ SV82 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV82 @ SY1809 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(2224,plain,
! [SV83: $i] :
( ( ! [SY1810: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV83 @ SY1810 @ tc_nat )
| ( SY1810 = SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1810 @ SV83 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(2225,plain,
! [SV84: $i] :
( ( ! [SY1811: $i] :
( ( SV84 = SY1811 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1811 @ SV84 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV84 @ SY1811 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(2226,plain,
! [SV85: $i] :
( ( ! [SY1812: $i] :
( ( SV85 = SY1812 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1812 @ SV85 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV85 @ SY1812 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(2227,plain,
! [SV86: $i] :
( ( ! [SY1813: $i,SY1814: $i] :
( ~ ( class_Orderings_Olinorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SY1813 @ SY1814 @ SV86 )
| ( SY1814 = SY1813 )
| ( c_HOL_Oord__class_Oless @ SY1814 @ SY1813 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(2228,plain,
! [SV87: $i] :
( ( ! [SY1815: $i,SY1816: $i] :
( ~ ( class_Orderings_Olinorder @ SV87 )
| ( SY1815 = SY1816 )
| ( c_HOL_Oord__class_Oless @ SY1815 @ SY1816 @ SV87 )
| ( c_HOL_Oord__class_Oless @ SY1816 @ SY1815 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(2229,plain,
! [SV88: $i] :
( ( ! [SY1817: $i,SY1818: $i] :
( ~ ( class_Orderings_Olinorder @ SV88 )
| ( SY1817 = SY1818 )
| ( c_HOL_Oord__class_Oless @ SY1818 @ SY1817 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SY1817 @ SY1818 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(2230,plain,
! [SV89: $i] :
( ( ! [SY1819: $i,SY1820: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SY1819 @ SY1820 @ SV89 )
| ( c_HOL_Oord__class_Oless @ SY1820 @ SY1819 @ SV89 )
| ( SY1820 = SY1819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(2231,plain,
! [SV90: $i] :
( ( ! [SY1821: $i,SY1822: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ SY1821 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ ( c_GCD_Ogcd__class_Ogcd @ SY1822 @ SY1821 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(2232,plain,
! [SV91: $i] :
( ( ! [SY1823: $i,SY1824: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ SY1823 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ ( c_GCD_Ogcd__class_Ogcd @ SY1823 @ SY1824 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(2233,plain,
! [SV92: $i] :
( ( ! [SY1825: $i,SY1826: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ SY1825 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ ( c_GCD_Ogcd__class_Ogcd @ SY1825 @ SY1826 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(2234,plain,
! [SV93: $i] :
( ( ! [SY1827: $i,SY1828: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ SY1827 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ ( c_GCD_Ogcd__class_Ogcd @ SY1828 @ SY1827 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(2235,plain,
! [SV94: $i] :
( ( ! [SY1829: $i,SY1830: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV94 @ SY1829 @ tc_nat ) @ SY1830 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SY1830 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(2236,plain,
! [SV95: $i] :
( ( ! [SY1831: $i,SY1832: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV95 @ SY1831 @ tc_nat ) @ SY1832 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1831 @ SY1832 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(2237,plain,
! [SV96: $i] :
( ( ! [SY1833: $i,SY1834: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ SY1833 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ ( c_GCD_Ogcd__class_Ogcd @ SY1833 @ SY1834 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(2238,plain,
! [SV97: $i] :
( ( ! [SY1835: $i,SY1836: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ SY1835 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ ( c_GCD_Ogcd__class_Ogcd @ SY1836 @ SY1835 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(2239,plain,
! [SV98: $i] :
( ( ! [SY1837: $i,SY1838: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SY1837 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1838 @ SY1837 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SY1838 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(2240,plain,
! [SV99: $i] :
( ( ! [SY1839: $i,SY1840: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SY1839 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1839 @ SY1840 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1840 @ SY1839 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1840 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SY1840 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(2241,plain,
! [SV100: $i] :
( ( ! [SY1841: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV100 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV100 @ SY1841 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1841 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(2242,plain,
! [SV101: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV101 @ SV101 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(2243,plain,
! [SV102: $i] :
( ( ! [SY1842: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV102 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1842 @ SY1842 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(2244,plain,
! [SV103: $i] :
( ( ! [SY1843: $i,SY1844: $i,SY1845: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1843 @ SY1844 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1845 @ SY1844 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1843 @ SY1845 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(2245,plain,
! [SV104: $i] :
( ( ! [SY1846: $i,SY1847: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SY1846 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY1847 @ SY1846 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SY1847 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(2246,plain,
! [SV105: $i] :
( ( c_HOL_Oord__class_Oless @ SV105 @ ( c_Suc @ SV105 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(2247,plain,
! [SV106: $i] :
( ( c_HOL_Oord__class_Oless @ SV106 @ ( c_Suc @ SV106 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(2248,plain,
! [SV107: $i] :
( ( ! [SY1848: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV107 )
| ( c_HOL_Oord__class_Oless @ SY1848 @ ( c_HOL_Oplus__class_Oplus @ SY1848 @ ( c_HOL_Oone__class_Oone @ SV107 ) @ SV107 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(2249,plain,
! [SV108: $i] :
( ( ! [SY1849: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV108 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SY1849 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY1849 @ SV108 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(2250,plain,
! [SV109: $i] :
( ( ! [SY1850: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV109 )
| ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SY1850 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SY1850
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(2251,plain,
! [SV110: $i] :
( ( ! [SY1851: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV110 )
| ~ ( class_Power_Opower @ SV110 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SY1851 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
| ( SY1851
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(2252,plain,
! [SV111: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1852 @ SY1853 @ SV111 ) @ SY1852 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ SY1853 @ SY1852 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(2253,plain,
! [SV112: $i] :
( ( ! [SY1854: $i,SY1855: $i] :
( ~ ( class_Divides_Osemiring__div @ SV112 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY1854 @ SY1855 @ SV112 ) @ SY1855 @ SV112 )
= ( c_Divides_Odiv__class_Omod @ SY1854 @ SY1855 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(2254,plain,
! [SV113: $i] :
( ( ! [SY1856: $i,SY1857: $i,SY1858: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 )
| ( c_HOL_Oord__class_Oless @ SY1856 @ ( c_HOL_Oplus__class_Oplus @ SY1857 @ SY1858 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SY1856 @ SY1858 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SY1857 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(2255,plain,
! [SV114: $i] :
( ( ! [SY1859: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV114 )
| ( c_HOL_Oord__class_Oless @ SY1859 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
| ( SY1859
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY1859 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(2256,plain,
! [SV115: $i] :
( ( ! [SY1860: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV115 @ SY1860 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV115 @ SY1860 @ tc_nat ) @ SY1860 @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ SV115 @ SY1860 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(2257,plain,
! [SV116: $i] :
( ( ! [SY1861: $i,SY1862: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV116 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
| ( c_HOL_Oord__class_Oless @ SY1861 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SY1861 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SY1861 @ SY1862 @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(2258,plain,
! [SV117: $i] :
( ( ! [SY1863: $i,SY1864: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV117 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
| ( c_HOL_Oord__class_Oless @ SY1863 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SY1864 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SY1864 @ SY1863 @ SV117 ) @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(2259,plain,
! [SV118: $i] :
( ( ! [SY1865: $i,SY1866: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV118 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
| ( c_HOL_Oord__class_Oless @ SY1865 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SY1866 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SY1865 @ SY1866 @ SV118 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(2260,plain,
! [SV119: $i] :
( ( ! [SY1867: $i,SY1868: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV119 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SY1867 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SY1867 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY1868 @ SY1867 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(2261,plain,
! [SV120: $i] :
( ( ! [SY1869: $i,SY1870: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV120 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
| ( c_HOL_Oord__class_Oless @ SY1869 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SY1870 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY1869 @ SY1870 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(2262,plain,
! [SV121: $i] :
( ( ! [SY1871: $i,SY1872: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV121 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY1871 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY1872 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY1872 @ SY1871 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(2263,plain,
! [SV122: $i] :
( ( ! [SY1873: $i,SY1874: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV122 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
| ( c_HOL_Oord__class_Oless @ SY1873 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SY1873 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY1873 @ SY1874 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(2264,plain,
! [SV123: $i] :
( ( ( SV123
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV123 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(2265,plain,
! [SV124: $i] :
( ( ! [SY1875: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV124 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1875 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(2266,plain,
! [SV125: $i] :
( ( ! [SY1876: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV125 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1876 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(2267,plain,
! [SV126: $i] :
( ( ! [SY1877: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV126 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1877 @ ( c_HOL_Ozero__class_Ozero @ SV126 ) @ SV126 )
= SY1877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(2268,plain,
! [SV127: $i] :
( ( ! [SY1878: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV127 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV127 ) @ SY1878 @ SV127 )
= SY1878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(2269,plain,
! [SV128: $i] :
( ( ! [SY1879: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV128 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1879 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 )
= SY1879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2270,plain,
! [SV129: $i] :
( ( ! [SY1880: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV129 )
| ~ ( class_Int_Onumber__ring @ SV129 )
| ( SY1880
= ( c_HOL_Oplus__class_Oplus @ SY1880 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2271,plain,
! [SV130: $i] :
( ( ! [SY1881: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV130 ) @ SY1881 @ SV130 )
= SY1881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2272,plain,
! [SV131: $i] :
( ( ! [SY1882: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV131 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV131 ) @ SY1882 @ SV131 )
= SY1882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(2273,plain,
! [SV132: $i] :
( ( SV132
= ( c_HOL_Oplus__class_Oplus @ SV132 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(2274,plain,
! [SV133: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV133 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV133 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2275,plain,
! [SV134: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV134 @ tc_nat )
= SV134 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2276,plain,
! [SV135: $i] :
( ( ! [SY1883: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ SY1883 @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= SY1883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2277,plain,
! [SV136: $i] :
( ( ! [SY1884: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV136 ) @ SY1884 @ SV136 )
= SY1884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2278,plain,
! [SV137: $i] :
( ( ! [SY1885: $i,SY1886: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SY1885 @ SY1886 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SY1886 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SY1885 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(2279,plain,
! [SV138: $i] :
( ( ! [SY1887: $i,SY1888: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SY1887 @ SY1888 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SY1888 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1888 @ SV138 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(2280,plain,
! [SV139: $i] :
( ( ! [SY1889: $i,SY1890: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SY1889 @ SY1890 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SY1889 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1889 @ SV139 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(2281,plain,
! [SV140: $i] :
( ( ! [SY1891: $i,SY1892: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SY1891 @ SY1892 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SY1892 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SY1891 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(2282,plain,
! [SV141: $i] :
( ( ! [SY1893: $i,SY1894: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SY1893 @ SY1894 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SY1894 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SY1893 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2283,plain,
! [SV142: $i] :
( ( ! [SY1895: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV142 @ SY1895 @ tc_nat ) @ SY1895 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2284,plain,
! [SV143: $i] :
( ( ! [SY1896: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV143 @ SY1896 @ tc_nat ) @ SV143 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2285,plain,
! [SV144: $i] :
( ( ! [SY1897: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV144 @ SY1897 @ tc_nat ) @ SV144 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2286,plain,
! [SV145: $i] :
( ( ! [SY1898: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV145 @ SY1898 @ tc_nat ) @ SY1898 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2287,plain,
! [SV146: $i] :
( ( ! [SY1899: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV146 @ SY1899 @ tc_nat ) @ SV146 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(2288,plain,
! [SV147: $i] :
( ( ! [SY1900: $i] : ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV147 @ SY1900 @ tc_nat ) @ SY1900 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2289,plain,
! [SV148: $i] :
( ( ! [SY1901: $i,SY1902: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SY1901 @ SY1902 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SY1902 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SY1901 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(2290,plain,
! [SV149: $i] :
( ( ! [SY1903: $i,SY1904: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SY1903 @ SY1904 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SY1904 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SY1903 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2291,plain,
! [SV150: $i] :
( ( ! [SY1905: $i,SY1906: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SY1905 @ SY1906 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SY1906 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SY1905 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2292,plain,
! [SV151: $i] :
( ( ! [SY1907: $i,SY1908: $i,SY1909: $i,SY1910: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1907 @ SY1908 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SY1909 @ SY1910 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SY1908 @ SY1910 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SY1907 @ SY1909 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2293,plain,
! [SV152: $i] :
( ( ! [SY1911: $i,SY1912: $i,SY1913: $i,SY1914: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY1911 @ SY1912 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SY1913 @ SY1914 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SY1912 @ SY1914 @ SV152 )
| ~ ( c_lessequals @ SY1911 @ SY1913 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2294,plain,
! [SV153: $i] :
( ( ! [SY1915: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV153 ) @ ( c_Suc @ SY1915 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV153 @ SY1915 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2295,plain,
! [SV154: $i] :
( ( ! [SY1916: $i] :
( ( c_HOL_Oord__class_Oless @ SV154 @ SY1916 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV154 ) @ ( c_Suc @ SY1916 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2296,plain,
! [SV155: $i] :
( ( ! [SY1917: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV155 ) @ ( c_Suc @ SY1917 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV155 @ SY1917 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2297,plain,
! [SV156: $i] :
( ( ! [SY1918: $i,SY1919: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SY1918 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SY1919 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1919 @ SV156 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1918 @ SY1919 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2298,plain,
! [SV157: $i] :
( ( ! [SY1920: $i,SY1921: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SY1920 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1921 @ SV157 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY1921 @ SY1920 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY1920 @ SY1921 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2299,plain,
! [SV158: $i] :
( ( ! [SY1922: $i,SY1923: $i,SY1924: $i] :
( ~ ( class_Orderings_Oorder @ SV158 )
| ( c_HOL_Oord__class_Oless @ SY1922 @ SY1923 @ SV158 )
| ~ ( c_lessequals @ SY1922 @ SY1924 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SY1924 @ SY1923 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2300,plain,
! [SV159: $i] :
( ( ! [SY1925: $i,SY1926: $i,SY1927: $i] :
( ~ ( class_Orderings_Oorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SY1925 @ SY1926 @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SY1925 @ SY1927 @ SV159 )
| ~ ( c_lessequals @ SY1927 @ SY1926 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2301,plain,
! [SV160: $i] :
( ( ! [SY1928: $i,SY1929: $i,SY1930: $i,SY1931: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
| ( c_lessequals @ SY1928 @ ( c_HOL_Oplus__class_Oplus @ SY1929 @ SY1930 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SY1931 @ SY1930 @ SV160 )
| ~ ( c_lessequals @ SY1928 @ ( c_HOL_Oplus__class_Oplus @ SY1929 @ SY1931 @ SV160 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2302,plain,
! [SV161: $i] :
( ( ! [SY1932: $i,SY1933: $i,SY1934: $i] :
( ~ ( class_Orderings_Opreorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SY1932 @ SY1933 @ SV161 )
| ~ ( c_lessequals @ SY1934 @ SY1933 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SY1932 @ SY1934 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(2303,plain,
! [SV162: $i] :
( ( ! [SY1935: $i,SY1936: $i,SY1937: $i] :
( ~ ( class_Orderings_Opreorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SY1935 @ SY1936 @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY1937 @ SY1936 @ SV162 )
| ~ ( c_lessequals @ SY1935 @ SY1937 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(2304,plain,
! [SV163: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ~ ( class_Orderings_Opreorder @ SV163 )
| ( c_lessequals @ SY1938 @ SY1939 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ SY1938 @ SY1939 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(2305,plain,
! [SV164: $i] :
( ( ! [SY1940: $i,SY1941: $i] :
( ~ ( class_Orderings_Oorder @ SV164 )
| ( c_lessequals @ SY1940 @ SY1941 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SY1940 @ SY1941 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2306,plain,
! [SV165: $i] :
( ( ! [SY1942: $i,SY1943: $i] :
( ~ ( class_Orderings_Opreorder @ SV165 )
| ( c_HOL_Oord__class_Oless @ SY1942 @ SY1943 @ SV165 )
| ( c_lessequals @ SY1943 @ SY1942 @ SV165 )
| ~ ( c_lessequals @ SY1942 @ SY1943 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2307,plain,
! [SV166: $i] :
( ( ! [SY1944: $i,SY1945: $i,SY1946: $i,SY1947: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1944 @ SY1945 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SY1946 @ SY1947 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SY1945 @ SY1947 @ SV166 )
| ~ ( c_lessequals @ SY1944 @ SY1946 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2308,plain,
! [SV167: $i] :
( ( ! [SY1948: $i,SY1949: $i] :
( ~ ( class_Orderings_Oorder @ SV167 )
| ( c_HOL_Oord__class_Oless @ SY1948 @ SY1949 @ SV167 )
| ( SY1949 = SY1948 )
| ~ ( c_lessequals @ SY1948 @ SY1949 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2309,plain,
! [SV168: $i] :
( ( ! [SY1950: $i,SY1951: $i] :
( ~ ( class_Orderings_Oorder @ SV168 )
| ( c_HOL_Oord__class_Oless @ SY1950 @ SY1951 @ SV168 )
| ~ ( c_lessequals @ SY1950 @ SY1951 @ SV168 )
| ( SY1951 = SY1950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2310,plain,
! [SV169: $i] :
( ( ! [SY1952: $i,SY1953: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( SY1952 = SY1953 )
| ( c_HOL_Oord__class_Oless @ SY1952 @ SY1953 @ SV169 )
| ~ ( c_lessequals @ SY1952 @ SY1953 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2311,plain,
! [SV170: $i] :
( ( ! [SY1954: $i,SY1955: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( SY1954 = SY1955 )
| ~ ( c_lessequals @ SY1954 @ SY1955 @ SV170 )
| ( c_HOL_Oord__class_Oless @ SY1954 @ SY1955 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2312,plain,
! [SV171: $i] :
( ( ! [SY1956: $i,SY1957: $i] :
( ~ ( class_Orderings_Oorder @ SV171 )
| ( c_HOL_Oord__class_Oless @ SY1956 @ SY1957 @ SV171 )
| ~ ( c_lessequals @ SY1956 @ SY1957 @ SV171 )
| ( SY1956 = SY1957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2313,plain,
! [SV172: $i] :
( ( ! [SY1958: $i,SY1959: $i] :
( ~ ( class_Orderings_Oorder @ SV172 )
| ( c_HOL_Oord__class_Oless @ SY1958 @ SY1959 @ SV172 )
| ( SY1958 = SY1959 )
| ~ ( c_lessequals @ SY1958 @ SY1959 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2314,plain,
! [SV173: $i] :
( ( ! [SY1960: $i,SY1961: $i] :
( ~ ( class_Orderings_Oorder @ SV173 )
| ( SY1960 = SY1961 )
| ( c_HOL_Oord__class_Oless @ SY1960 @ SY1961 @ SV173 )
| ~ ( c_lessequals @ SY1960 @ SY1961 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2315,plain,
! [SV174: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ~ ( class_Orderings_Oorder @ SV174 )
| ( c_HOL_Oord__class_Oless @ SY1962 @ SY1963 @ SV174 )
| ( SY1962 = SY1963 )
| ~ ( c_lessequals @ SY1962 @ SY1963 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2316,plain,
! [SV175: $i] :
( ( ! [SY1964: $i,SY1965: $i,SY1966: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1964 @ SY1965 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY1966 @ SY1965 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SY1964 @ SY1966 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2317,plain,
! [SV176: $i] :
( ( ! [SY1967: $i,SY1968: $i,SY1969: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
| ( c_lessequals @ SY1967 @ SY1968 @ SV176 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1967 @ SY1969 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SY1968 @ SY1969 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2318,plain,
! [SV177: $i] :
( ( ! [SY1970: $i,SY1971: $i,SY1972: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1970 @ SY1971 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SY1970 @ SY1972 @ SV177 ) @ SV177 )
| ~ ( c_lessequals @ SY1971 @ SY1972 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2319,plain,
! [SV178: $i] :
( ( ! [SY1973: $i,SY1974: $i,SY1975: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
| ( c_lessequals @ SY1973 @ SY1974 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1975 @ SY1973 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SY1975 @ SY1974 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2320,plain,
! [SV179: $i] :
( ( ! [SY1976: $i,SY1977: $i,SY1978: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1976 @ SY1977 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SY1978 @ SY1977 @ SV179 ) @ SV179 )
| ~ ( c_lessequals @ SY1976 @ SY1978 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2321,plain,
! [SV180: $i] :
( ( ! [SY1979: $i,SY1980: $i,SY1981: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY1979 @ SY1980 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SY1979 @ SY1981 @ SV180 ) @ SV180 )
| ~ ( c_lessequals @ SY1980 @ SY1981 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2322,plain,
! [SV181: $i] :
( ( ! [SY1982: $i,SY1983: $i] :
( ~ ( class_Orderings_Opreorder @ SV181 )
| ~ ( c_lessequals @ SY1982 @ SY1983 @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ SY1983 @ SY1982 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2323,plain,
! [SV182: $i] :
( ( ! [SY1984: $i,SY1985: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_HOL_Oord__class_Oless @ SY1984 @ SY1985 @ SV182 )
| ( c_lessequals @ SY1985 @ SY1984 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2324,plain,
! [SV183: $i] :
( ( ! [SY1986: $i] :
( ~ ( class_Orderings_Olinorder @ SV183 )
| ~ ( c_lessequals @ SY1986 @ SY1986 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SY1986 @ SY1986 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2325,plain,
! [SV184: $i] :
( ( ! [SY1987: $i] :
( ~ ( class_Orderings_Olinorder @ SV184 )
| ( c_HOL_Oord__class_Oless @ SY1987 @ SY1987 @ SV184 )
| ( c_lessequals @ SY1987 @ SY1987 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2326,plain,
! [SV185: $i] :
( ( ! [SY1988: $i,SY1989: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY1988 @ SY1989 @ SV185 )
| ~ ( c_lessequals @ SY1989 @ SY1988 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2327,plain,
! [SV186: $i] :
( ( ! [SY1990: $i,SY1991: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SY1990 @ SY1991 @ SV186 )
| ( c_HOL_Oord__class_Oless @ SY1991 @ SY1990 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2328,plain,
! [SV187: $i] :
( ( ! [SY1992: $i,SY1993: $i] :
( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_HOL_Oord__class_Oless @ SY1992 @ SY1993 @ SV187 )
| ( c_lessequals @ SY1993 @ SY1992 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2329,plain,
! [SV188: $i] :
( ( ! [SY1994: $i,SY1995: $i] :
( ~ ( class_Orderings_Olinorder @ SV188 )
| ~ ( c_lessequals @ SY1994 @ SY1995 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SY1995 @ SY1994 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2330,plain,
! [SV189: $i] :
( ( ! [SY1996: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV189 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY1996 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
| ~ ( c_lessequals @ SY1996 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2331,plain,
! [SV190: $i] :
( ( ! [SY1997: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV190 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SY1997 @ SV190 )
| ( c_lessequals @ SY1997 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY1997 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2332,plain,
! [SV191: $i] :
( ( ! [SY1998: $i,SY1999: $i,SY2000: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SY1998 @ SY1999 @ SV191 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SY1999 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY1998 @ ( c_Suc @ SY2000 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SY1999 @ ( c_Suc @ SY2000 ) @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2333,plain,
! [SV192: $i] :
( ( ! [SY2001: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV192 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2001 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV192 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2334,plain,
! [SV193: $i] :
( ( ! [SY2002: $i,SY2003: $i,SY2004: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_HOL_Oord__class_Oless @ SY2002 @ SY2003 @ SV193 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SY2003 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2002 @ SY2004 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SY2003 @ SY2004 @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2335,plain,
! [SV194: $i] :
( ( ! [SY2005: $i,SY2006: $i,SY2007: $i,SY2008: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV194 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2005 @ SY2006 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2007 @ SY2008 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SY2008 @ SY2006 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY2008 @ SV194 )
| ~ ( c_lessequals @ SY2005 @ SY2007 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY2005 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2336,plain,
! [SV195: $i] :
( ( ! [SY2009: $i,SY2010: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV195 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2009 @ SY2010 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SY2010 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
| ~ ( c_lessequals @ SY2009 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2337,plain,
! [SV196: $i] :
( ( ! [SY2011: $i,SY2012: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2011 @ SY2012 @ SV196 ) @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SY2012 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SY2011 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2338,plain,
! [SV197: $i] :
( ( ! [SY2013: $i,SY2014: $i,SY2015: $i,SY2016: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV197 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2013 @ SY2014 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2015 @ SY2016 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SY2016 @ SY2014 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY2016 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SY2013 @ SY2015 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY2013 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2339,plain,
! [SV198: $i] :
( ( ! [SY2017: $i,SY2018: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV198 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2017 @ SY2018 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SY2018 @ SV198 )
| ~ ( c_lessequals @ SY2017 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2340,plain,
! [SV199: $i] :
( ( ! [SY2019: $i,SY2020: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV199 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2019 @ SY2020 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SY2020 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SY2019 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2341,plain,
! [SV200: $i] :
( ( ! [SY2021: $i,SY2022: $i,SY2023: $i,SY2024: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2021 @ SY2022 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2023 @ SY2024 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SY2024 @ SY2022 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SY2024 @ SV200 )
| ~ ( c_lessequals @ SY2021 @ SY2023 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SY2021 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2342,plain,
! [SV201: $i] :
( ( ! [SY2025: $i,SY2026: $i,SY2027: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV201 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
| ( c_lessequals @ SY2025 @ ( c_HOL_Oinverse__class_Odivide @ SY2026 @ SY2027 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SY2025 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SY2027 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SY2027 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2343,plain,
! [SV202: $i] :
( ( ! [SY2028: $i,SY2029: $i,SY2030: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( c_lessequals @ SY2028 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SY2029 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SY2029 @ SV202 )
| ~ ( c_lessequals @ SY2028 @ ( c_HOL_Oinverse__class_Odivide @ SY2030 @ SY2029 @ SV202 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2344,plain,
! [SV203: $i] :
( ( ! [SY2031: $i,SY2032: $i,SY2033: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2031 @ SY2032 @ SV203 ) @ SY2033 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SY2033 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SY2032 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SY2032 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2345,plain,
! [SV204: $i] :
( ( ! [SY2034: $i,SY2035: $i,SY2036: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV204 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY2034 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SY2035 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY2035 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2036 @ SY2035 @ SV204 ) @ SY2034 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2346,plain,
! [SV205: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV205 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV205 ) @ SV205 )
= ( c_HOL_Oone__class_Oone @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2347,plain,
! [SV206: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV206 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV206 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= ( c_HOL_Oone__class_Oone @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2348,plain,
! [SV207: $i] :
( ( ! [SY2037: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV207 ) @ SY2037 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2349,plain,
! [SV208: $i] :
( ( ! [SY2038: $i,SY2039: $i,SY2040: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV208 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2038 @ SY2039 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SY2038 @ SY2040 @ SV208 ) @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ SY2039 @ SY2040 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SY2038 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2350,plain,
! [SV209: $i] :
( ( ! [SY2041: $i,SY2042: $i,SY2043: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV209 )
| ( c_HOL_Oord__class_Oless @ SY2041 @ SY2042 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2043 @ SY2041 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SY2043 @ SY2042 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SY2043 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2351,plain,
! [SV210: $i] :
( ( ! [SY2044: $i,SY2045: $i,SY2046: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV210 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2044 @ SY2045 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SY2044 @ SY2046 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SY2044 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SY2045 @ SY2046 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2352,plain,
! [SV211: $i] :
( ( ! [SY2047: $i,SY2048: $i,SY2049: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV211 )
| ( c_HOL_Oord__class_Oless @ SY2047 @ SY2048 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2049 @ SY2047 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SY2049 @ SY2048 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SY2049 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2353,plain,
! [SV212: $i] :
( ( ! [SY2050: $i,SY2051: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV212 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SY2050 @ ( c_Suc @ SY2051 ) @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SY2050 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2354,plain,
! [SV213: $i] :
( ( ! [SY2052: $i,SY2053: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV213 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
| ( c_HOL_Oord__class_Oless @ SY2052 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SY2052 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2053 @ SY2052 @ SV213 ) @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2355,plain,
! [SV214: $i] :
( ( ! [SY2054: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV214 @ SY2054 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2054 @ SV214 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2356,plain,
! [SV215: $i] :
( ( ! [SY2055: $i] :
( ( c_HOL_Oord__class_Oless @ SV215 @ SY2055 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2055 @ SV215 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2357,plain,
! [SV216: $i] :
( ( ! [SY2056: $i] :
( ( c_HOL_Oord__class_Oless @ SV216 @ ( c_Suc @ SY2056 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV216 @ SY2056 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2358,plain,
! [SV217: $i] :
( ( ! [SY2057: $i] :
( ( c_HOL_Oord__class_Oless @ SV217 @ SY2057 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV217 ) @ SY2057 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2359,plain,
! [SV218: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV218 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV218 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2360,plain,
! [SV219: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV219 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2361,plain,
! [SV220: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV220 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV220 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV220 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2362,plain,
! [SV221: $i] :
( ( ! [SY2058: $i,SY2059: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV221 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SY2058 @ SY2059 @ tc_nat ) @ SV221 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2058 @ SV221 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2059 @ SV221 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2363,plain,
! [SV222: $i] :
( ( ! [SY2060: $i,SY2061: $i,SY2062: $i] :
( ~ ( class_Divides_Osemiring__div @ SV222 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2060 @ ( c_Divides_Odiv__class_Omod @ SY2061 @ SY2062 @ SV222 ) @ SV222 ) @ SY2062 @ SV222 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2060 @ SY2061 @ SV222 ) @ SY2062 @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2364,plain,
! [SV223: $i] :
( ( ! [SY2063: $i,SY2064: $i,SY2065: $i] :
( ~ ( class_Divides_Osemiring__div @ SV223 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SY2063 @ SY2064 @ SV223 ) @ SY2065 @ SV223 ) @ SY2064 @ SV223 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2063 @ SY2065 @ SV223 ) @ SY2064 @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2365,plain,
! [SV224: $i] :
( ( ! [SY2066: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV224 @ SY2066 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2066 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2366,plain,
! [SV225: $i] :
( ( ! [SY2067: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV225 @ SY2067 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV225 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2367,plain,
! [SV226: $i] :
( ( ! [SY2068: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV226 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SY2068 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ ( c_HOL_Oplus__class_Oplus @ SY2068 @ SY2068 @ SV226 ) @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2368,plain,
! [SV227: $i] :
( ( ! [SY2069: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV227 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SY2069 @ SY2069 @ SV227 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SY2069 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2369,plain,
! [SV228: $i] :
( ( ! [SY2070: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV228 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2070 @ SV228 ) @ SV228 )
| ~ ( c_lessequals @ SY2070 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SY2070 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2370,plain,
! [SV229: $i] :
( ( ! [SY2071: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV229 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV229 ) @ ( c_Power_Opower__class_Opower @ SY2071 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV229 ) @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2371,plain,
! [SV230: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV230 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV230 ) @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 ) @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2372,plain,
! [SV231: $i] :
( ( ! [SY2072: $i,SY2073: $i,SY2074: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV231 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SY2072 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SY2073 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SY2073 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2074 @ SY2073 @ SV231 ) @ SY2072 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2373,plain,
! [SV232: $i] :
( ( ! [SY2075: $i,SY2076: $i,SY2077: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV232 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2075 @ SY2076 @ SV232 ) @ SY2077 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SY2077 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SY2076 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SY2076 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2374,plain,
! [SV233: $i] :
( ( ! [SY2078: $i,SY2079: $i,SY2080: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV233 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
| ( c_HOL_Oord__class_Oless @ SY2078 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SY2079 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SY2079 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SY2078 @ ( c_HOL_Oinverse__class_Odivide @ SY2080 @ SY2079 @ SV233 ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2375,plain,
! [SV234: $i] :
( ( ! [SY2081: $i,SY2082: $i,SY2083: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV234 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
| ( c_HOL_Oord__class_Oless @ SY2081 @ ( c_HOL_Oinverse__class_Odivide @ SY2082 @ SY2083 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SY2081 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SY2083 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SY2083 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2376,plain,
! [SV235: $i] :
( ( ! [SY2084: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SY2084 @ tc_nat ) @ SY2084 @ tc_nat )
| ( SY2084
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2377,plain,
! [SV236: $i] :
( ( ! [SY2085: $i] :
( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ SV236 @ SY2085 @ tc_nat ) @ SV236 @ tc_nat )
| ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2378,plain,
! [SV237: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV237 @ SV237 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV237 @ ( c_Suc @ SV237 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2379,plain,
! [SV238: $i] :
( ( ! [SY2086: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV238 @ SY2086 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2086 @ ( c_Suc @ SV238 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2380,plain,
! [SV239: $i] :
( ( ! [SY2087: $i] :
( ( c_HOL_Oord__class_Oless @ SV239 @ ( c_Suc @ SY2087 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2087 @ SV239 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2381,plain,
! [SV240: $i] :
( ( ! [SY2088: $i,SY2089: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV240 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2088 @ SY2089 @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SY2089 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SY2088 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2382,plain,
! [SV241: $i] :
( ( ! [SY2090: $i,SY2091: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV241 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2090 @ SY2091 @ SV241 ) @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SY2091 @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SY2090 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2383,plain,
! [SV242: $i] :
( ( ! [SY2092: $i,SY2093: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV242 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2092 @ SY2093 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SY2093 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SY2092 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2384,plain,
! [SV243: $i] :
( ( ! [SY2094: $i,SY2095: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV243 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2094 @ SY2095 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SY2095 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SY2094 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2385,plain,
! [SV244: $i] :
( ( ! [SY2096: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV244 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
| ( c_HOL_Oord__class_Oless @ SY2096 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2096 @ SV244 ) @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2386,plain,
! [SV245: $i] :
( ( ! [SY2097: $i,SY2098: $i,SY2099: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2097 @ ( c_HOL_Oplus__class_Oplus @ SY2098 @ SY2099 @ SV245 ) @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2097 @ SY2099 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2097 @ SY2098 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2387,plain,
! [SV246: $i] :
( ( ! [SY2100: $i,SY2101: $i,SY2102: $i,SY2103: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2100 @ SY2101 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SY2102 @ SY2103 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SY2100 @ SY2102 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SY2101 @ SY2103 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2388,plain,
! [SV247: $i] :
( ( ! [SY2104: $i,SY2105: $i,SY2106: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV247 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2104 @ SY2105 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2106 @ SY2105 @ SV247 ) @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SY2105 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SY2104 @ SY2106 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2389,plain,
! [SV248: $i] :
( ( ! [SY2107: $i,SY2108: $i,SY2109: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV248 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2107 @ SY2108 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2109 @ SY2108 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SY2108 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SY2109 @ SY2107 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2390,plain,
! [SV249: $i] :
( ( ! [SY2110: $i,SY2111: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SY2110 @ SY2111 @ SV249 ) @ SV249 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SY2111 @ SV249 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SY2110 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2391,plain,
! [SV250: $i] :
( ( ! [SY2112: $i,SY2113: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SY2112 @ SY2113 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SY2113 @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SY2112 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2392,plain,
! [SV251: $i] :
( ( ! [SY2114: $i,SY2115: $i] :
( ~ ( class_Divides_Osemiring__div @ SV251 )
| ( ( c_Divides_Odiv__class_Omod @ SY2114 @ SY2115 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2115 @ SY2114 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2393,plain,
! [SV252: $i] :
( ( ! [SY2116: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV252 )
| ( SY2116
= ( c_HOL_Ozero__class_Ozero @ SV252 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SY2116 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2394,plain,
! [SV253: $i] :
( ( ! [SY2117: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV253 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SY2117 @ SV253 ) @ SV253 )
= SY2117 )
| ( SY2117
= ( c_HOL_Ozero__class_Ozero @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2395,plain,
! [SV254: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV254 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV254 )
= ( c_HOL_Ozero__class_Ozero @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2396,plain,
! [SV255: $i] :
( ( ! [SY2118: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV255 ) @ SY2118 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV255 @ ( c_Suc @ SY2118 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2397,plain,
! [SV256: $i] :
( ( ! [SY2119: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV256 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SY2119 ) @ SV256 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV256 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2119 @ SV256 ) @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2398,plain,
! [SV257: $i] :
( ( ! [SY2120: $i,SY2121: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SY2120 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SY2121 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2121 @ SV257 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2121 @ SY2120 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2120 @ SY2121 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2399,plain,
! [SV258: $i] :
( ( ! [SY2122: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV258 @ SY2122 @ tc_nat ) @ SY2122 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2122 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2400,plain,
! [SV259: $i] :
( ( ! [SY2123: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV259 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SY2123 @ SV259 )
| ( SY2123
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2123 @ SV259 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2401,plain,
! [SV260: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV260 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2402,plain,
! [SV261: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV261 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2403,plain,
! [SV262: $i] :
( ( ! [SY2124: $i,SY2125: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV262 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2124 @ ( c_Suc @ SY2125 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ SY2124 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SY2124 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2404,plain,
! [SV263: $i] :
( ( ! [SY2126: $i,SY2127: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV263 )
| ( c_HOL_Oord__class_Oless @ SY2126 @ SY2127 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SY2127 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2127 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2126 @ SV263 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2405,plain,
! [SV264: $i] :
( ( ! [SY2128: $i,SY2129: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV264 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2128 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2129 @ SV264 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SY2129 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SY2129 @ SY2128 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2406,plain,
! [SV265: $i] :
( ( ! [SY2130: $i,SY2131: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV265 )
| ( c_HOL_Oord__class_Oless @ SY2130 @ SY2131 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SY2130 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2131 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2130 @ SV265 ) @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2407,plain,
! [SV266: $i] :
( ( ! [SY2132: $i,SY2133: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV266 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2132 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2133 @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SY2132 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SY2133 @ SY2132 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2408,plain,
! [SV267: $i] :
( ( ! [SY2134: $i,SY2135: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SY2134 @ SY2135 @ SV267 ) @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SY2135 @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SY2134 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2409,plain,
! [SV268: $i] :
( ( ! [SY2136: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV268 @ SY2136 @ tc_nat ) @ ( c_Suc @ SV268 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2410,plain,
! [SV269: $i] :
( ( ~ ( class_SEQ_Obanach @ SV269 )
| ~ ( class_RealVector_Oreal__normed__field @ SV269 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= ( c_HOL_Oone__class_Oone @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2411,plain,
! [SV270: $i] :
( ( ! [SY2137: $i] :
( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Suc @ SY2137 ) @ tc_nat )
| ~ ( c_lessequals @ SV270 @ SY2137 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2412,plain,
! [SV271: $i] :
( ( ! [SY2138: $i] :
( ( c_lessequals @ SV271 @ SY2138 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV271 @ ( c_Suc @ SY2138 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2413,plain,
! [SV272: $i] :
( ( ~ ( c_lessequals @ SV272 @ SV272 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV272 @ ( c_Suc @ SV272 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2414,plain,
! [SV273: $i] :
( ( ! [SY2139: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV273 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SY2139 @ SV273 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2139 @ SV273 ) @ SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2415,plain,
! [SV274: $i] :
( ( ! [SY2140: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV274 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2140 @ SV274 ) @ SV274 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SY2140 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2416,plain,
! [SV275: $i] :
( ( ! [SY2141: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV275 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ SY2141 @ SV275 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ ( c_HOL_Oplus__class_Oplus @ SY2141 @ SY2141 @ SV275 ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2417,plain,
! [SV276: $i] :
( ( ! [SY2142: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV276 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ ( c_HOL_Oplus__class_Oplus @ SY2142 @ SY2142 @ SV276 ) @ SV276 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SY2142 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2418,plain,
! [SV277: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV277 @ tc_nat )
= SV277 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2419,plain,
! [SV278: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV278 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV278 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2420,plain,
! [SV279: $i] :
( ( ! [SY2143: $i,SY2144: $i] :
( ~ ( class_Divides_Osemiring__div @ SV279 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SY2143 @ SY2144 @ SV279 ) @ SY2144 @ SV279 )
= ( c_Divides_Odiv__class_Omod @ SY2143 @ SY2144 @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2421,plain,
! [SV280: $i] :
( ( ! [SY2145: $i,SY2146: $i,SY2147: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
| ( c_HOL_Oord__class_Oless @ SY2145 @ ( c_HOL_Oplus__class_Oplus @ SY2146 @ SY2147 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SY2145 @ SY2147 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SY2146 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2422,plain,
! [SV281: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV281 @ SV281 @ tc_nat )
= SV281 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2423,plain,
! [SV282: $i] :
( ( ! [SY2148: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV282 ) @ SY2148 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV282 @ SY2148 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2424,plain,
! [SV283: $i] :
( ( ! [SY2149: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV283 @ ( c_Suc @ SY2149 ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV283 @ SY2149 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2425,plain,
! [SV284: $i] :
( ( ! [SY2150: $i,SY2151: $i,SY2152: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV284 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2150 @ SY2151 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SY2150 @ SY2152 @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SY2150 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SY2150 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SY2152 @ SY2151 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2426,plain,
! [SV285: $i] :
( ( ! [SY2153: $i] :
( ~ ( class_Divides_Osemiring__div @ SV285 )
| ( ( c_Divides_Odiv__class_Omod @ SY2153 @ ( c_HOL_Ozero__class_Ozero @ SV285 ) @ SV285 )
= SY2153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2427,plain,
! [SV286: $i] :
( ( ! [SY2154: $i] :
( ~ ( class_Divides_Osemiring__div @ SV286 )
| ( ( c_Divides_Odiv__class_Omod @ SY2154 @ SY2154 @ SV286 )
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2428,plain,
! [SV287: $i] :
( ( ! [SY2155: $i,SY2156: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2155 @ SY2156 @ SV287 )
= ( c_HOL_Oplus__class_Oplus @ SY2156 @ SY2155 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2429,plain,
! [SV288: $i] :
( ( ! [SY2157: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV288 @ SY2157 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SY2157 @ SV288 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2430,plain,
! [SV289: $i] :
( ( ! [SY2158: $i,SY2159: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV289 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2158 @ SY2159 @ SV289 )
= ( c_HOL_Oplus__class_Oplus @ SY2159 @ SY2158 @ SV289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2431,plain,
! [SV290: $i] :
( ( ! [SY2160: $i,SY2161: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2160 @ SY2161 @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SY2161 @ SY2160 @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2432,plain,
! [SV291: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV291 )
| ( c_lessequals @ SY2162 @ SY2163 @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SY2163 @ SV291 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2163 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2162 @ SV291 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2433,plain,
! [SV292: $i] :
( ( ! [SY2164: $i,SY2165: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV292 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2164 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2165 @ SV292 ) @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SY2165 @ SV292 )
| ~ ( c_lessequals @ SY2165 @ SY2164 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2434,plain,
! [SV293: $i] :
( ( ! [SY2166: $i,SY2167: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV293 )
| ( c_lessequals @ SY2166 @ SY2167 @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SY2166 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2167 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2166 @ SV293 ) @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2435,plain,
! [SV294: $i] :
( ( ! [SY2168: $i,SY2169: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV294 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2168 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2169 @ SV294 ) @ SV294 )
| ~ ( c_HOL_Oord__class_Oless @ SY2168 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
| ~ ( c_lessequals @ SY2169 @ SY2168 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2436,plain,
! [SV295: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV295 )
| ~ ( class_Power_Opower @ SV295 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV295 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV295 )
= ( c_HOL_Oone__class_Oone @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2437,plain,
! [SV296: $i] :
( ( ! [SY2170: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV296 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SY2170 @ SV296 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SY2170 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2438,plain,
! [SV297: $i] :
( ( ! [SY2171: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV297 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SY2171 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SY2171 @ SV297 ) @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2439,plain,
! [SV298: $i] :
( ( ! [SY2172: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV298 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SY2172 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SY2172 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2440,plain,
! [SV299: $i] :
( ( ! [SY2173: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV299 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
| ( c_HOL_Oord__class_Oless @ SY2173 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SY2173 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2441,plain,
! [SV300: $i] :
( ( ! [SY2174: $i,SY2175: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV300 )
| ( c_HOL_Oord__class_Oless @ SY2174 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SY2174 @ SY2175 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SY2174 @ SY2175 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2442,plain,
! [SV301: $i] :
( ( ! [SY2176: $i,SY2177: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SY2176 @ SY2177 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SY2177 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SY2176 @ SY2177 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2443,plain,
! [SV302: $i] :
( ( ! [SY2178: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV302 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2178 @ SV302 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV302 ) @ SY2178 @ SV302 ) )
| ( SY2178
= ( c_HOL_Ozero__class_Ozero @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2444,plain,
! [SV303: $i] :
( ( ! [SY2179: $i,SY2180: $i,SY2181: $i] :
( ~ ( class_Divides_Oring__div @ SV303 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2179 @ SY2180 @ SV303 ) @ SY2181 @ SV303 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2179 @ ( c_Divides_Odiv__class_Omod @ SY2180 @ SY2181 @ SV303 ) @ SV303 ) @ SY2181 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2445,plain,
! [SV304: $i] :
( ( ! [SY2182: $i,SY2183: $i,SY2184: $i] :
( ~ ( class_Divides_Oring__div @ SV304 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2182 @ SY2183 @ SV304 ) @ SY2184 @ SV304 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SY2182 @ SY2184 @ SV304 ) @ SY2183 @ SV304 ) @ SY2184 @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2446,plain,
! [SV305: $i] :
( ( ! [SY2185: $i,SY2186: $i,SY2187: $i] :
( ~ ( class_Divides_Oring__div @ SV305 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2185 @ SY2186 @ SV305 ) @ SY2187 @ SV305 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SY2185 @ SY2187 @ SV305 ) @ ( c_Divides_Odiv__class_Omod @ SY2186 @ SY2187 @ SV305 ) @ SV305 ) @ SY2187 @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2447,plain,
! [SV306: $i] :
( ( ! [SY2188: $i,SY2189: $i,SY2190: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2188 @ ( c_HOL_Ominus__class_Ominus @ SY2189 @ SY2190 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2188 @ SY2190 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2188 @ SY2189 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2448,plain,
! [SV307: $i] :
( ( ! [SY2191: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2191 @ SY2191 @ SV307 )
= ( c_HOL_Ozero__class_Ozero @ SV307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2449,plain,
! [SV308: $i] :
( ( ! [SY2192: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV308 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2192 @ SY2192 @ SV308 )
= ( c_HOL_Ozero__class_Ozero @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2450,plain,
! [SV309: $i] :
( ( ! [SY2193: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV309 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2193 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 )
= SY2193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2451,plain,
! [SV310: $i] :
( ( ! [SY2194: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV310 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2194 @ SY2194 @ SV310 )
= ( c_HOL_Ozero__class_Ozero @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2452,plain,
! [SV311: $i] :
( ( ! [SY2195: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV311 )
| ~ ( class_Int_Onumber__ring @ SV311 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2195 @ SY2195 @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2453,plain,
! [SV312: $i] :
( ( ! [SY2196: $i,SY2197: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV312 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2196 @ SY2197 @ SV312 ) @ SY2197 @ SV312 )
= SY2196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2454,plain,
! [SV313: $i] :
( ( ! [SY2198: $i,SY2199: $i,SY2200: $i,SY2201: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV313 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY2198 @ SY2199 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SY2200 @ SY2201 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2198 @ SY2200 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SY2199 @ SY2201 @ SV313 ) @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2455,plain,
! [SV314: $i] :
( ( ! [SY2202: $i,SY2203: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY2202 @ SY2203 @ SV314 ) @ SY2203 @ SV314 )
= SY2202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2456,plain,
! [SV315: $i] :
( ( ! [SY2204: $i,SY2205: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV315 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV315 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SY2204 @ SY2205 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SY2204 @ SV315 ) @ SY2205 @ SV315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2457,plain,
! [SV316: $i] :
( ( ! [SY2206: $i,SY2207: $i,SY2208: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY2206 @ SY2207 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SY2208 @ SY2207 @ SV316 ) @ SV316 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2206 @ SY2208 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2458,plain,
! [SV317: $i] :
( ( ! [SY2209: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV317 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV317 )
| ( ( c_HOL_Ozero__class_Ozero @ SV317 )
= ( c_HOL_Oinverse__class_Odivide @ SY2209 @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2459,plain,
! [SV318: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV318 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV318 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2460,plain,
! [SV319: $i] :
( ( ! [SY2210: $i,SY2211: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV319 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV319 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SY2210 @ SY2211 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SY2211 @ SY2210 @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2461,plain,
! [SV320: $i] :
( ( ! [SY2212: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV320 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ SY2212 @ SV320 )
= ( c_HOL_Ozero__class_Ozero @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2462,plain,
! [SV321: $i] :
( ( ! [SY2213: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV321 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV321 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2213 @ ( c_HOL_Ozero__class_Ozero @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2463,plain,
! [SV322: $i] :
( ( ! [SY2214: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV322 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV322 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2214 @ ( c_HOL_Ozero__class_Ozero @ SV322 ) @ SV322 )
= ( c_HOL_Ozero__class_Ozero @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2464,plain,
! [SV323: $i] :
( ( ! [SY2215: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SY2215 @ SV323 )
= ( c_HOL_Ozero__class_Ozero @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2465,plain,
! [SV324: $i] :
( ( ! [SY2216: $i,SY2217: $i,SY2218: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV324 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SY2216 @ SY2217 @ SV324 ) @ SY2218 @ SV324 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SY2216 @ SY2218 @ SV324 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2217 @ SY2218 @ SV324 ) @ SV324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2466,plain,
! [SV325: $i] :
( ( ! [SY2219: $i,SY2220: $i,SY2221: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV325 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SY2219 @ SY2220 @ SV325 ) @ SY2221 @ SV325 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SY2219 @ SY2221 @ SV325 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2220 @ SY2221 @ SV325 ) @ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2467,plain,
! [SV326: $i] :
( ( ! [SY2222: $i] :
( ( c_lessequals @ SV326 @ SY2222 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV326 ) @ ( c_Suc @ SY2222 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2468,plain,
! [SV327: $i] :
( ( ! [SY2223: $i] :
( ( c_lessequals @ ( c_Suc @ SV327 ) @ ( c_Suc @ SY2223 ) @ tc_nat )
| ~ ( c_lessequals @ SV327 @ SY2223 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2469,plain,
! [SV328: $i] :
( ( ~ ( c_lessequals @ ( c_Suc @ SV328 ) @ SV328 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2470,plain,
! [SV329: $i] :
( ( ! [SY2224: $i] :
( ( c_lessequals @ SV329 @ SY2224 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV329 ) @ SY2224 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2471,plain,
! [SV330: $i] :
( ( ! [SY2225: $i] :
( ( c_lessequals @ SV330 @ ( c_Suc @ SY2225 ) @ tc_nat )
| ~ ( c_lessequals @ SV330 @ SY2225 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2472,plain,
! [SV331: $i] :
( ( ! [SY2226: $i] :
( ( c_lessequals @ SV331 @ SY2226 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV331 @ SY2226 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2473,plain,
! [SV332: $i] :
( ( ! [SY2227: $i] :
( ( c_lessequals @ SV332 @ SY2227 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV332 @ SY2227 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2474,plain,
! [SV333: $i] :
( ( ! [SY2228: $i] : ( c_lessequals @ SV333 @ ( c_HOL_Oplus__class_Oplus @ SV333 @ SY2228 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2475,plain,
! [SV334: $i] :
( ( ! [SY2229: $i] : ( c_lessequals @ SV334 @ ( c_HOL_Oplus__class_Oplus @ SY2229 @ SV334 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2476,plain,
! [SV335: $i] :
( ( ! [SY2230: $i] : ( c_lessequals @ SV335 @ ( c_HOL_Oplus__class_Oplus @ SV335 @ SY2230 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2477,plain,
! [SV336: $i] :
( ( ! [SY2231: $i] : ( c_lessequals @ SV336 @ ( c_HOL_Oplus__class_Oplus @ SV336 @ SY2231 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2478,plain,
! [SV337: $i] :
( ( ! [SY2232: $i,SY2233: $i,SY2234: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SY2232 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2233 @ SY2234 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2232 @ SY2234 @ tc_nat )
| ~ ( c_lessequals @ SV337 @ SY2233 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2479,plain,
! [SV338: $i] :
( ( ! [SY2235: $i] :
( ( SV338
= ( c_Suc @ SY2235 ) )
| ( c_lessequals @ SV338 @ SY2235 @ tc_nat )
| ~ ( c_lessequals @ SV338 @ ( c_Suc @ SY2235 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2480,plain,
! [SV339: $i] :
( ( ! [SY2236: $i] :
( ( c_HOL_Oord__class_Oless @ SV339 @ SY2236 @ tc_nat )
| ( SV339 = SY2236 )
| ~ ( c_lessequals @ SV339 @ SY2236 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2481,plain,
! [SV340: $i] :
( ( ! [SY2237: $i] :
( ( SV340 = SY2237 )
| ( c_HOL_Oord__class_Oless @ SV340 @ SY2237 @ tc_nat )
| ~ ( c_lessequals @ SV340 @ SY2237 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2482,plain,
! [SV341: $i] :
( ( ! [SY2238: $i] :
( ( c_HOL_Oord__class_Oless @ SV341 @ SY2238 @ tc_nat )
| ( SV341 = SY2238 )
| ~ ( c_lessequals @ SV341 @ SY2238 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2483,plain,
! [SV342: $i] :
( ( ! [SY2239: $i,SY2240: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV342 @ SY2239 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2240 @ SY2239 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV342 @ SY2240 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2484,plain,
! [SV343: $i] :
( ( ! [SY2241: $i,SY2242: $i] :
( ( c_lessequals @ SV343 @ SY2241 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2242 @ SV343 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2242 @ SY2241 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2485,plain,
! [SV344: $i] :
( ( ! [SY2243: $i,SY2244: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SY2243 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SY2244 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2243 @ SY2244 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2486,plain,
! [SV345: $i] :
( ( ( SV345
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV345 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2487,plain,
! [SV346: $i] :
( ( ! [SY2245: $i,SY2246: $i] :
( ( c_lessequals @ SV346 @ ( c_HOL_Oplus__class_Oplus @ SY2245 @ SY2246 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV346 @ SY2245 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2488,plain,
! [SV347: $i] :
( ( ! [SY2247: $i,SY2248: $i] :
( ( c_lessequals @ SV347 @ ( c_HOL_Oplus__class_Oplus @ SY2247 @ SY2248 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV347 @ SY2248 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2489,plain,
! [SV348: $i] :
( ( ! [SY2249: $i,SY2250: $i] :
( ( c_lessequals @ SV348 @ SY2249 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV348 @ SY2250 @ tc_nat ) @ SY2249 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2490,plain,
! [SV349: $i] :
( ( ! [SY2251: $i,SY2252: $i] :
( ( c_lessequals @ SV349 @ SY2251 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2252 @ SV349 @ tc_nat ) @ SY2251 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2491,plain,
! [SV350: $i] :
( ( ! [SY2253: $i,SY2254: $i] :
( ( c_lessequals @ SV350 @ ( c_HOL_Oplus__class_Oplus @ SY2253 @ SY2254 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SY2253 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2492,plain,
! [SV351: $i] :
( ( ! [SY2255: $i,SY2256: $i] :
( ( c_lessequals @ SV351 @ ( c_HOL_Oplus__class_Oplus @ SY2255 @ SY2256 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV351 @ SY2256 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2493,plain,
! [SV352: $i] :
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV352 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2494,plain,
! [SV353: $i] :
( ( ! [SY2257: $i] :
( ( c_lessequals @ ( c_Suc @ SV353 ) @ SY2257 @ tc_nat )
| ( c_lessequals @ SY2257 @ SV353 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2495,plain,
! [SV354: $i] :
( ( ! [SY2258: $i] :
( ~ ( c_lessequals @ SV354 @ SY2258 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SY2258 ) @ SV354 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2496,plain,
! [SV355: $i] :
( ( ! [SY2259: $i] : ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV355 @ SY2259 @ tc_nat ) @ SV355 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2497,plain,
! [SV356: $i] :
( ( c_lessequals @ ( c_Suc @ SV356 ) @ ( c_Suc @ SV356 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2498,plain,
! [SV357: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV357 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SY2260 @ SY2261 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV357 @ SY2261 @ tc_nat ) @ ( c_Suc @ SY2260 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2261 @ SY2260 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2499,plain,
! [SV358: $i] :
( ( ! [SY2262: $i,SY2263: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SY2262 @ tc_nat ) ) @ SY2263 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV358 ) @ ( c_HOL_Oplus__class_Oplus @ SY2262 @ SY2263 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2262 @ SV358 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2500,plain,
! [SV359: $i] :
( ( ! [SY2264: $i,SY2265: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SY2264 @ tc_nat ) @ SY2265 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SY2265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2501,plain,
! [SV360: $i] :
( ( ! [SY2266: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV360 ) @ ( c_Suc @ SY2266 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV360 @ SY2266 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2502,plain,
! [SV361: $i] :
( ( ! [SY2267: $i,SY2268: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SY2267 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SY2268 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2268 @ SV361 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2268 @ SY2267 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2503,plain,
! [SV362: $i] :
( ( ! [SY2269: $i,SY2270: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV362 @ SY2269 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV362 @ SY2270 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SY2269 @ SY2270 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2504,plain,
! [SV363: $i] :
( ( ! [SY2271: $i,SY2272: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV363 @ SY2271 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2272 @ SY2271 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV363 @ SY2272 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2505,plain,
! [SV364: $i] :
( ( ! [SY2273: $i,SY2274: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV364 ) @ SY2273 @ tc_nat ) @ ( c_Suc @ SY2274 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV364 @ SY2273 @ tc_nat ) @ SY2274 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2506,plain,
! [SV365: $i] :
( ( ! [SY2275: $i,SY2276: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SY2275 @ SY2276 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SY2276 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SY2275 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2507,plain,
! [SV366: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV366 @ SV366 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2508,plain,
! [SV367: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV367 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV367 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2509,plain,
! [SV368: $i] :
( ( ! [SY2277: $i,SY2278: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV368 @ SY2277 @ tc_nat ) @ SY2278 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV368 @ ( c_HOL_Oplus__class_Oplus @ SY2277 @ SY2278 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2510,plain,
! [SV369: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV369 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2511,plain,
! [SV370: $i] :
( ( ! [SY2279: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV370 @ SY2279 @ tc_nat ) @ SV370 @ tc_nat )
= SY2279 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2512,plain,
! [SV371: $i] :
( ( ! [SY2280: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV371 @ SY2280 @ tc_nat ) @ SY2280 @ tc_nat )
= SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2513,plain,
! [SV372: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV372 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2514,plain,
! [SV373: $i] :
( ( ! [SY2281: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV373 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( c_lessequals @ SY2281 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2281 @ SV373 ) @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2515,plain,
! [SV374: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV374 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ ( c_HOL_Oone__class_Oone @ SV374 ) @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2516,plain,
! [SV375: $i] :
( ( ! [SY2282: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV375 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2282 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SY2282 @ SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2517,plain,
! [SV376: $i] :
( ( ! [SY2283: $i,SY2284: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV376 )
| ( c_lessequals @ SY2283 @ SY2284 @ SV376 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2283 @ SY2284 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2518,plain,
! [SV377: $i] :
( ( ! [SY2285: $i,SY2286: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV377 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2285 @ SY2286 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
| ~ ( c_lessequals @ SY2285 @ SY2286 @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2519,plain,
! [SV378: $i] :
( ( ! [SY2287: $i,SY2288: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV378 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SY2287 @ SY2288 @ SV378 ) @ SV378 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SY2287 @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2520,plain,
! [SV379: $i] :
( ( ! [SY2289: $i,SY2290: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV379 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SY2289 @ SY2290 @ SV379 ) @ SV379 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SY2289 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2521,plain,
! [SV380: $i] :
( ( ! [SY2291: $i,SY2292: $i,SY2293: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV380 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2291 @ SY2292 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SY2293 @ SY2292 @ SV380 ) @ SV380 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SY2291 @ SV380 )
| ~ ( c_lessequals @ SY2291 @ SY2293 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2522,plain,
! [SV381: $i] :
( ( ! [SY2294: $i,SY2295: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV381 )
| ( SY2294
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
| ( c_lessequals @ SY2294 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2294 @ SY2295 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2523,plain,
! [SV382: $i] :
( ( ! [SY2296: $i,SY2297: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV382 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2296 @ SY2297 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SY2297 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SY2296 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2524,plain,
! [SV383: $i] :
( ( ! [SY2298: $i,SY2299: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV383 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2298 @ SY2299 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SY2299 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SY2298 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2525,plain,
! [SV384: $i] :
( ( ! [SY2300: $i,SY2301: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV384 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SY2300 @ SY2301 @ SV384 ) @ SV384 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SY2300 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2526,plain,
! [SV385: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV385 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV385 ) @ ( c_HOL_Ozero__class_Ozero @ SV385 ) @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2527,plain,
! [SV386: $i] :
( ( ! [SY2302: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV386 @ SY2302 @ tc_nat ) @ tc_nat )
| ( SY2302
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2528,plain,
! [SV387: $i] :
( ( ! [SY2303: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV387 @ SY2303 @ tc_nat ) @ tc_nat )
| ( SV387
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2529,plain,
! [SV388: $i] :
( ( ! [SY2304: $i,SY2305: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV388 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SY2304 @ SY2305 @ SV388 ) @ SV388 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SY2304 @ SV388 ) @ SY2305 @ SV388 ) )
| ( SY2304
= ( c_HOL_Ozero__class_Ozero @ SV388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2530,plain,
! [SV389: $i] :
( ( ! [SY2306: $i,SY2307: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV389 @ ( c_GCD_Ogcd__class_Ogcd @ SY2306 @ SY2307 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY2306 @ ( c_GCD_Ogcd__class_Ogcd @ SV389 @ SY2307 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2531,plain,
! [SV390: $i] :
( ( ! [SY2308: $i,SY2309: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV390 @ SY2308 @ tc_nat ) @ SY2309 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV390 @ ( c_GCD_Ogcd__class_Ogcd @ SY2308 @ SY2309 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2532,plain,
! [SV391: $i] :
( ( ! [SY2310: $i,SY2311: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV391 @ SY2310 @ tc_nat ) @ SY2311 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV391 @ ( c_GCD_Ogcd__class_Ogcd @ SY2310 @ SY2311 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2533,plain,
! [SV392: $i] :
( ( ! [SY2312: $i] :
( ( SV392 = SY2312 )
| ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SY2312 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV392 @ SY2312 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2534,plain,
! [SV393: $i] :
( ( ! [SY2313: $i] :
( ( SV393 = SY2313 )
| ~ ( c_HOL_Oord__class_Oless @ SY2313 @ ( c_Suc @ SV393 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2313 @ SV393 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2535,plain,
! [SV394: $i] :
( ( ! [SY2314: $i] :
( ( SV394 = SY2314 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SY2314 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ ( c_Suc @ SY2314 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2536,plain,
! [SV395: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV395 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2537,plain,
! [SV396: $i] :
( ( ! [SY2315: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV396 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2315 @ ( c_HOL_Ozero__class_Ozero @ SV396 ) @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2538,plain,
! [SV397: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV397 @ ( 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)],[1839]) ).
thf(2539,plain,
! [SV398: $i] :
( ( ! [SY2316: $i] :
( ~ ( class_Divides_Osemiring__div @ SV398 )
| ( ( c_Divides_Odiv__class_Omod @ SY2316 @ ( c_HOL_Oone__class_Oone @ SV398 ) @ SV398 )
= ( c_HOL_Ozero__class_Ozero @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2540,plain,
! [SV399: $i] :
( ( ! [SY2317: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ ( c_HOL_Oplus__class_Oplus @ SY2317 @ SV399 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ SY2317 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2541,plain,
! [SV400: $i] :
( ( ! [SY2318: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ SY2318 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ ( c_HOL_Oplus__class_Oplus @ SY2318 @ SV400 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2542,plain,
! [SV401: $i] :
( ( ! [SY2319: $i] :
( ~ ( class_Orderings_Oorder @ SV401 )
| ~ ( c_HOL_Oord__class_Oless @ SY2319 @ SY2319 @ SV401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2543,plain,
! [SV402: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV402 @ SV402 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2544,plain,
! [SV403: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV403 @ SV403 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2545,plain,
! [SV404: $i] :
( ( ! [SY2320: $i] :
( ~ ( class_Orderings_Olinorder @ SV404 )
| ~ ( c_HOL_Oord__class_Oless @ SY2320 @ SY2320 @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2546,plain,
! [SV405: $i] :
( ( ! [SY2321: $i] :
( ~ ( class_Orderings_Opreorder @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SY2321 @ SY2321 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2547,plain,
! [SV406: $i] :
( ( ! [SY2322: $i,SY2323: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SY2322 @ SY2323 @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SY2323 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SY2322 @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2548,plain,
! [SV407: $i] :
( ( ! [SY2324: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV407 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
| ( c_HOL_Oord__class_Oless @ SY2324 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2324 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2549,plain,
! [SV408: $i] :
( ( ! [SY2325: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV408 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2325 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ SY2325 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2550,plain,
! [SV409: $i] :
( ( ! [SY2326: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV409 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2326 @ SV409 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ SY2326 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2551,plain,
! [SV410: $i] :
( ( ! [SY2327: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SY2327 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2327 @ SV410 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2327 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2552,plain,
! [SV411: $i] :
( ( ! [SY2328: $i,SY2329: $i,SY2330: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SY2328 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2329 @ SY2330 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2328 @ SY2330 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SY2329 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2553,plain,
! [SV412: $i] :
( ( ! [SY2331: $i,SY2332: $i,SY2333: $i,SY2334: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2331 @ SY2332 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SY2333 @ SY2334 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SY2332 @ SY2334 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SY2331 @ SY2333 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2554,plain,
! [SV413: $i] :
( ( ! [SY2335: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV413 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2335 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SY2335 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SY2335 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2555,plain,
! [SV414: $i] :
( ( ! [SY2336: $i,SY2337: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY2336 @ SY2337 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ SY2336 @ SY2337 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2556,plain,
! [SV415: $i] :
( ( ! [SY2338: $i,SY2339: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
| ( c_HOL_Oord__class_Oless @ SY2338 @ SY2339 @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY2338 @ SY2339 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2557,plain,
! [SV416: $i] :
( ( ! [SY2340: $i,SY2341: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 )
| ( c_HOL_Oord__class_Oless @ SY2340 @ SY2341 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2340 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2341 @ SV416 ) @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2558,plain,
! [SV417: $i] :
( ( ! [SY2342: $i,SY2343: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2342 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2343 @ SV417 ) @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SY2342 @ SY2343 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2559,plain,
! [SV418: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV418 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ ( c_HOL_Oone__class_Oone @ SV418 ) @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2560,plain,
! [SV419: $i] :
( ( ! [SY2344: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV419 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2344 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2344 @ SV419 ) @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2561,plain,
! [SV420: $i] :
( ( ! [SY2345: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV420 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV420 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2345 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2345 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2562,plain,
! [SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV421 @ tc_nat )
| ( SV421
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2563,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)],[1869]) ).
thf(2564,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2565,plain,
! [SV422: $i] :
( ( ! [SY2346: $i,SY2347: $i,SY2348: $i] :
( ~ ( class_Divides_Osemiring__div @ SV422 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SY2346 @ SY2347 @ SV422 ) @ SY2348 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SY2346 @ SY2348 @ SV422 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2348 @ SY2347 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2566,plain,
! [SV423: $i] :
( ( ! [SY2349: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV423 )
| ( c_lessequals @ SY2349 @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2349 @ SY2349 @ SV423 ) @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2567,plain,
! [SV424: $i] :
( ( ! [SY2350: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV424 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2350 @ SY2350 @ SV424 ) @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
| ~ ( c_lessequals @ SY2350 @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2568,plain,
! [SV425: $i] :
( ( ! [SY2351: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV425 @ SY2351 @ tc_nat ) @ SY2351 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2569,plain,
! [SV426: $i] :
( ( ! [SY2352: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV426 @ SY2352 @ tc_nat ) @ SV426 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2570,plain,
! [SV427: $i] :
( ( ! [SY2353: $i,SY2354: $i] :
( ( c_HOL_Oord__class_Oless @ SV427 @ ( c_HOL_Ominus__class_Ominus @ SY2353 @ SY2354 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV427 @ SY2354 @ tc_nat ) @ SY2353 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2571,plain,
! [SV428: $i] :
( ( ! [SY2355: $i,SY2356: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV428 @ SY2355 @ tc_nat ) @ SY2356 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV428 @ ( c_HOL_Ominus__class_Ominus @ SY2356 @ SY2355 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2572,plain,
! [SV429: $i] :
( ( ! [SY2357: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV429 @ SY2357 @ tc_nat )
= SY2357 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2357 @ SV429 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2573,plain,
! [SV430: $i] :
( ( ! [SY2358: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV430 @ SY2358 @ tc_nat )
= SV430 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV430 @ SY2358 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2574,plain,
! [SV431: $i] :
( ( ! [SY2359: $i] :
( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV431 ) @ SY2359 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV431 @ SY2359 @ tc_nat ) ) @ SY2359 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2575,plain,
! [SV432: $i] :
( ( ! [SY2360: $i,SY2361: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV432 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2360 @ SY2361 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SY2361 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ SY2360 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2576,plain,
! [SV433: $i] :
( ( ! [SY2362: $i,SY2363: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV433 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2362 @ SY2363 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ SY2363 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SY2362 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2577,plain,
! [SV434: $i] :
( ( ! [SY2364: $i,SY2365: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV434 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2364 @ SY2365 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SY2365 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SY2364 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2578,plain,
! [SV435: $i] :
( ( ! [SY2366: $i,SY2367: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV435 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2366 @ SY2367 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SY2367 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SY2366 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2579,plain,
! [SV436: $i] :
( ( ! [SY2368: $i,SY2369: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2368 @ ( c_Power_Opower__class_Opower @ SY2368 @ SY2369 @ SV436 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2369 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2580,plain,
! [SV437: $i] :
( ( ! [SY2370: $i,SY2371: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SY2370 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2371 @ SY2370 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV437 @ SY2371 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2581,plain,
! [SV438: $i] :
( ( ! [SY2372: $i,SY2373: $i] :
( ( c_HOL_Oord__class_Oless @ SV438 @ SY2372 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2373 @ SV438 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2373 @ SY2372 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2582,plain,
! [SV439: $i] :
( ( ! [SY2374: $i,SY2375: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SY2374 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SY2375 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2374 @ SY2375 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2583,plain,
! [SV440: $i] :
( ( ! [SY2376: $i,SY2377: $i,SY2378: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
| ( c_HOL_Oord__class_Oless @ SY2376 @ SY2377 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2378 @ SY2376 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SY2378 @ SY2377 @ SV440 ) @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2584,plain,
! [SV441: $i] :
( ( ! [SY2379: $i,SY2380: $i,SY2381: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2379 @ SY2380 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SY2379 @ SY2381 @ SV441 ) @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SY2380 @ SY2381 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2585,plain,
! [SV442: $i] :
( ( ! [SY2382: $i,SY2383: $i,SY2384: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2382 @ SY2383 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SY2382 @ SY2384 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SY2383 @ SY2384 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2586,plain,
! [SV443: $i] :
( ( ! [SY2385: $i,SY2386: $i,SY2387: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
| ( c_HOL_Oord__class_Oless @ SY2385 @ SY2386 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2385 @ SY2387 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SY2386 @ SY2387 @ SV443 ) @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2587,plain,
! [SV444: $i] :
( ( ! [SY2388: $i,SY2389: $i,SY2390: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2388 @ SY2389 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SY2390 @ SY2389 @ SV444 ) @ SV444 )
| ~ ( c_HOL_Oord__class_Oless @ SY2388 @ SY2390 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2588,plain,
! [SV445: $i] :
( ( ! [SY2391: $i,SY2392: $i,SY2393: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY2391 @ SY2392 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SY2393 @ SY2392 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SY2391 @ SY2393 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2589,plain,
! [SV446: $i] :
( ( ! [SY2394: $i,SY2395: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2394 @ SY2395 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SY2395 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SY2394 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2590,plain,
! [SV447: $i] :
( ( ! [SY2396: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV447 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2396 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SY2396 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2591,plain,
! [SV448: $i] :
( ( ! [SY2397: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV448 @ SY2397 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY2397 @ SV448 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2592,plain,
! [SV449: $i] :
( ( ! [SY2398: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV449 @ SY2398 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY2398 @ SV449 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2593,plain,
! [SV450: $i] :
( ( ! [SY2399: $i] :
( ( SV450 = SY2399 )
| ~ ( c_HOL_Oord__class_Oless @ SV450 @ ( c_Suc @ SY2399 ) @ tc_nat )
| ~ ( c_lessequals @ SY2399 @ SV450 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2594,plain,
! [SV451: $i] :
( ( ! [SY2400: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV451 @ SY2400 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY2400 @ ( c_Divides_Odiv__class_Omod @ SV451 @ SY2400 @ tc_nat ) @ tc_nat ) )
| ( SY2400
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2595,plain,
! [SV452: $i] :
( ( ! [SY2401: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV452 @ SY2401 @ tc_nat ) @ SV452 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV452 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2401 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2596,plain,
! [SV453: $i] :
( ( ! [SY2402: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV453 @ ( c_HOL_Ominus__class_Ominus @ SY2402 @ SV453 @ tc_nat ) @ tc_nat )
= SY2402 )
| ( c_HOL_Oord__class_Oless @ SY2402 @ SV453 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2597,plain,
! [SV454: $i] :
( ( ! [SY2403: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV454 @ ( c_Suc @ SY2403 ) @ tc_nat ) @ SV454 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV454 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2598,plain,
! [SV455: $i] :
( ( ! [SY2404: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV455 @ ( c_GCD_Ogcd__class_Ogcd @ SV455 @ SY2404 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV455 @ SY2404 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2599,plain,
! [SV456: $i] :
( ( ! [SY2405: $i] :
( ( c_lessequals @ SV456 @ SY2405 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2405 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV456 @ SY2405 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2600,plain,
! [SV457: $i] :
( ( ! [SY2406: $i,SY2407: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV457 @ SY2406 @ tc_nat ) @ SY2407 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2407 @ SV457 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV457 @ SY2407 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2601,plain,
! [SV458: $i] :
( ( ! [SY2408: $i,SY2409: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV458 @ SY2408 @ tc_nat ) @ SY2409 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2409 @ SY2408 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2408 @ SY2409 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2602,plain,
! [SV459: $i] :
( ( ! [SY2410: $i,SY2411: $i] :
( ~ ( class_Orderings_Opreorder @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SY2410 @ SY2411 @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SY2411 @ SY2410 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2603,plain,
! [SV460: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SY2412 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2413 @ SY2412 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2413 @ SV460 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SY2413 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2604,plain,
! [SV461: $i] :
( ( ! [SY2414: $i,SY2415: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SY2414 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2414 @ SY2415 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2415 @ SY2414 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SY2415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2605,plain,
! [SV462: $i] :
( ( ! [SY2416: $i,SY2417: $i] :
( ~ ( class_Orderings_Opreorder @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SY2416 @ SY2417 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SY2417 @ SY2416 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2606,plain,
! [SV463: $i] :
( ( ! [SY2418: $i,SY2419: $i] :
( ~ ( class_Orderings_Olinorder @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SY2418 @ SY2419 @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SY2419 @ SY2418 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2607,plain,
! [SV464: $i] :
( ( ! [SY2420: $i,SY2421: $i] :
( ~ ( class_Orderings_Oorder @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SY2420 @ SY2421 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SY2421 @ SY2420 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2608,plain,
! [SV465: $i] :
( ( ! [SY2422: $i,SY2423: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV465 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SY2422 @ SV465 )
| ( c_lessequals @ SY2422 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2423 @ SY2422 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2609,plain,
! [SV466: $i] :
( ( ! [SY2424: $i,SY2425: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV466 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
| ( c_lessequals @ SY2424 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SY2425 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2424 @ SY2425 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2610,plain,
! [SV467: $i] :
( ( ! [SY2426: $i,SY2427: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV467 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SY2426 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SY2427 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2427 @ SY2426 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2611,plain,
! [SV468: $i] :
( ( ! [SY2428: $i,SY2429: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV468 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
| ( c_lessequals @ SY2428 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SY2428 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2428 @ SY2429 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2612,plain,
! [SV469: $i] :
( ( ! [SY2430: $i,SY2431: $i,SY2432: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV469 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2430 @ SY2431 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2432 @ SY2431 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SY2431 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SY2432 @ SY2430 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2613,plain,
! [SV470: $i] :
( ( ! [SY2433: $i,SY2434: $i,SY2435: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV470 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2433 @ SY2434 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2435 @ SY2434 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SY2434 @ SV470 )
| ~ ( c_lessequals @ SY2433 @ SY2435 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2614,plain,
! [SV471: $i] :
( ( ! [SY2436: $i,SY2437: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV471 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2436 @ SY2437 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SY2437 @ SV471 )
| ~ ( c_lessequals @ SY2436 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2615,plain,
! [SV472: $i] :
( ( ! [SY2438: $i,SY2439: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV472 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2438 @ SY2439 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SY2439 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SY2438 @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2616,plain,
! [SV473: $i] :
( ( ! [SY2440: $i,SY2441: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV473 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
| ( c_lessequals @ SY2440 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SY2440 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2441 @ SY2440 @ SV473 ) @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2617,plain,
! [SV474: $i] :
( ( ! [SY2442: $i,SY2443: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV474 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
| ( c_lessequals @ SY2442 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SY2443 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2442 @ SY2443 @ SV474 ) @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2618,plain,
! [SV475: $i] :
( ( ! [SY2444: $i,SY2445: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV475 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
| ( c_lessequals @ SY2444 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SY2445 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2445 @ SY2444 @ SV475 ) @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2619,plain,
! [SV476: $i] :
( ( ! [SY2446: $i,SY2447: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV476 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
| ( c_lessequals @ SY2446 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SY2446 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2446 @ SY2447 @ SV476 ) @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2620,plain,
! [SV477: $i] :
( ( ! [SY2448: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV477 )
| ( ( c_Power_Opower__class_Opower @ SY2448 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV477 )
= ( c_HOL_Oone__class_Oone @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2621,plain,
! [SV478: $i] :
( ( ! [SY2449: $i] :
( ~ ( class_Power_Opower @ SV478 )
| ( ( c_Power_Opower__class_Opower @ SY2449 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV478 )
= ( c_HOL_Oone__class_Oone @ SV478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2622,plain,
! [SV479: $i] :
( ( ! [SY2450: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV479 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV479 ) @ SY2450 @ SV479 ) @ SV479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2623,plain,
! [SV480: $i] :
( ( ! [SY2451: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV480 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2451 @ SV480 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV480 ) @ SY2451 @ SV480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2624,plain,
! [SV481: $i] :
( ( ! [SY2452: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV481 )
| ~ ( class_Int_Onumber__ring @ SV481 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2452 @ SV481 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV481 ) @ SY2452 @ SV481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2625,plain,
! [SV482: $i] :
( ( ! [SY2453: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV482 )
| ( SY2453
= ( c_HOL_Ozero__class_Ozero @ SV482 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2453 @ SY2453 @ SV482 )
= ( c_HOL_Oone__class_Oone @ SV482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2626,plain,
! [SV483: $i] :
( ( ! [SY2454: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV483 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2454 @ SY2454 @ SV483 )
= ( c_HOL_Oone__class_Oone @ SV483 ) )
| ( SY2454
= ( c_HOL_Ozero__class_Ozero @ SV483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2627,plain,
! [SV484: $i] :
( ( ! [SY2455: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV484 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV484 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2455 @ SY2455 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
| ( SY2455
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2628,plain,
! [SV485: $i] :
( ( ! [SY2456: $i,SY2457: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV485 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2456 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2457 @ SV485 ) @ SV485 )
| ~ ( c_lessequals @ SY2456 @ SY2457 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2629,plain,
! [SV486: $i] :
( ( ! [SY2458: $i,SY2459: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV486 )
| ( c_lessequals @ SY2458 @ SY2459 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2458 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2459 @ SV486 ) @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2630,plain,
! [SV487: $i] :
( ( ! [SY2460: $i,SY2461: $i] :
( ~ ( class_SEQ_Obanach @ SV487 )
| ~ ( class_RealVector_Oreal__normed__field @ SV487 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SY2460 @ SY2461 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SY2460 @ SV487 ) @ ( c_Transcendental_Oexp @ SY2461 @ SV487 ) @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2631,plain,
! [SV488: $i] :
( ( ! [SY2462: $i,SY2463: $i,SY2464: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SY2462 @ SY2463 @ SV488 ) @ SY2464 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SY2462 @ SY2464 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SY2463 @ SY2464 @ SV488 ) @ SV488 ) )
| ( SY2463
= ( c_HOL_Ozero__class_Ozero @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2632,plain,
! [SV489: $i] :
( ( ! [SY2465: $i,SY2466: $i,SY2467: $i,SY2468: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY2465 @ SY2466 @ SV489 ) @ SY2467 @ SV489 )
| ~ ( c_lessequals @ SY2466 @ SY2468 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY2465 @ SY2468 @ SV489 ) @ SY2467 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2633,plain,
! [SV490: $i] :
( ( ! [SY2469: $i,SY2470: $i,SY2471: $i,SY2472: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY2469 @ SY2470 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SY2471 @ SY2472 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SY2470 @ SY2472 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2469 @ SY2471 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2634,plain,
! [SV491: $i] :
( ( ! [SY2473: $i,SY2474: $i,SY2475: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SY2473 @ SY2474 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SY2473 @ SY2475 @ SV491 ) @ SV491 )
| ~ ( c_lessequals @ SY2474 @ SY2475 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2635,plain,
! [SV492: $i] :
( ( ! [SY2476: $i,SY2477: $i,SY2478: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV492 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SY2476 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SY2477 @ SY2478 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SY2476 @ SY2478 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SY2476 @ SY2477 @ SV492 ) @ SV492 ) )
| ~ ( c_lessequals @ SY2478 @ SY2477 @ tc_nat )
| ( SY2476
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2636,plain,
! [SV493: $i] :
( ( ! [SY2479: $i,SY2480: $i] :
( ( c_HOL_Oord__class_Oless @ SV493 @ SY2479 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SY2480 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2479 @ SY2480 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2480 @ SY2479 @ tc_nat )
| ~ ( c_lessequals @ SY2480 @ SV493 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2637,plain,
! [SV494: $i] :
( ( ! [SY2481: $i,SY2482: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SY2481 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2482 @ SY2481 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ SY2482 @ tc_nat )
| ~ ( c_lessequals @ SY2481 @ SY2482 @ tc_nat )
| ~ ( c_lessequals @ SY2481 @ SV494 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2638,plain,
! [SV495: $i] :
( ( ! [SY2483: $i,SY2484: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV495 @ ( c_HOL_Ominus__class_Ominus @ SY2483 @ SY2484 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV495 @ SY2483 @ tc_nat ) @ SY2484 @ tc_nat ) )
| ~ ( c_lessequals @ SY2484 @ SY2483 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2639,plain,
! [SV496: $i] :
( ( ! [SY2485: $i,SY2486: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV496 @ SY2485 @ tc_nat ) @ SY2486 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV496 @ SY2486 @ tc_nat ) @ SY2485 @ tc_nat ) )
| ~ ( c_lessequals @ SY2485 @ SV496 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2640,plain,
! [SV497: $i] :
( ( ! [SY2487: $i] :
( ~ ( c_lessequals @ SV497 @ SY2487 @ tc_nat )
| ( SY2487
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SY2487 @ SV497 @ tc_nat ) @ SV497 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2641,plain,
! [SV498: $i] :
( ( ! [SY2488: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV498 @ ( c_HOL_Ominus__class_Ominus @ SY2488 @ SV498 @ tc_nat ) @ tc_nat )
= SY2488 )
| ~ ( c_lessequals @ SV498 @ SY2488 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2642,plain,
! [SV499: $i] :
( ( ! [SY2489: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV499 @ SY2489 @ tc_nat ) @ SY2489 @ tc_nat )
= SV499 )
| ~ ( c_lessequals @ SY2489 @ SV499 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2643,plain,
! [SV500: $i] :
( ( ! [SY2490: $i] :
( ~ ( c_lessequals @ SV500 @ ( c_HOL_Oplus__class_Oplus @ SY2490 @ SV500 @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY2490 @ SV500 @ tc_nat ) @ SV500 @ tc_nat )
= SY2490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2644,plain,
! [SV501: $i] :
( ( ! [SY2491: $i,SY2492: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV501 @ ( c_HOL_Ominus__class_Ominus @ SY2491 @ SY2492 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SY2492 @ tc_nat ) @ SY2491 @ tc_nat ) )
| ~ ( c_lessequals @ SY2492 @ SY2491 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2645,plain,
! [SV502: $i] :
( ( ! [SY2493: $i,SY2494: $i] :
( ( c_lessequals @ SV502 @ ( c_HOL_Oplus__class_Oplus @ SY2493 @ SY2494 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV502 @ SY2494 @ tc_nat ) @ SY2493 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2646,plain,
! [SV503: $i] :
( ( ! [SY2495: $i,SY2496: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV503 @ SY2495 @ tc_nat ) @ SY2496 @ tc_nat )
| ~ ( c_lessequals @ SV503 @ ( c_HOL_Oplus__class_Oplus @ SY2496 @ SY2495 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2647,plain,
! [SV504: $i] :
( ( ! [SY2497: $i,SY2498: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SY2497 @ tc_nat )
| ~ ( c_lessequals @ SY2498 @ SY2497 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SY2498 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SY2497 @ SY2498 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2648,plain,
! [SV505: $i] :
( ( ! [SY2499: $i,SY2500: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SY2499 @ tc_nat )
| ~ ( c_lessequals @ SY2499 @ SY2500 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SY2500 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SY2500 @ SY2499 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2649,plain,
! [SV506: $i] :
( ( ! [SY2501: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV506 @ SY2501 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV506 @ SY2501 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2650,plain,
! [SV507: $i] :
( ( ! [SY2502: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV507 @ SY2502 @ tc_nat ) @ SY2502 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV507 @ SY2502 @ tc_nat ) )
| ~ ( c_lessequals @ SY2502 @ SV507 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2651,plain,
! [SV508: $i] :
( ( ! [SY2503: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV508 @ SY2503 @ tc_nat ) @ SV508 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SY2503 @ SV508 @ tc_nat ) )
| ~ ( c_lessequals @ SY2503 @ SV508 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2652,plain,
! [SV509: $i] :
( ( ! [SY2504: $i,SY2505: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV509 @ SY2504 @ tc_nat ) @ SY2505 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ominus__class_Ominus @ SY2504 @ SY2505 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2505 @ SY2504 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2653,plain,
! [SV510: $i] :
( ( ! [SY2506: $i,SY2507: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV510 @ SY2506 @ tc_nat ) @ SY2507 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV510 @ SY2507 @ tc_nat ) @ SY2506 @ tc_nat ) )
| ~ ( c_lessequals @ SY2507 @ SV510 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2654,plain,
! [SV511: $i] :
( ( ! [SY2508: $i] :
( ( ( c_Divides_Odiv__class_Omod @ SV511 @ SY2508 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV511 @ SY2508 @ tc_nat ) @ SY2508 @ tc_nat ) )
| ~ ( c_lessequals @ SY2508 @ SV511 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2655,plain,
! [SV512: $i] :
( ( ! [SY2509: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV512 ) @ SY2509 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV512 @ SY2509 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY2509 @ SV512 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2656,plain,
! [SV513: $i] :
( ( ! [SY2510: $i,SY2511: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SY2510 @ tc_nat ) @ SY2511 @ tc_nat )
| ~ ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SY2511 @ SY2510 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2510 @ SY2511 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2657,plain,
! [SV514: $i] :
( ( ! [SY2512: $i,SY2513: $i] :
( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SY2512 @ SY2513 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SY2513 @ tc_nat ) @ SY2512 @ tc_nat )
| ~ ( c_lessequals @ SY2513 @ SY2512 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2658,plain,
! [SV515: $i] :
( ( ! [SY2514: $i,SY2515: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SY2514 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2515 @ SY2514 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2514 @ SV515 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV515 @ SY2515 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2659,plain,
! [SV516: $i] :
( ( ! [SY2516: $i,SY2517: $i] :
( ( c_lessequals @ SV516 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SY2516 @ SV516 @ tc_nat ) @ SY2517 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2517 @ SY2516 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2660,plain,
! [SV517: $i] :
( ( ! [SY2518: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV517 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SY2518 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
| ~ ( c_lessequals @ SY2518 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2661,plain,
! [SV518: $i] :
( ( ! [SY2519: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV518 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
| ( c_lessequals @ SY2519 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SY2519 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2662,plain,
! [SV519: $i] :
( ( ! [SY2520: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV519 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SY2520 @ SV519 ) @ SV519 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SY2520 @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2663,plain,
! [SV520: $i] :
( ( ! [SY2521: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV520 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SY2521 @ SV520 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SY2521 @ SV520 ) @ SV520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2664,plain,
! [SV521: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV521 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SY2522 @ SY2523 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2522 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2523 @ SV521 ) @ SV521 ) )
| ~ ( c_lessequals @ SY2523 @ SY2522 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2665,plain,
! [SV522: $i] :
( ( ! [SY2524: $i,SY2525: $i,SY2526: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV522 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2524 @ SY2525 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SY2524 @ SY2526 @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ SY2524 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SY2524 @ SV522 )
| ~ ( c_lessequals @ SY2526 @ SY2525 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2666,plain,
! [SV523: $i] :
( ( ! [SY2527: $i,SY2528: $i,SY2529: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV523 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2527 @ SY2528 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SY2527 @ SY2529 @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SY2528 @ SY2529 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SY2527 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2667,plain,
! [SV524: $i] :
( ( ! [SY2530: $i,SY2531: $i,SY2532: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV524 )
| ( c_lessequals @ SY2530 @ SY2531 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2532 @ SY2530 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SY2532 @ SY2531 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SY2532 @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2668,plain,
! [SV525: $i] :
( ( ! [SY2533: $i,SY2534: $i,SY2535: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV525 )
| ( c_lessequals @ SY2533 @ SY2534 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2535 @ SY2533 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SY2535 @ SY2534 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SY2535 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2669,plain,
! [SV526: $i] :
( ( ! [SY2536: $i,SY2537: $i,SY2538: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV526 )
| ( ( c_Power_Opower__class_Opower @ SY2536 @ ( c_HOL_Ominus__class_Ominus @ SY2537 @ SY2538 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SY2536 @ SY2537 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SY2536 @ SY2538 @ SV526 ) @ SV526 ) )
| ~ ( c_lessequals @ SY2538 @ SY2537 @ tc_nat )
| ( SY2536
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2670,plain,
! [SV527: $i] :
( ( ! [SY2539: $i] :
( ( c_lessequals @ SV527 @ SY2539 @ tc_nat )
| ( c_lessequals @ SY2539 @ SV527 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2671,plain,
! [SV528: $i] :
( ( ! [SY2540: $i,SY2541: $i] :
( ~ ( class_Orderings_Olinorder @ SV528 )
| ( c_lessequals @ SY2540 @ SY2541 @ SV528 )
| ( c_lessequals @ SY2541 @ SY2540 @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2672,plain,
! [SV529: $i] :
( ( ! [SY2542: $i,SY2543: $i,SY2544: $i] :
( ~ ( class_Orderings_Oorder @ SV529 )
| ( c_lessequals @ SY2542 @ SY2543 @ SV529 )
| ~ ( c_lessequals @ SY2542 @ SY2544 @ SV529 )
| ~ ( c_lessequals @ SY2544 @ SY2543 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2673,plain,
! [SV530: $i] :
( ( ! [SY2545: $i,SY2546: $i,SY2547: $i] :
( ~ ( class_Orderings_Opreorder @ SV530 )
| ( c_lessequals @ SY2545 @ SY2546 @ SV530 )
| ~ ( c_lessequals @ SY2547 @ SY2546 @ SV530 )
| ~ ( c_lessequals @ SY2545 @ SY2547 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2674,plain,
! [SV531: $i] :
( ( c_lessequals @ SV531 @ SV531 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2675,plain,
! [SV532: $i] :
( ( ! [SY2548: $i,SY2549: $i] :
( ( c_lessequals @ SV532 @ SY2548 @ tc_nat )
| ~ ( c_lessequals @ SY2549 @ SY2548 @ tc_nat )
| ~ ( c_lessequals @ SV532 @ SY2549 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2676,plain,
! [SV533: $i] :
( ( c_lessequals @ SV533 @ SV533 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2677,plain,
! [SV534: $i] :
( ( ! [SY2550: $i] :
( ~ ( class_Orderings_Oorder @ SV534 )
| ( c_lessequals @ SY2550 @ SY2550 @ SV534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2678,plain,
! [SV535: $i] :
( ( ! [SY2551: $i] :
( ~ ( class_Orderings_Opreorder @ SV535 )
| ( c_lessequals @ SY2551 @ SY2551 @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2679,plain,
! [SV536: $i] :
( ( ! [SY2552: $i,SY2553: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SY2552 @ SY2553 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SY2552 @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2680,plain,
! [SV537: $i] :
( ( ! [SY2554: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV537 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV537 ) @ SY2554 @ SV537 )
= ( c_HOL_Oone__class_Oone @ SV537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2681,plain,
! [SV538: $i] :
( ( ! [SY2555: $i,SY2556: $i,SY2557: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV538 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2555 @ SY2556 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SY2555 @ SY2557 @ SV538 ) @ SV538 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SY2555 @ SV538 )
| ~ ( c_lessequals @ SY2556 @ SY2557 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2682,plain,
! [SV539: $i] :
( ( ! [SY2558: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV539 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2558 @ ( c_HOL_Oone__class_Oone @ SV539 ) @ SV539 )
= SY2558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2683,plain,
! [SV540: $i] :
( ( ! [SY2559: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV540 @ SY2559 @ tc_nat ) @ tc_nat )
= SY2559 )
| ~ ( c_lessequals @ SY2559 @ SV540 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2684,plain,
! [SV541: $i] :
( ( ! [SY2560: $i,SY2561: $i] :
( ~ ( class_Orderings_Oorder @ SV541 )
| ( SY2560 = SY2561 )
| ~ ( c_lessequals @ SY2560 @ SY2561 @ SV541 )
| ~ ( c_lessequals @ SY2561 @ SY2560 @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2685,plain,
! [SV542: $i] :
( ( ! [SY2562: $i] :
( ( SV542 = SY2562 )
| ~ ( c_lessequals @ SY2562 @ SV542 @ tc_nat )
| ~ ( c_lessequals @ SV542 @ SY2562 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2686,plain,
! [SV543: $i] :
( ( ! [SY2563: $i,SY2564: $i] :
( ~ ( class_Orderings_Oorder @ SV543 )
| ( SY2563 = SY2564 )
| ~ ( c_lessequals @ SY2564 @ SY2563 @ SV543 )
| ~ ( c_lessequals @ SY2563 @ SY2564 @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2687,plain,
! [SV544: $i] :
( ( ! [SY2565: $i,SY2566: $i] :
( ~ ( class_Orderings_Oorder @ SV544 )
| ( SY2565 = SY2566 )
| ~ ( c_lessequals @ SY2566 @ SY2565 @ SV544 )
| ~ ( c_lessequals @ SY2565 @ SY2566 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2688,plain,
! [SV545: $i] :
( ( ! [SY2567: $i,SY2568: $i,SY2569: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV545 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SY2567 @ SY2568 @ SV545 ) @ SY2569 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SY2567 @ SY2569 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SY2568 @ SY2569 @ SV545 ) @ SV545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2689,plain,
! [SV546: $i] :
( ( ! [SY2570: $i,SY2571: $i,SY2572: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV546 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SY2570 @ SY2571 @ SV546 ) @ SY2572 @ SV546 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SY2570 @ SY2572 @ SV546 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2571 @ SY2572 @ SV546 ) @ SV546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2690,plain,
! [SV547: $i] :
( ( ! [SY2573: $i,SY2574: $i,SY2575: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV547 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SY2573 @ SY2574 @ SV547 ) @ SY2575 @ SV547 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SY2573 @ SY2575 @ SV547 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2574 @ SY2575 @ SV547 ) @ SV547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2691,plain,
! [SV548: $i] :
( ( ! [SY2576: $i,SY2577: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV548 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV548 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SY2576 @ SY2577 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SY2576 @ SV548 ) @ SY2577 @ SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2692,plain,
! [SV549: $i] :
( ( ! [SY2578: $i,SY2579: $i] :
( ( c_lessequals @ SV549 @ SY2578 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SY2579 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2578 @ SY2579 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2579 @ SY2578 @ tc_nat )
| ~ ( c_lessequals @ SY2579 @ SV549 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2693,plain,
! [SV550: $i] :
( ( ! [SY2580: $i,SY2581: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SY2580 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2581 @ SY2580 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV550 @ SY2581 @ tc_nat )
| ~ ( c_lessequals @ SY2580 @ SY2581 @ tc_nat )
| ~ ( c_lessequals @ SY2580 @ SV550 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2694,plain,
! [SV551: $i] :
( ( ! [SY2582: $i,SY2583: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV551 @ SY2582 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2583 @ SY2582 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV551 @ SY2583 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2695,plain,
! [SV552: $i] :
( ( ! [SY2584: $i,SY2585: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SY2584 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SY2585 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2585 @ SY2584 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2696,plain,
! [SV553: $i] :
( ( ! [SY2586: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV553 @ SY2586 @ tc_nat ) @ SV553 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2697,plain,
! [SV554: $i] :
( ( ! [SY2587: $i,SY2588: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV554 @ SY2587 @ tc_nat ) @ SY2588 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV554 @ SY2588 @ tc_nat ) @ SY2587 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2698,plain,
! [SV555: $i] :
( ( ! [SY2589: $i,SY2590: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SY2589 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2590 @ SY2589 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SY2590 @ tc_nat ) )
| ~ ( c_lessequals @ SY2589 @ SY2590 @ tc_nat )
| ~ ( c_lessequals @ SY2589 @ SV555 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2699,plain,
! [SV556: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV556 )
| ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2700,plain,
! [SV557: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV557 )
| ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2701,plain,
! [SV558: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV558 )
| ( class_OrderedGroup_Ocancel__semigroup__add @ SV558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2702,plain,
! [SV559: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV559 )
| ( class_Ring__and__Field_Ono__zero__divisors @ SV559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2703,plain,
! [SV560: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV560 )
| ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2704,plain,
! [SV561: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV561 )
| ( class_OrderedGroup_Oab__semigroup__add @ SV561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2705,plain,
! [SV562: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV562 )
| ( class_Ring__and__Field_Odivision__ring @ SV562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2706,plain,
! [SV563: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV563 )
| ( class_OrderedGroup_Ocomm__monoid__add @ SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2707,plain,
! [SV564: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV564 )
| ( class_Ring__and__Field_Ozero__neq__one @ SV564 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2708,plain,
! [SV565: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV565 )
| ( class_Ring__and__Field_Ocomm__ring__1 @ SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2709,plain,
! [SV566: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV566 )
| ( class_Ring__and__Field_Osemiring__1 @ SV566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2710,plain,
! [SV567: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV567 )
| ( class_Ring__and__Field_Osemiring__0 @ SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2711,plain,
! [SV568: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV568 )
| ( class_OrderedGroup_Oab__group__add @ SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2712,plain,
! [SV569: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV569 )
| ( class_Ring__and__Field_Omult__zero @ SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2713,plain,
! [SV570: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV570 )
| ( class_OrderedGroup_Omonoid__mult @ SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2714,plain,
! [SV571: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV571 )
| ( class_OrderedGroup_Omonoid__add @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2715,plain,
! [SV572: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV572 )
| ( class_OrderedGroup_Ogroup__add @ SV572 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2716,plain,
! [SV573: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV573 )
| ( class_Ring__and__Field_Oring__1 @ SV573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2717,plain,
! [SV574: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV574 )
| ( class_Ring__and__Field_Oidom @ SV574 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2718,plain,
! [SV575: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV575 )
| ( class_Power_Opower @ SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2719,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2720,plain,
! [SV576: $i] :
( ( ! [SY2591: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV576 @ SY2591 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV576
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2721,plain,
! [SV577: $i] :
( ( ! [SY2592: $i,SY2593: $i,SY2594: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2592 @ SY2593 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SY2592 @ SY2594 @ SV577 ) )
| ( SY2593 = SY2594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2722,plain,
! [SV578: $i] :
( ( ! [SY2595: $i,SY2596: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 )
| ( ( c_Power_Opower__class_Opower @ SY2595 @ SY2596 @ SV578 )
!= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
| ( SY2595
= ( c_HOL_Ozero__class_Ozero @ SV578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2723,plain,
! [SV579: $i] :
( ( ! [SY2597: $i,SY2598: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV579 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2597 @ SY2598 @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
| ( SY2597 = SY2598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2724,plain,
! [SV580: $i] :
( ( ! [SY2599: $i] :
( ( ( c_Suc @ SV580 )
!= ( c_Suc @ SY2599 ) )
| ( SV580 = SY2599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2725,plain,
! [SV581: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV581 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2726,plain,
! [SV582: $i] :
( ( ! [SY2600: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SY2600 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV582
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2727,plain,
! [SV583: $i] :
( ( ! [SY2601: $i] :
( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV583 @ SY2601 @ tc_nat ) )
!= SY2601 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV583 ) @ SY2601 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2728,plain,
! [SV584: $i] :
( ( ! [SY2602: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV584 @ SY2602 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY2602
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY2602
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2729,plain,
! [SV585: $i] :
( ( SV585
!= ( c_Suc @ SV585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2730,plain,
! [SV586: $i] :
( ( ! [SY2603: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV586 @ SY2603 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2603
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2731,plain,
! [SV587: $i] :
( ( ! [SY2604: $i] :
( ~ ( class_SEQ_Obanach @ SV587 )
| ~ ( class_RealVector_Oreal__normed__field @ SV587 )
| ( ( c_Transcendental_Oexp @ SY2604 @ SV587 )
!= ( c_HOL_Ozero__class_Ozero @ SV587 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2732,plain,
! [SV588: $i] :
( ( ! [SY2605: $i,SY2606: $i,SY2607: $i,SY2608: $i,SY2609: $i] :
( ~ ( class_Divides_Osemiring__div @ SV588 )
| ( ( c_Divides_Odiv__class_Omod @ SY2605 @ SY2606 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY2607 @ SY2606 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2608 @ SY2606 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY2609 @ SY2606 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2608 @ SY2605 @ SV588 ) @ SY2606 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY2609 @ SY2607 @ SV588 ) @ SY2606 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2733,plain,
! [SV589: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2734,plain,
! [SV590: $i] :
( ( ! [SY2610: $i,SY2611: $i,SY2612: $i,SY2613: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2610 @ SY2611 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SY2612 @ SY2613 @ SV590 ) )
| ( c_lessequals @ SY2613 @ SY2612 @ SV590 )
| ~ ( c_lessequals @ SY2611 @ SY2610 @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2735,plain,
! [SV591: $i] :
( ( ! [SY2614: $i] :
( ( SV591
!= ( c_HOL_Oplus__class_Oplus @ SV591 @ SY2614 @ tc_nat ) )
| ( SY2614
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2736,plain,
! [SV592: $i] :
( ( ! [SY2615: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV592 @ SY2615 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2615
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2737,plain,
! [SV593: $i] :
( ( ! [SY2616: $i,SY2617: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV593 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2616 @ SV593 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY2617 @ SV593 ) )
| ( SY2616 = SY2617 )
| ( SY2617
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SY2616
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2738,plain,
! [SV594: $i] :
( ( ! [SY2618: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV594 @ SY2618 @ tc_nat ) )
| ( SY2618
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY2618
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2739,plain,
! [SV595: $i] :
( ( ! [SY2619: $i,SY2620: $i,SY2621: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2619 @ SY2620 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SY2621 @ SY2620 @ SV595 ) )
| ( SY2619 = SY2621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2740,plain,
! [SV596: $i] :
( ( ! [SY2622: $i,SY2623: $i,SY2624: $i,SY2625: $i,SY2626: $i] :
( ~ ( class_Divides_Oring__div @ SV596 )
| ( ( c_Divides_Odiv__class_Omod @ SY2622 @ SY2623 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY2624 @ SY2623 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY2625 @ SY2623 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY2626 @ SY2623 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2625 @ SY2622 @ SV596 ) @ SY2623 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY2626 @ SY2624 @ SV596 ) @ SY2623 @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2741,plain,
! [SV597: $i] :
( ( ! [SY2627: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV597 @ SY2627 @ tc_nat )
!= SV597 )
| ( SY2627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2742,plain,
! [SV598: $i] :
( ( ! [SY2628: $i,SY2629: $i,SY2630: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV598 )
| ( ( c_Power_Opower__class_Opower @ SY2628 @ SY2629 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SY2630 @ SY2629 @ SV598 ) )
| ( SY2628 = SY2630 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2629 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SY2630 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SY2628 @ SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2743,plain,
! [SV599: $i] :
( ( ! [SY2631: $i,SY2632: $i,SY2633: $i,SY2634: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2631 @ SY2632 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SY2633 @ SY2634 @ SV599 ) )
| ( c_lessequals @ SY2632 @ SY2631 @ SV599 )
| ~ ( c_lessequals @ SY2634 @ SY2633 @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2744,plain,
! [SV600: $i] :
( ( ! [SY2635: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV600 @ SY2635 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV600
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2745,plain,
! [SV601: $i] :
( ( ! [SY2636: $i,SY2637: $i,SY2638: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SY2636 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY2637 @ SY2638 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2637 @ SY2636 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV601 @ SY2638 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2746,plain,
! [SV602: $i] :
( ( ! [SY2639: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV602 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2639 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
| ( SY2639
= ( c_HOL_Oone__class_Oone @ SV602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2747,plain,
! [SV603: $i] :
( ( ! [SY2640: $i,SY2641: $i,SY2642: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV603 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2640 @ SY2640 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SY2641 @ SY2642 @ SV603 ) )
| ( SY2641 = SY2642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2748,plain,
! [SV604: $i] :
( ( ! [SY2643: $i,SY2644: $i,SY2645: $i,SY2646: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV604 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2643 @ ( c_HOL_Oplus__class_Oplus @ SY2644 @ SY2645 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SY2644 @ SY2646 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SY2643 @ SY2645 @ SV604 )
= SY2646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2749,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2750,plain,
! [SV605: $i] :
( ( ! [SY2647: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV605 @ SY2647 @ tc_nat ) )
| ( SV605
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV605
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2751,plain,
! [SV606: $i] :
( ( ! [SY2648: $i,SY2649: $i] :
( ~ ( class_Divides_Osemiring__div @ SV606 )
| ( ( c_Divides_Odiv__class_Omod @ SY2648 @ SY2649 @ SV606 )
!= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2649 @ SY2648 @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2752,plain,
! [SV607: $i] :
( ( ! [SY2650: $i,SY2651: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV607 @ SY2650 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV607 @ SY2651 @ tc_nat ) )
| ( SY2650 = SY2651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2753,plain,
! [SV608: $i] :
( ( ! [SY2652: $i,SY2653: $i,SY2654: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2652 @ SY2653 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SY2652 @ SY2654 @ SV608 ) )
| ( SY2653 = SY2654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2754,plain,
! [SV609: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV609 )
| ( ( c_HOL_Oone__class_Oone @ SV609 )
!= ( c_HOL_Ozero__class_Ozero @ SV609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2755,plain,
! [SV610: $i] :
( ( ! [SY2655: $i,SY2656: $i,SY2657: $i,SY2658: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2655 @ SY2656 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SY2657 @ SY2658 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SY2657 @ SY2658 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SY2655 @ SY2656 @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2756,plain,
! [SV611: $i] :
( ( ! [SY2659: $i,SY2660: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV611 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2659 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY2660 @ SV611 ) )
| ( SY2659 = SY2660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2757,plain,
! [SV612: $i] :
( ( ! [SY2661: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV612 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2661 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SY2661
= ( c_HOL_Ozero__class_Ozero @ SV612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2758,plain,
( ( ( ~ ( class_Ring__and__Field_Ofield @ t_a ) )
= $true )
| ( ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2759,plain,
! [SV613: $i] :
( ( ! [SY2662: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV613 @ SY2662 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY2662 @ SV613 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2662 = SV613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2760,plain,
! [SV614: $i] :
( ( ! [SY2663: $i,SY2664: $i,SY2665: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV614 )
| ( ( c_Power_Opower__class_Opower @ SY2663 @ SY2664 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SY2663 @ SY2665 @ SV614 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SY2663 @ SV614 )
| ( SY2664 = SY2665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2761,plain,
! [SV615: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV615 )
| ( ( c_HOL_Ozero__class_Ozero @ SV615 )
!= ( c_HOL_Oone__class_Oone @ SV615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2762,plain,
! [SV616: $i] :
( ( ! [SY2666: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ SY2666 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV616 @ SY2666 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2763,plain,
! [SV617: $i] :
( ( ! [SY2667: $i,SY2668: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV617 )
| ~ ( class_Int_Onumber__ring @ SV617 )
| ( SY2667
!= ( c_HOL_Oplus__class_Oplus @ SY2667 @ SY2668 @ SV617 ) )
| ( SY2668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2764,plain,
! [SV618: $i] :
( ( ! [SY2669: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV618 @ SY2669 @ tc_nat ) )
| ( SY2669
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV618
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2765,plain,
! [SV619: $i] :
( ( ! [SY2670: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV619 @ SY2670 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2670
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2766,plain,
! [SV620: $i] :
( ( ! [SY2671: $i,SY2672: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV620 )
| ~ ( class_Int_Onumber__ring @ SV620 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2671 @ SY2672 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SY2671 = SY2672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2767,plain,
! [SV621: $i] :
( ( ( c_Suc @ SV621 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2768,plain,
! [SV622: $i] :
( ( ! [SY2673: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV622 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2673 @ SY2673 @ SV622 )
!= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
| ( SY2673
= ( c_HOL_Ozero__class_Ozero @ SV622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2769,plain,
! [SV623: $i] :
( ( ! [SY2674: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV623 @ SY2674 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SY2674
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2770,plain,
! [SV624: $i] :
( ( ! [SY2675: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV624 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SY2675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SY2675
= ( c_HOL_Ozero__class_Ozero @ SV624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2771,plain,
! [SV625: $i] :
( ( ! [SY2676: $i,SY2677: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV625 @ SY2676 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY2677 @ SY2676 @ tc_nat ) )
| ( SV625 = SY2677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2772,plain,
! [SV626: $i] :
( ( ( c_Suc @ SV626 )
!= SV626 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2773,plain,
( ( ( ~ ( class_Ring__and__Field_Ofield @ t_a ) )
= $true )
| ( ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2774,plain,
! [SV627: $i] :
( ( ! [SY2678: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV627 @ SY2678 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2775,plain,
! [SV628: $i] :
( ( ! [SY2679: $i,SY2680: $i,SY2681: $i,SY2682: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2679 @ SY2680 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SY2681 @ SY2682 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SY2679 @ SY2680 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SY2681 @ SY2682 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2776,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
= $true )
| ( ( ~ ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2777,plain,
! [SV629: $i] :
( ( ! [SY2683: $i] :
( ( ( c_Suc @ SV629 )
!= ( c_Suc @ SY2683 ) )
| ( SV629 = SY2683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2778,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
= $true )
| ( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2779,plain,
! [SV630: $i] :
( ( ! [SY2684: $i,SY2685: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV630 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2684 @ SY2685 @ SV630 )
!= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
| ( SY2684 = SY2685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2780,plain,
! [SV631: $i] :
( ( ! [SY2686: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV631 @ SY2686 @ tc_nat )
!= SV631 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV631 @ SY2686 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2781,plain,
! [SV632: $i] :
( ( ! [SY2687: $i,SY2688: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2687 @ SY2688 @ SV632 )
!= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SY2688 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SY2687 @ SV632 )
| ( SY2688
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2782,plain,
! [SV633: $i] :
( ( ! [SY2689: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV633 )
| ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SY2689 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2783,plain,
! [SV634: $i] :
( ( ! [SY2690: $i,SY2691: $i,SY2692: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV634 )
| ~ ( class_Int_Onumber__ring @ SV634 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2690 @ SY2691 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SY2690 @ SY2692 @ SV634 ) )
| ( SY2691 = SY2692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2784,plain,
! [SV635: $i] :
( ( ! [SY2693: $i,SY2694: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SY2693 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY2694 @ SY2693 @ tc_nat ) )
| ~ ( c_lessequals @ SY2693 @ SY2694 @ tc_nat )
| ~ ( c_lessequals @ SY2693 @ SV635 @ tc_nat )
| ( SV635 = SY2694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2785,plain,
! [SV636: $i] :
( ( ! [SY2695: $i,SY2696: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV636 @ SY2695 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV636 @ SY2696 @ tc_nat ) )
| ( SY2695 = SY2696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2786,plain,
! [SV637: $i] :
( ( ! [SY2697: $i,SY2698: $i,SY2699: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV637 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2697 @ SY2698 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SY2699 @ SY2699 @ SV637 ) )
| ( SY2697 = SY2698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2787,plain,
! [SV638: $i] :
( ( ! [SY2700: $i,SY2701: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
| ( ( c_HOL_Oplus__class_Oplus @ SY2700 @ SY2701 @ SV638 )
!= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SY2701 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SY2700 @ SV638 )
| ( SY2700
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2788,plain,
! [SV639: $i] :
( ( ! [SY2702: $i,SY2703: $i,SY2704: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SY2702 @ ( c_Suc @ SY2703 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SY2704 @ ( c_Suc @ SY2703 ) @ SV639 ) )
| ( SY2702 = SY2704 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SY2704 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SY2702 @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2789,plain,
! [SV640: $i] :
( ( ! [SY2705: $i] :
( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV640 @ SY2705 @ tc_nat ) )
| ( SV640
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2705
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2790,plain,
! [SV641: $i] :
( ( ! [SY2706: $i,SY2707: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SY2706 @ SY2707 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SY2706
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2791,plain,
! [SV642: $i] :
( ( ( c_Suc @ SV642 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2792,plain,
! [SV643: $i] :
( ( ! [SY2708: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV643 @ SY2708 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY2708
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2793,plain,
! [SV644: $i] :
( ( ! [SY2709: $i,SY2710: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV644 )
| ( ( c_HOL_Oinverse__class_Odivide @ SY2709 @ SY2710 @ SV644 )
!= ( c_HOL_Oone__class_Oone @ SV644 ) )
| ( SY2710
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SY2709 = SY2710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2794,plain,
! [SV645: $i] :
( ( ! [SY2711: $i,SY2712: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV645 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY2711 @ SV645 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY2712 @ SV645 ) )
| ( SY2711 = SY2712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2795,plain,
! [SV646: $i,SV1: $i] :
( ( ! [SY2713: $i,SY2714: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV1 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV646 @ SY2713 @ SV1 ) @ SY2714 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV646 @ ( c_HOL_Oplus__class_Oplus @ SY2713 @ SY2714 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2796,plain,
! [SV647: $i,SV2: $i] :
( ( ! [SY2715: $i,SY2716: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Oplus__class_Oplus @ SV647 @ ( c_HOL_Oplus__class_Oplus @ SY2715 @ SY2716 @ SV2 ) @ SV2 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV647 @ SY2715 @ SV2 ) @ SY2716 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2797,plain,
! [SV648: $i,SV3: $i] :
( ( ! [SY2717: $i,SY2718: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV3 )
| ( ( c_HOL_Oplus__class_Oplus @ SV648 @ ( c_HOL_Oplus__class_Oplus @ SY2717 @ SY2718 @ SV3 ) @ SV3 )
= ( c_HOL_Oplus__class_Oplus @ SY2717 @ ( c_HOL_Oplus__class_Oplus @ SV648 @ SY2718 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2798,plain,
! [SV649: $i,SV4: $i] :
( ( ! [SY2719: $i] :
( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV4 @ SV649 @ tc_nat ) @ SY2719 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV4 @ ( c_HOL_Oplus__class_Oplus @ SV649 @ SY2719 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2799,plain,
! [SV650: $i,SV5: $i] :
( ( ! [SY2720: $i] :
( ( c_HOL_Oplus__class_Oplus @ SV5 @ ( c_HOL_Oplus__class_Oplus @ SV650 @ SY2720 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV650 @ ( c_HOL_Oplus__class_Oplus @ SV5 @ SY2720 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2800,plain,
! [SV651: $i,SV6: $i] :
( ( ! [SY2721: $i,SY2722: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV6 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SY2721 @ SV6 ) @ SY2722 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ SV651 @ ( c_HOL_Oplus__class_Oplus @ SY2721 @ SY2722 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2801,plain,
! [SV652: $i,SV7: $i] :
( ( ! [SY2723: $i,SY2724: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
| ( ( c_HOL_Oplus__class_Oplus @ SV652 @ ( c_HOL_Oplus__class_Oplus @ SY2723 @ SY2724 @ SV7 ) @ SV7 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV652 @ SY2723 @ SV7 ) @ SY2724 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2802,plain,
! [SV653: $i,SV8: $i] :
( ( ! [SY2725: $i,SY2726: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV8 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SY2725 @ SV8 ) @ SY2726 @ SV8 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SY2726 @ SV8 ) @ SY2725 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2803,plain,
! [SV654: $i,SV9: $i] :
( ( ! [SY2727: $i,SY2728: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( c_HOL_Oplus__class_Oplus @ SV654 @ ( c_HOL_Oplus__class_Oplus @ SY2727 @ SY2728 @ SV9 ) @ SV9 )
= ( c_HOL_Oplus__class_Oplus @ SY2727 @ ( c_HOL_Oplus__class_Oplus @ SV654 @ SY2728 @ SV9 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2804,plain,
! [SV655: $i,SV10: $i] :
( ( ! [SY2729: $i,SY2730: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV10 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV655 @ SY2729 @ SV10 ) @ SY2730 @ SV10 )
= ( c_HOL_Oplus__class_Oplus @ SV655 @ ( c_HOL_Oplus__class_Oplus @ SY2729 @ SY2730 @ SV10 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2805,plain,
! [SV656: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV11 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV656 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV656 @ SV11 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2806,plain,
! [SV657: $i,SV13: $i] :
( ( ! [SY2731: $i,SY2732: $i] :
( ~ ( class_Divides_Osemiring__div @ SV13 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ SY2731 @ SV13 ) @ SY2732 @ SV13 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ ( c_Divides_Odiv__class_Omod @ SY2731 @ SY2732 @ SV13 ) @ SV13 ) @ SY2732 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2807,plain,
! [SV658: $i,SV14: $i] :
( ( ! [SY2733: $i,SY2734: $i] :
( ~ ( class_Divides_Osemiring__div @ SV14 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV658 @ SY2733 @ SV14 ) @ SY2734 @ SV14 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV658 @ SY2734 @ SV14 ) @ SY2733 @ SV14 ) @ SY2734 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2808,plain,
! [SV659: $i,SV15: $i] :
( ( ! [SY2735: $i,SY2736: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SY2735 @ SY2736 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SY2736 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SY2735 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2809,plain,
! [SV660: $i,SV16: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV16 @ ( c_HOL_Oplus__class_Oplus @ SV16 @ SV660 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2810,plain,
! [SV661: $i,SV17: $i] :
( ( ! [SY2737: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 )
| ( c_HOL_Oord__class_Oless @ SV661 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV661 @ SY2737 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2811,plain,
! [SV18: $i] :
( ( ( SV18
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV18
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV18 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2812,plain,
! [SV662: $i,SV21: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV21 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2813,plain,
! [SV663: $i,SV22: $i] :
( ( ! [SY2738: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV22 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SY2738 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2738 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2814,plain,
! [SV664: $i,SV23: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Oplus__class_Oplus @ SV23 @ SV664 @ tc_nat ) @ SV664 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV23 @ SV664 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2815,plain,
! [SV665: $i,SV24: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV24 @ ( c_HOL_Oplus__class_Oplus @ SV24 @ SV665 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV24 @ SV665 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2816,plain,
! [SV666: $i,SV25: $i] :
( ( ! [SY2739: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SY2739 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY2739 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2817,plain,
! [SV667: $i,SV26: $i] :
( ( ! [SY2740: $i,SY2741: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SY2740 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SY2741 @ SY2740 @ SV26 ) @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2740 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SY2741 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2818,plain,
! [SV668: $i,SV27: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV27 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
| ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2819,plain,
! [SV669: $i,SV28: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV28 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2820,plain,
! [SV670: $i,SV29: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV29 ) @ SV670 @ tc_nat )
| ( ( c_Suc @ SV29 )
= SV670 )
| ~ ( c_HOL_Oord__class_Oless @ SV29 @ SV670 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2821,plain,
! [SV671: $i,SV30: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV30 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
| ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2822,plain,
! [SV672: $i,SV31: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV31 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV672 @ SV31 ) @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV672 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2823,plain,
! [SV673: $i,SV32: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV32 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2824,plain,
! [SV674: $i,SV33: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV33 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2825,plain,
! [SV675: $i,SV34: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV34 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV675 @ SV34 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2826,plain,
! [SV676: $i,SV35: $i] :
( ( ! [SY2742: $i,SY2743: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SV676 @ ( c_HOL_Oplus__class_Oplus @ SY2742 @ SY2743 @ SV35 ) @ SV35 )
= ( c_HOL_Oplus__class_Oplus @ SY2742 @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SY2743 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2827,plain,
! [SV677: $i,SV36: $i] :
( ( ! [SY2744: $i,SY2745: $i] :
( ~ ( class_Orderings_Opreorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV677 @ SY2744 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY2745 @ SY2744 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY2745 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2828,plain,
! [SV678: $i,SV37: $i] :
( ( ! [SY2746: $i,SY2747: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SV678 @ SY2746 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SY2747 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SY2747 @ SY2746 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2829,plain,
! [SV679: $i,SV38: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV38 )
| ( SV679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV679 @ SV38 ) @ SV38 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2830,plain,
! [SV680: $i,SV39: $i] :
( ( ! [SY2748: $i,SY2749: $i] :
( ~ ( class_Divides_Osemiring__div @ SV39 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SY2748 @ SV39 ) @ SY2749 @ SV39 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV680 @ SY2749 @ SV39 ) @ ( c_Divides_Odiv__class_Omod @ SY2748 @ SY2749 @ SV39 ) @ SV39 ) @ SY2749 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2831,plain,
! [SV40: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV40 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2832,plain,
! [SV41: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2833,plain,
! [SV681: $i,SV42: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV42 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV42 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV42 ) @ SV42 )
= SV681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2834,plain,
! [SV682: $i,SV43: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV43 ) @ SV682 @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV43 @ SV682 @ tc_nat ) ) )
| ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV43 @ SV682 @ tc_nat ) )
= SV682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2835,plain,
! [SV44: $i] :
( ( ( SV44
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV44 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2185]) ).
thf(2836,plain,
! [SV683: $i,SV45: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV45 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ SV683 @ SV45 )
= ( c_HOL_Ozero__class_Ozero @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2837,plain,
! [SV684: $i,SV46: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV46 )
| ~ ( class_Power_Opower @ SV46 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Suc @ SV684 ) @ SV46 )
= ( c_HOL_Ozero__class_Ozero @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2838,plain,
! [SV685: $i,SV47: $i] :
( ( c_HOL_Oord__class_Oless @ SV47 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV47 @ SV685 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2839,plain,
! [SV686: $i,SV48: $i] :
( ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV686 @ SV48 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2840,plain,
! [SV687: $i,SV49: $i] :
( ( c_HOL_Oord__class_Oless @ SV49 @ ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV49 @ SV687 @ tc_nat ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2841,plain,
! [SV688: $i,SV50: $i] :
( ( ! [SY2750: $i,SY2751: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SY2750 @ SY2751 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SY2751 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SY2750 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2842,plain,
! [SV689: $i,SV51: $i] :
( ( ! [SY2752: $i,SY2753: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
| ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SY2752 @ SY2753 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SY2752 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SY2753 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2843,plain,
! [SV690: $i,SV52: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV52 @ SV690 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV52 ) @ SV690 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2844,plain,
! [SV691: $i,SV53: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV53 ) @ SV691 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV53 @ SV691 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2845,plain,
! [SV692: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV692 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV54 ) @ SV692 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2846,plain,
! [SV693: $i,SV55: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV55 ) @ SV693 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV55 @ SV693 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2847,plain,
! [SV694: $i,SV56: $i] :
( ( ! [SY2754: $i] :
( ( c_HOL_Oord__class_Oless @ SV56 @ ( c_HOL_Oplus__class_Oplus @ SV694 @ SY2754 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SY2754 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2848,plain,
! [SV695: $i,SV57: $i] :
( ( ! [SY2755: $i] :
( ( c_HOL_Oord__class_Oless @ SV57 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SY2755 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV695 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2849,plain,
! [SV696: $i,SV58: $i] :
( ( ! [SY2756: $i] :
( ( c_HOL_Oord__class_Oless @ SV58 @ SV696 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV58 @ SY2756 @ tc_nat ) @ SV696 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2850,plain,
! [SV697: $i,SV59: $i] :
( ( ! [SY2757: $i] :
( ( c_HOL_Oord__class_Oless @ SV59 @ ( c_HOL_Oplus__class_Oplus @ SV697 @ SY2757 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SY2757 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2851,plain,
! [SV698: $i,SV60: $i] :
( ( ! [SY2758: $i] :
( ( c_HOL_Oord__class_Oless @ SV60 @ ( c_HOL_Oplus__class_Oplus @ SV698 @ SY2758 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV60 @ SV698 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2852,plain,
! [SV699: $i,SV61: $i] :
( ( ! [SY2759: $i,SY2760: $i] :
( ~ ( class_Divides_Osemiring__div @ SV61 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SY2759 @ SY2760 @ SV61 ) @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SY2760 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SY2759 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2853,plain,
! [SV700: $i,SV62: $i] :
( ( ! [SY2761: $i,SY2762: $i] :
( ~ ( class_Divides_Osemiring__div @ SV62 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SY2761 @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SY2761 @ SY2762 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SY2762 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2854,plain,
! [SV701: $i,SV63: $i] :
( ( ! [SY2763: $i,SY2764: $i] :
( ~ ( class_Divides_Osemiring__div @ SV63 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SY2763 @ SY2764 @ SV63 ) @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SY2763 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SY2764 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2855,plain,
! [SV702: $i,SV64: $i] :
( ( ! [SY2765: $i,SY2766: $i] :
( ~ ( class_Divides_Osemiring__div @ SV64 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SY2765 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SY2766 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SY2765 @ SY2766 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2856,plain,
! [SV703: $i,SV65: $i] :
( ( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV65 @ SV703 @ tc_nat ) @ SV703 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV703 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2857,plain,
! [SV704: $i,SV66: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV66 @ SV704 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV704 @ ( c_Divides_Odiv__class_Omod @ SV66 @ SV704 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2858,plain,
! [SV705: $i,SV67: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV67 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV705 @ SV705 @ SV67 ) @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
| ~ ( c_HOL_Oord__class_Oless @ SV705 @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2859,plain,
! [SV706: $i,SV68: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV68 )
| ( c_HOL_Oord__class_Oless @ SV706 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV706 @ SV706 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2860,plain,
! [SV707: $i,SV69: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
| ( c_HOL_Oord__class_Oless @ SV707 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV707 @ SV707 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2861,plain,
! [SV708: $i,SV70: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV70 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV708 @ SV708 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ SV708 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2862,plain,
! [SV709: $i,SV72: $i] :
( ( ! [SY2767: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SY2767 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_lessequals @ SY2767 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2863,plain,
! [SV710: $i,SV73: $i] :
( ( ! [SY2768: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SY2768 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_HOL_Oord__class_Oless @ SY2768 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2864,plain,
! [SV711: $i,SV74: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV74 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
| ~ ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2865,plain,
! [SV712: $i,SV75: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV75 @ SV712 @ tc_nat )
= SV75 )
| ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV712 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2866,plain,
! [SV713: $i,SV76: $i] :
( ( ! [SY2769: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV713 @ SY2769 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SY2769 @ SV713 @ SV76 )
| ( SY2769 = SV713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2867,plain,
! [SV714: $i,SV77: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV77 @ SV714 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV714 @ SV77 @ tc_nat )
| ( SV714 = SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2868,plain,
! [SV715: $i,SV78: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV78 @ SV715 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV715 @ SV78 @ tc_nat )
| ( SV715 = SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2869,plain,
! [SV716: $i,SV79: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV79 @ SV716 @ tc_nat )
| ( SV716 = SV79 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV716 @ SV79 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2870,plain,
! [SV717: $i,SV80: $i] :
( ( ( SV80 = SV717 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV80 @ SV717 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV80 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2871,plain,
! [SV718: $i,SV81: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV81 @ SV718 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV718 @ SV81 @ tc_nat )
| ( SV718 = SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2872,plain,
! [SV719: $i,SV82: $i] :
( ( ( SV82 = SV719 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV719 @ SV82 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV82 @ SV719 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2873,plain,
! [SV720: $i,SV83: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV83 @ SV720 @ tc_nat )
| ( SV720 = SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV720 @ SV83 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2874,plain,
! [SV721: $i,SV84: $i] :
( ( ( SV84 = SV721 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV721 @ SV84 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV84 @ SV721 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2875,plain,
! [SV722: $i,SV85: $i] :
( ( ( SV85 = SV722 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV85 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV85 @ SV722 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2876,plain,
! [SV723: $i,SV86: $i] :
( ( ! [SY2770: $i] :
( ~ ( class_Orderings_Olinorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV723 @ SY2770 @ SV86 )
| ( SY2770 = SV723 )
| ( c_HOL_Oord__class_Oless @ SY2770 @ SV723 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2877,plain,
! [SV724: $i,SV87: $i] :
( ( ! [SY2771: $i] :
( ~ ( class_Orderings_Olinorder @ SV87 )
| ( SV724 = SY2771 )
| ( c_HOL_Oord__class_Oless @ SV724 @ SY2771 @ SV87 )
| ( c_HOL_Oord__class_Oless @ SY2771 @ SV724 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2878,plain,
! [SV725: $i,SV88: $i] :
( ( ! [SY2772: $i] :
( ~ ( class_Orderings_Olinorder @ SV88 )
| ( SV725 = SY2772 )
| ( c_HOL_Oord__class_Oless @ SY2772 @ SV725 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SY2772 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2879,plain,
! [SV726: $i,SV89: $i] :
( ( ! [SY2773: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV726 @ SY2773 @ SV89 )
| ( c_HOL_Oord__class_Oless @ SY2773 @ SV726 @ SV89 )
| ( SY2773 = SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2880,plain,
! [SV727: $i,SV90: $i] :
( ( ! [SY2774: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ SV727 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ ( c_GCD_Ogcd__class_Ogcd @ SY2774 @ SV727 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2881,plain,
! [SV728: $i,SV91: $i] :
( ( ! [SY2775: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ SV728 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ ( c_GCD_Ogcd__class_Ogcd @ SV728 @ SY2775 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2882,plain,
! [SV729: $i,SV92: $i] :
( ( ! [SY2776: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ SV729 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ ( c_GCD_Ogcd__class_Ogcd @ SV729 @ SY2776 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2883,plain,
! [SV730: $i,SV93: $i] :
( ( ! [SY2777: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ SV730 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ ( c_GCD_Ogcd__class_Ogcd @ SY2777 @ SV730 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2884,plain,
! [SV731: $i,SV94: $i] :
( ( ! [SY2778: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV94 @ SV731 @ tc_nat ) @ SY2778 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SY2778 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2885,plain,
! [SV732: $i,SV95: $i] :
( ( ! [SY2779: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV95 @ SV732 @ tc_nat ) @ SY2779 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV732 @ SY2779 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2886,plain,
! [SV733: $i,SV96: $i] :
( ( ! [SY2780: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ SV733 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ ( c_GCD_Ogcd__class_Ogcd @ SV733 @ SY2780 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2887,plain,
! [SV734: $i,SV97: $i] :
( ( ! [SY2781: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ SV734 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ ( c_GCD_Ogcd__class_Ogcd @ SY2781 @ SV734 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2888,plain,
! [SV735: $i,SV98: $i] :
( ( ! [SY2782: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV735 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2782 @ SV735 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SY2782 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2889,plain,
! [SV736: $i,SV99: $i] :
( ( ! [SY2783: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SY2783 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2783 @ SV736 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2783 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SY2783 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2890,plain,
! [SV737: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV100 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV100 @ SV737 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV737 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2891,plain,
! [SV738: $i,SV102: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV102 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV738 @ SV738 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2892,plain,
! [SV739: $i,SV103: $i] :
( ( ! [SY2784: $i,SY2785: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SY2784 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2785 @ SY2784 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SY2785 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2893,plain,
! [SV740: $i,SV104: $i] :
( ( ! [SY2786: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SV740 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2786 @ SV740 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SY2786 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2894,plain,
! [SV741: $i,SV107: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV107 )
| ( c_HOL_Oord__class_Oless @ SV741 @ ( c_HOL_Oplus__class_Oplus @ SV741 @ ( c_HOL_Oone__class_Oone @ SV107 ) @ SV107 ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2895,plain,
! [SV742: $i,SV108: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV108 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2896,plain,
! [SV743: $i,SV109: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV109 )
| ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2897,plain,
! [SV744: $i,SV110: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV110 )
| ~ ( class_Power_Opower @ SV110 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV744 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2898,plain,
! [SV745: $i,SV111: $i] :
( ( ! [SY2787: $i] :
( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SY2787 @ SV111 ) @ SV745 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ SY2787 @ SV745 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2899,plain,
! [SV746: $i,SV112: $i] :
( ( ! [SY2788: $i] :
( ~ ( class_Divides_Osemiring__div @ SV112 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV746 @ SY2788 @ SV112 ) @ SY2788 @ SV112 )
= ( c_Divides_Odiv__class_Omod @ SV746 @ SY2788 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2900,plain,
! [SV747: $i,SV113: $i] :
( ( ! [SY2789: $i,SY2790: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SY2789 @ SY2790 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY2790 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SY2789 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2901,plain,
! [SV748: $i,SV114: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV114 )
| ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
| ( SV748
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV748 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2902,plain,
! [SV749: $i,SV115: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV115 @ SV749 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV115 @ SV749 @ tc_nat ) @ SV749 @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ SV115 @ SV749 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2903,plain,
! [SV750: $i,SV116: $i] :
( ( ! [SY2791: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV116 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SY2791 @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2904,plain,
! [SV751: $i,SV117: $i] :
( ( ! [SY2792: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV117 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
| ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SY2792 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2792 @ SV751 @ SV117 ) @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2905,plain,
! [SV752: $i,SV118: $i] :
( ( ! [SY2793: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV118 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
| ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SY2793 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SY2793 @ SV118 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2906,plain,
! [SV753: $i,SV119: $i] :
( ( ! [SY2794: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV119 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2794 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2907,plain,
! [SV754: $i,SV120: $i] :
( ( ! [SY2795: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV120 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SY2795 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SY2795 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2908,plain,
! [SV755: $i,SV121: $i] :
( ( ! [SY2796: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV121 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SY2796 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2796 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2909,plain,
! [SV756: $i,SV122: $i] :
( ( ! [SY2797: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV122 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SY2797 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2910,plain,
! [SV123: $i] :
( ( ( SV123
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV123 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2911,plain,
! [SV757: $i,SV124: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV124 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV757 @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2912,plain,
! [SV758: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV125 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV758 @ SV125 ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2913,plain,
! [SV759: $i,SV126: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV126 )
| ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV126 ) @ SV126 )
= SV759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2914,plain,
! [SV760: $i,SV127: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV127 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV127 ) @ SV760 @ SV127 )
= SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2915,plain,
! [SV761: $i,SV128: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV128 )
| ( ( c_HOL_Oplus__class_Oplus @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 )
= SV761 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2916,plain,
! [SV762: $i,SV129: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV129 )
| ~ ( class_Int_Onumber__ring @ SV129 )
| ( SV762
= ( c_HOL_Oplus__class_Oplus @ SV762 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2917,plain,
! [SV763: $i,SV130: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV130 ) @ SV763 @ SV130 )
= SV763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2918,plain,
! [SV764: $i,SV131: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV131 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV131 ) @ SV764 @ SV131 )
= SV764 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2919,plain,
! [SV765: $i,SV135: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 )
| ( ( c_HOL_Oplus__class_Oplus @ SV765 @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2920,plain,
! [SV766: $i,SV136: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV136 ) @ SV766 @ SV136 )
= SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2921,plain,
! [SV767: $i,SV137: $i] :
( ( ! [SY2798: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SV767 @ SY2798 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SY2798 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV767 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2922,plain,
! [SV768: $i,SV138: $i] :
( ( ! [SY2799: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SV768 @ SY2799 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SY2799 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2799 @ SV138 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2923,plain,
! [SV769: $i,SV139: $i] :
( ( ! [SY2800: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SV769 @ SY2800 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SV769 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV769 @ SV139 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2924,plain,
! [SV770: $i,SV140: $i] :
( ( ! [SY2801: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SV770 @ SY2801 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SY2801 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV770 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2925,plain,
! [SV771: $i,SV141: $i] :
( ( ! [SY2802: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SV771 @ SY2802 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SY2802 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV771 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2926,plain,
! [SV772: $i,SV142: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV142 @ SV772 @ tc_nat ) @ SV772 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2927,plain,
! [SV773: $i,SV143: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV143 @ SV773 @ tc_nat ) @ SV143 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2928,plain,
! [SV774: $i,SV144: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV144 @ SV774 @ tc_nat ) @ SV144 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2929,plain,
! [SV775: $i,SV145: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV145 @ SV775 @ tc_nat ) @ SV775 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2930,plain,
! [SV776: $i,SV146: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV146 @ SV776 @ tc_nat ) @ SV146 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2931,plain,
! [SV777: $i,SV147: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV147 @ SV777 @ tc_nat ) @ SV777 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2932,plain,
! [SV778: $i,SV148: $i] :
( ( ! [SY2803: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SV778 @ SY2803 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SY2803 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV778 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2933,plain,
! [SV779: $i,SV149: $i] :
( ( ! [SY2804: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SV779 @ SY2804 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SY2804 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV779 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2934,plain,
! [SV780: $i,SV150: $i] :
( ( ! [SY2805: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SV780 @ SY2805 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SY2805 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV780 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2935,plain,
! [SV781: $i,SV151: $i] :
( ( ! [SY2806: $i,SY2807: $i,SY2808: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SY2806 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SY2807 @ SY2808 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SY2806 @ SY2808 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SY2807 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2936,plain,
! [SV782: $i,SV152: $i] :
( ( ! [SY2809: $i,SY2810: $i,SY2811: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SY2809 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SY2810 @ SY2811 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SY2809 @ SY2811 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SY2810 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2937,plain,
! [SV783: $i,SV153: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV153 ) @ ( c_Suc @ SV783 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV153 @ SV783 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2938,plain,
! [SV784: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV154 @ SV784 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV154 ) @ ( c_Suc @ SV784 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2939,plain,
! [SV785: $i,SV155: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV155 ) @ ( c_Suc @ SV785 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV155 @ SV785 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2940,plain,
! [SV786: $i,SV156: $i] :
( ( ! [SY2812: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SY2812 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2812 @ SV156 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SY2812 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2941,plain,
! [SV787: $i,SV157: $i] :
( ( ! [SY2813: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2813 @ SV157 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2813 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SY2813 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2942,plain,
! [SV788: $i,SV158: $i] :
( ( ! [SY2814: $i,SY2815: $i] :
( ~ ( class_Orderings_Oorder @ SV158 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SY2814 @ SV158 )
| ~ ( c_lessequals @ SV788 @ SY2815 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SY2815 @ SY2814 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2943,plain,
! [SV789: $i,SV159: $i] :
( ( ! [SY2816: $i,SY2817: $i] :
( ~ ( class_Orderings_Oorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SY2816 @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV789 @ SY2817 @ SV159 )
| ~ ( c_lessequals @ SY2817 @ SY2816 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2944,plain,
! [SV790: $i,SV160: $i] :
( ( ! [SY2818: $i,SY2819: $i,SY2820: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
| ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SY2818 @ SY2819 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SY2820 @ SY2819 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SY2818 @ SY2820 @ SV160 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2945,plain,
! [SV791: $i,SV161: $i] :
( ( ! [SY2821: $i,SY2822: $i] :
( ~ ( class_Orderings_Opreorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SV791 @ SY2821 @ SV161 )
| ~ ( c_lessequals @ SY2822 @ SY2821 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV791 @ SY2822 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2946,plain,
! [SV792: $i,SV162: $i] :
( ( ! [SY2823: $i,SY2824: $i] :
( ~ ( class_Orderings_Opreorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SV792 @ SY2823 @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY2824 @ SY2823 @ SV162 )
| ~ ( c_lessequals @ SV792 @ SY2824 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2947,plain,
! [SV793: $i,SV163: $i] :
( ( ! [SY2825: $i] :
( ~ ( class_Orderings_Opreorder @ SV163 )
| ( c_lessequals @ SV793 @ SY2825 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SY2825 @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2948,plain,
! [SV794: $i,SV164: $i] :
( ( ! [SY2826: $i] :
( ~ ( class_Orderings_Oorder @ SV164 )
| ( c_lessequals @ SV794 @ SY2826 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SY2826 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2949,plain,
! [SV795: $i,SV165: $i] :
( ( ! [SY2827: $i] :
( ~ ( class_Orderings_Opreorder @ SV165 )
| ( c_HOL_Oord__class_Oless @ SV795 @ SY2827 @ SV165 )
| ( c_lessequals @ SY2827 @ SV795 @ SV165 )
| ~ ( c_lessequals @ SV795 @ SY2827 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2950,plain,
! [SV796: $i,SV166: $i] :
( ( ! [SY2828: $i,SY2829: $i,SY2830: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SY2828 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SY2829 @ SY2830 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SY2828 @ SY2830 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SY2829 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2951,plain,
! [SV797: $i,SV167: $i] :
( ( ! [SY2831: $i] :
( ~ ( class_Orderings_Oorder @ SV167 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SY2831 @ SV167 )
| ( SY2831 = SV797 )
| ~ ( c_lessequals @ SV797 @ SY2831 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2952,plain,
! [SV798: $i,SV168: $i] :
( ( ! [SY2832: $i] :
( ~ ( class_Orderings_Oorder @ SV168 )
| ( c_HOL_Oord__class_Oless @ SV798 @ SY2832 @ SV168 )
| ~ ( c_lessequals @ SV798 @ SY2832 @ SV168 )
| ( SY2832 = SV798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2953,plain,
! [SV799: $i,SV169: $i] :
( ( ! [SY2833: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( SV799 = SY2833 )
| ( c_HOL_Oord__class_Oless @ SV799 @ SY2833 @ SV169 )
| ~ ( c_lessequals @ SV799 @ SY2833 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2954,plain,
! [SV800: $i,SV170: $i] :
( ( ! [SY2834: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( SV800 = SY2834 )
| ~ ( c_lessequals @ SV800 @ SY2834 @ SV170 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SY2834 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2955,plain,
! [SV801: $i,SV171: $i] :
( ( ! [SY2835: $i] :
( ~ ( class_Orderings_Oorder @ SV171 )
| ( c_HOL_Oord__class_Oless @ SV801 @ SY2835 @ SV171 )
| ~ ( c_lessequals @ SV801 @ SY2835 @ SV171 )
| ( SV801 = SY2835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2956,plain,
! [SV802: $i,SV172: $i] :
( ( ! [SY2836: $i] :
( ~ ( class_Orderings_Oorder @ SV172 )
| ( c_HOL_Oord__class_Oless @ SV802 @ SY2836 @ SV172 )
| ( SV802 = SY2836 )
| ~ ( c_lessequals @ SV802 @ SY2836 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2957,plain,
! [SV803: $i,SV173: $i] :
( ( ! [SY2837: $i] :
( ~ ( class_Orderings_Oorder @ SV173 )
| ( SV803 = SY2837 )
| ( c_HOL_Oord__class_Oless @ SV803 @ SY2837 @ SV173 )
| ~ ( c_lessequals @ SV803 @ SY2837 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2958,plain,
! [SV804: $i,SV174: $i] :
( ( ! [SY2838: $i] :
( ~ ( class_Orderings_Oorder @ SV174 )
| ( c_HOL_Oord__class_Oless @ SV804 @ SY2838 @ SV174 )
| ( SV804 = SY2838 )
| ~ ( c_lessequals @ SV804 @ SY2838 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2959,plain,
! [SV805: $i,SV175: $i] :
( ( ! [SY2839: $i,SY2840: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SY2839 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY2840 @ SY2839 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV805 @ SY2840 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2960,plain,
! [SV806: $i,SV176: $i] :
( ( ! [SY2841: $i,SY2842: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
| ( c_lessequals @ SV806 @ SY2841 @ SV176 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SY2842 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SY2841 @ SY2842 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2961,plain,
! [SV807: $i,SV177: $i] :
( ( ! [SY2843: $i,SY2844: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SY2843 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SY2844 @ SV177 ) @ SV177 )
| ~ ( c_lessequals @ SY2843 @ SY2844 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2962,plain,
! [SV808: $i,SV178: $i] :
( ( ! [SY2845: $i,SY2846: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
| ( c_lessequals @ SV808 @ SY2845 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2846 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SY2846 @ SY2845 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2963,plain,
! [SV809: $i,SV179: $i] :
( ( ! [SY2847: $i,SY2848: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SY2847 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SY2848 @ SY2847 @ SV179 ) @ SV179 )
| ~ ( c_lessequals @ SV809 @ SY2848 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2964,plain,
! [SV810: $i,SV180: $i] :
( ( ! [SY2849: $i,SY2850: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SY2849 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SY2850 @ SV180 ) @ SV180 )
| ~ ( c_lessequals @ SY2849 @ SY2850 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2965,plain,
! [SV811: $i,SV181: $i] :
( ( ! [SY2851: $i] :
( ~ ( class_Orderings_Opreorder @ SV181 )
| ~ ( c_lessequals @ SV811 @ SY2851 @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ SY2851 @ SV811 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2966,plain,
! [SV812: $i,SV182: $i] :
( ( ! [SY2852: $i] :
( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_HOL_Oord__class_Oless @ SV812 @ SY2852 @ SV182 )
| ( c_lessequals @ SY2852 @ SV812 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2967,plain,
! [SV813: $i,SV183: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV183 )
| ~ ( c_lessequals @ SV813 @ SV813 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV813 @ SV813 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2968,plain,
! [SV814: $i,SV184: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV184 )
| ( c_HOL_Oord__class_Oless @ SV814 @ SV814 @ SV184 )
| ( c_lessequals @ SV814 @ SV814 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2969,plain,
! [SV815: $i,SV185: $i] :
( ( ! [SY2853: $i] :
( ~ ( class_Orderings_Olinorder @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ SY2853 @ SV185 )
| ~ ( c_lessequals @ SY2853 @ SV815 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2970,plain,
! [SV816: $i,SV186: $i] :
( ( ! [SY2854: $i] :
( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SV816 @ SY2854 @ SV186 )
| ( c_HOL_Oord__class_Oless @ SY2854 @ SV816 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2971,plain,
! [SV817: $i,SV187: $i] :
( ( ! [SY2855: $i] :
( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_HOL_Oord__class_Oless @ SV817 @ SY2855 @ SV187 )
| ( c_lessequals @ SY2855 @ SV817 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2972,plain,
! [SV818: $i,SV188: $i] :
( ( ! [SY2856: $i] :
( ~ ( class_Orderings_Olinorder @ SV188 )
| ~ ( c_lessequals @ SV818 @ SY2856 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SY2856 @ SV818 @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2973,plain,
! [SV819: $i,SV189: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV189 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
| ~ ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2974,plain,
! [SV820: $i,SV190: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV190 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
| ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2975,plain,
! [SV821: $i,SV191: $i] :
( ( ! [SY2857: $i,SY2858: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SV821 @ SY2857 @ SV191 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SY2857 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SY2858 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SY2857 @ ( c_Suc @ SY2858 ) @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2976,plain,
! [SV822: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV192 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV822 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV192 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2977,plain,
! [SV823: $i,SV193: $i] :
( ( ! [SY2859: $i,SY2860: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_HOL_Oord__class_Oless @ SV823 @ SY2859 @ SV193 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SY2859 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SY2860 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SY2859 @ SY2860 @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2978,plain,
! [SV824: $i,SV194: $i] :
( ( ! [SY2861: $i,SY2862: $i,SY2863: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV194 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SY2861 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2862 @ SY2863 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SY2863 @ SY2861 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY2863 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SY2862 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2979,plain,
! [SV825: $i,SV195: $i] :
( ( ! [SY2864: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV195 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SY2864 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SY2864 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
| ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2980,plain,
! [SV826: $i,SV196: $i] :
( ( ! [SY2865: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SY2865 @ SV196 ) @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SY2865 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2981,plain,
! [SV827: $i,SV197: $i] :
( ( ! [SY2866: $i,SY2867: $i,SY2868: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV197 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SY2866 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2867 @ SY2868 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SY2868 @ SY2866 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY2868 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SY2867 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2982,plain,
! [SV828: $i,SV198: $i] :
( ( ! [SY2869: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV198 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SY2869 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SY2869 @ SV198 )
| ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2983,plain,
! [SV829: $i,SV199: $i] :
( ( ! [SY2870: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV199 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SY2870 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SY2870 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2984,plain,
! [SV830: $i,SV200: $i] :
( ( ! [SY2871: $i,SY2872: $i,SY2873: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SY2871 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2872 @ SY2873 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SY2873 @ SY2871 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SY2873 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SY2872 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2985,plain,
! [SV831: $i,SV201: $i] :
( ( ! [SY2874: $i,SY2875: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV201 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
| ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SY2874 @ SY2875 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SY2875 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SY2875 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2986,plain,
! [SV832: $i,SV202: $i] :
( ( ! [SY2876: $i,SY2877: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SY2876 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SY2876 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SY2877 @ SY2876 @ SV202 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2987,plain,
! [SV833: $i,SV203: $i] :
( ( ! [SY2878: $i,SY2879: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SY2878 @ SV203 ) @ SY2879 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SY2879 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SY2878 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SY2878 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2988,plain,
! [SV834: $i,SV204: $i] :
( ( ! [SY2880: $i,SY2881: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV204 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SY2880 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SY2880 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY2881 @ SY2880 @ SV204 ) @ SV834 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2989,plain,
! [SV205: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV205 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV205 ) @ SV205 )
= ( c_HOL_Oone__class_Oone @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2990,plain,
! [SV206: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV206 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV206 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= ( c_HOL_Oone__class_Oone @ SV206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2991,plain,
! [SV835: $i,SV207: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV207 ) @ SV835 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2992,plain,
! [SV836: $i,SV208: $i] :
( ( ! [SY2882: $i,SY2883: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV208 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SY2882 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SY2883 @ SV208 ) @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ SY2882 @ SY2883 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2993,plain,
! [SV837: $i,SV209: $i] :
( ( ! [SY2884: $i,SY2885: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV209 )
| ( c_HOL_Oord__class_Oless @ SV837 @ SY2884 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2885 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SY2885 @ SY2884 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SY2885 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2994,plain,
! [SV838: $i,SV210: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV210 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SY2886 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SY2887 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SY2886 @ SY2887 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2995,plain,
! [SV839: $i,SV211: $i] :
( ( ! [SY2888: $i,SY2889: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV211 )
| ( c_HOL_Oord__class_Oless @ SV839 @ SY2888 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2889 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SY2889 @ SY2888 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SY2889 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2996,plain,
! [SV840: $i,SV212: $i] :
( ( ! [SY2890: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV212 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV840 @ ( c_Suc @ SY2890 ) @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SV840 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2997,plain,
! [SV841: $i,SV213: $i] :
( ( ! [SY2891: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV213 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
| ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2891 @ SV841 @ SV213 ) @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2998,plain,
! [SV842: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV214 @ SV842 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV842 @ SV214 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2999,plain,
! [SV843: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV215 @ SV843 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV843 @ SV215 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(3000,plain,
! [SV844: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV216 @ ( c_Suc @ SV844 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV216 @ SV844 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3001,plain,
! [SV845: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV217 @ SV845 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV217 ) @ SV845 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3002,plain,
! [SV218: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV218 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV218 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(3003,plain,
! [SV219: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV219 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(3004,plain,
! [SV220: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV220 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV220 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV220 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(3005,plain,
! [SV846: $i,SV221: $i] :
( ( ! [SY2892: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV221 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV846 @ SY2892 @ tc_nat ) @ SV221 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV846 @ SV221 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2892 @ SV221 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(3006,plain,
! [SV847: $i,SV222: $i] :
( ( ! [SY2893: $i,SY2894: $i] :
( ~ ( class_Divides_Osemiring__div @ SV222 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ ( c_Divides_Odiv__class_Omod @ SY2893 @ SY2894 @ SV222 ) @ SV222 ) @ SY2894 @ SV222 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ SY2893 @ SV222 ) @ SY2894 @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3007,plain,
! [SV848: $i,SV223: $i] :
( ( ! [SY2895: $i,SY2896: $i] :
( ~ ( class_Divides_Osemiring__div @ SV223 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV848 @ SY2895 @ SV223 ) @ SY2896 @ SV223 ) @ SY2895 @ SV223 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV848 @ SY2896 @ SV223 ) @ SY2895 @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3008,plain,
! [SV849: $i,SV224: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV224 @ SV849 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV849 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(3009,plain,
! [SV850: $i,SV225: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV225 @ SV850 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV225 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3010,plain,
! [SV851: $i,SV226: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV226 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV851 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ ( c_HOL_Oplus__class_Oplus @ SV851 @ SV851 @ SV226 ) @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3011,plain,
! [SV852: $i,SV227: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV227 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV852 @ SV852 @ SV227 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV852 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3012,plain,
! [SV853: $i,SV228: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV228 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
| ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3013,plain,
! [SV854: $i,SV229: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV229 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV854 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV229 ) @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(3014,plain,
! [SV230: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV230 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV230 ) @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(3015,plain,
! [SV855: $i,SV231: $i] :
( ( ! [SY2897: $i,SY2898: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV231 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SY2897 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SY2897 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY2898 @ SY2897 @ SV231 ) @ SV855 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(3016,plain,
! [SV856: $i,SV232: $i] :
( ( ! [SY2899: $i,SY2900: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV232 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SY2899 @ SV232 ) @ SY2900 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SY2900 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SY2899 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SY2899 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(3017,plain,
! [SV857: $i,SV233: $i] :
( ( ! [SY2901: $i,SY2902: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV233 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SY2901 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SY2901 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SY2902 @ SY2901 @ SV233 ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(3018,plain,
! [SV858: $i,SV234: $i] :
( ( ! [SY2903: $i,SY2904: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV234 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SY2903 @ SY2904 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SY2904 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SY2904 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(3019,plain,
! [SV859: $i,SV235: $i] :
( ( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SV859 @ tc_nat ) @ SV859 @ tc_nat )
| ( SV859
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(3020,plain,
! [SV860: $i,SV236: $i] :
( ( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ SV236 @ SV860 @ tc_nat ) @ SV236 @ tc_nat )
| ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(3021,plain,
! [SV237: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV237 @ SV237 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV237 @ ( c_Suc @ SV237 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(3022,plain,
! [SV861: $i,SV238: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV238 @ SV861 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_Suc @ SV238 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(3023,plain,
! [SV862: $i,SV239: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV239 @ ( c_Suc @ SV862 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV862 @ SV239 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3024,plain,
! [SV863: $i,SV240: $i] :
( ( ! [SY2905: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV240 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SY2905 @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SY2905 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3025,plain,
! [SV864: $i,SV241: $i] :
( ( ! [SY2906: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV241 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SY2906 @ SV241 ) @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SY2906 @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(3026,plain,
! [SV865: $i,SV242: $i] :
( ( ! [SY2907: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV242 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SY2907 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SY2907 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(3027,plain,
! [SV866: $i,SV243: $i] :
( ( ! [SY2908: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV243 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SY2908 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SY2908 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(3028,plain,
! [SV867: $i,SV244: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV244 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
| ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(3029,plain,
! [SV868: $i,SV245: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SY2909 @ SY2910 @ SV245 ) @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SY2910 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SY2909 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(3030,plain,
! [SV869: $i,SV246: $i] :
( ( ! [SY2911: $i,SY2912: $i,SY2913: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SY2911 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SY2912 @ SY2913 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SY2912 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SY2911 @ SY2913 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(3031,plain,
! [SV870: $i,SV247: $i] :
( ( ! [SY2914: $i,SY2915: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV247 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SY2914 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2915 @ SY2914 @ SV247 ) @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SY2914 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ SY2915 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3032,plain,
! [SV871: $i,SV248: $i] :
( ( ! [SY2916: $i,SY2917: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV248 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SY2916 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2917 @ SY2916 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SY2916 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SY2917 @ SV871 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3033,plain,
! [SV872: $i,SV249: $i] :
( ( ! [SY2918: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SY2918 @ SV249 ) @ SV249 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SY2918 @ SV249 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3034,plain,
! [SV873: $i,SV250: $i] :
( ( ! [SY2919: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SY2919 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SY2919 @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3035,plain,
! [SV874: $i,SV251: $i] :
( ( ! [SY2920: $i] :
( ~ ( class_Divides_Osemiring__div @ SV251 )
| ( ( c_Divides_Odiv__class_Omod @ SV874 @ SY2920 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2920 @ SV874 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3036,plain,
! [SV875: $i,SV252: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV252 )
| ( SV875
= ( c_HOL_Ozero__class_Ozero @ SV252 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV875 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3037,plain,
! [SV876: $i,SV253: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV253 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV876 @ SV253 ) @ SV253 )
= SV876 )
| ( SV876
= ( c_HOL_Ozero__class_Ozero @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(3038,plain,
! [SV254: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV254 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV254 )
= ( c_HOL_Ozero__class_Ozero @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(3039,plain,
! [SV877: $i,SV255: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV255 ) @ SV877 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV255 @ ( c_Suc @ SV877 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(3040,plain,
! [SV878: $i,SV256: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV256 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV878 ) @ SV256 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV256 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV878 @ SV256 ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(3041,plain,
! [SV879: $i,SV257: $i] :
( ( ! [SY2921: $i] :
( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SY2921 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY2921 @ SV257 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY2921 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SY2921 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(3042,plain,
! [SV880: $i,SV258: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV258 @ SV880 @ tc_nat ) @ SV880 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV880 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(3043,plain,
! [SV881: $i,SV259: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV259 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV881 @ SV259 )
| ( SV881
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV881 @ SV259 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(3044,plain,
! [SV260: $i] :
( ( c_HOL_Oord__class_Oless @ SV260 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(3045,plain,
! [SV261: $i] :
( ( c_HOL_Oord__class_Oless @ SV261 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(3046,plain,
! [SV882: $i,SV262: $i] :
( ( ! [SY2922: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV262 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SY2922 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3047,plain,
! [SV883: $i,SV263: $i] :
( ( ! [SY2923: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV263 )
| ( c_HOL_Oord__class_Oless @ SV883 @ SY2923 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SY2923 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2923 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3048,plain,
! [SV884: $i,SV264: $i] :
( ( ! [SY2924: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV264 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2924 @ SV264 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SY2924 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SY2924 @ SV884 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3049,plain,
! [SV885: $i,SV265: $i] :
( ( ! [SY2925: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV265 )
| ( c_HOL_Oord__class_Oless @ SV885 @ SY2925 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SY2925 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(3050,plain,
! [SV886: $i,SV266: $i] :
( ( ! [SY2926: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV266 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2926 @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SY2926 @ SV886 @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3051,plain,
! [SV887: $i,SV267: $i] :
( ( ! [SY2927: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SY2927 @ SV267 ) @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SY2927 @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3052,plain,
! [SV888: $i,SV268: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV268 @ SV888 @ tc_nat ) @ ( c_Suc @ SV268 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3053,plain,
! [SV269: $i] :
( ( ( ~ ( class_SEQ_Obanach @ SV269 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__field @ SV269 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= ( c_HOL_Oone__class_Oone @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(3054,plain,
! [SV889: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Suc @ SV889 ) @ tc_nat )
| ~ ( c_lessequals @ SV270 @ SV889 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3055,plain,
! [SV890: $i,SV271: $i] :
( ( ( c_lessequals @ SV271 @ SV890 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV271 @ ( c_Suc @ SV890 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(3056,plain,
! [SV272: $i] :
( ( ( ~ ( c_lessequals @ SV272 @ SV272 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV272 @ ( c_Suc @ SV272 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(3057,plain,
! [SV891: $i,SV273: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV273 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3058,plain,
! [SV892: $i,SV274: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV274 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3059,plain,
! [SV893: $i,SV275: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV275 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ SV893 @ SV275 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ ( c_HOL_Oplus__class_Oplus @ SV893 @ SV893 @ SV275 ) @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3060,plain,
! [SV894: $i,SV276: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV276 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ ( c_HOL_Oplus__class_Oplus @ SV894 @ SV894 @ SV276 ) @ SV276 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV894 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3061,plain,
! [SV895: $i,SV279: $i] :
( ( ! [SY2928: $i] :
( ~ ( class_Divides_Osemiring__div @ SV279 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV895 @ SY2928 @ SV279 ) @ SY2928 @ SV279 )
= ( c_Divides_Odiv__class_Omod @ SV895 @ SY2928 @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3062,plain,
! [SV896: $i,SV280: $i] :
( ( ! [SY2929: $i,SY2930: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
| ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SY2929 @ SY2930 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SY2930 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SY2929 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3063,plain,
! [SV897: $i,SV282: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_Suc @ SV282 ) @ SV897 @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV282 @ SV897 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3064,plain,
! [SV898: $i,SV283: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV283 @ ( c_Suc @ SV898 ) @ tc_nat )
= ( c_Suc @ ( c_HOL_Oplus__class_Oplus @ SV283 @ SV898 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3065,plain,
! [SV899: $i,SV284: $i] :
( ( ! [SY2931: $i,SY2932: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV284 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SY2931 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SY2932 @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SY2932 @ SY2931 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3066,plain,
! [SV900: $i,SV285: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV285 )
| ( ( c_Divides_Odiv__class_Omod @ SV900 @ ( c_HOL_Ozero__class_Ozero @ SV285 ) @ SV285 )
= SV900 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3067,plain,
! [SV901: $i,SV286: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV286 )
| ( ( c_Divides_Odiv__class_Omod @ SV901 @ SV901 @ SV286 )
= ( c_HOL_Ozero__class_Ozero @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3068,plain,
! [SV902: $i,SV287: $i] :
( ( ! [SY2933: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SV902 @ SY2933 @ SV287 )
= ( c_HOL_Oplus__class_Oplus @ SY2933 @ SV902 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3069,plain,
! [SV903: $i,SV288: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV288 @ SV903 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV903 @ SV288 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3070,plain,
! [SV904: $i,SV289: $i] :
( ( ! [SY2934: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV289 )
| ( ( c_HOL_Oplus__class_Oplus @ SV904 @ SY2934 @ SV289 )
= ( c_HOL_Oplus__class_Oplus @ SY2934 @ SV904 @ SV289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3071,plain,
! [SV905: $i,SV290: $i] :
( ( ! [SY2935: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV905 @ SY2935 @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SY2935 @ SV905 @ SV290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3072,plain,
! [SV906: $i,SV291: $i] :
( ( ! [SY2936: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV291 )
| ( c_lessequals @ SV906 @ SY2936 @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SY2936 @ SV291 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2936 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3073,plain,
! [SV907: $i,SV292: $i] :
( ( ! [SY2937: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV292 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2937 @ SV292 ) @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SY2937 @ SV292 )
| ~ ( c_lessequals @ SY2937 @ SV907 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3074,plain,
! [SV908: $i,SV293: $i] :
( ( ! [SY2938: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV293 )
| ( c_lessequals @ SV908 @ SY2938 @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SY2938 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3075,plain,
! [SV909: $i,SV294: $i] :
( ( ! [SY2939: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV294 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SY2939 @ SV294 ) @ SV294 )
| ~ ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
| ~ ( c_lessequals @ SY2939 @ SV909 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3076,plain,
! [SV295: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV295 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV295 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV295 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV295 )
= ( c_HOL_Oone__class_Oone @ SV295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(3077,plain,
! [SV910: $i,SV296: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV296 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3078,plain,
! [SV911: $i,SV297: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV297 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3079,plain,
! [SV912: $i,SV298: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV298 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3080,plain,
! [SV913: $i,SV299: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV299 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
| ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3081,plain,
! [SV914: $i,SV300: $i] :
( ( ! [SY2940: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV300 )
| ( c_HOL_Oord__class_Oless @ SV914 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV914 @ SY2940 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SY2940 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3082,plain,
! [SV915: $i,SV301: $i] :
( ( ! [SY2941: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV915 @ SY2941 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SY2941 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV915 @ SY2941 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3083,plain,
! [SV916: $i,SV302: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV302 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV916 @ SV302 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV302 ) @ SV916 @ SV302 ) )
| ( SV916
= ( c_HOL_Ozero__class_Ozero @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3084,plain,
! [SV917: $i,SV303: $i] :
( ( ! [SY2942: $i,SY2943: $i] :
( ~ ( class_Divides_Oring__div @ SV303 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ SY2942 @ SV303 ) @ SY2943 @ SV303 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ ( c_Divides_Odiv__class_Omod @ SY2942 @ SY2943 @ SV303 ) @ SV303 ) @ SY2943 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3085,plain,
! [SV918: $i,SV304: $i] :
( ( ! [SY2944: $i,SY2945: $i] :
( ~ ( class_Divides_Oring__div @ SV304 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SY2944 @ SV304 ) @ SY2945 @ SV304 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV918 @ SY2945 @ SV304 ) @ SY2944 @ SV304 ) @ SY2945 @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3086,plain,
! [SV919: $i,SV305: $i] :
( ( ! [SY2946: $i,SY2947: $i] :
( ~ ( class_Divides_Oring__div @ SV305 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV919 @ SY2946 @ SV305 ) @ SY2947 @ SV305 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV919 @ SY2947 @ SV305 ) @ ( c_Divides_Odiv__class_Omod @ SY2946 @ SY2947 @ SV305 ) @ SV305 ) @ SY2947 @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3087,plain,
! [SV920: $i,SV306: $i] :
( ( ! [SY2948: $i,SY2949: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SY2948 @ SY2949 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SY2949 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SY2948 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3088,plain,
! [SV921: $i,SV307: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV307 )
| ( ( c_HOL_Ominus__class_Ominus @ SV921 @ SV921 @ SV307 )
= ( c_HOL_Ozero__class_Ozero @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3089,plain,
! [SV922: $i,SV308: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV308 )
| ( ( c_HOL_Ominus__class_Ominus @ SV922 @ SV922 @ SV308 )
= ( c_HOL_Ozero__class_Ozero @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3090,plain,
! [SV923: $i,SV309: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV309 )
| ( ( c_HOL_Ominus__class_Ominus @ SV923 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 )
= SV923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3091,plain,
! [SV924: $i,SV310: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV310 )
| ( ( c_HOL_Ominus__class_Ominus @ SV924 @ SV924 @ SV310 )
= ( c_HOL_Ozero__class_Ozero @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3092,plain,
! [SV925: $i,SV311: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV311 )
| ~ ( class_Int_Onumber__ring @ SV311 )
| ( ( c_HOL_Ominus__class_Ominus @ SV925 @ SV925 @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3093,plain,
! [SV926: $i,SV312: $i] :
( ( ! [SY2950: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV312 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV926 @ SY2950 @ SV312 ) @ SY2950 @ SV312 )
= SV926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3094,plain,
! [SV927: $i,SV313: $i] :
( ( ! [SY2951: $i,SY2952: $i,SY2953: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV313 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV927 @ SY2951 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SY2952 @ SY2953 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV927 @ SY2952 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SY2951 @ SY2953 @ SV313 ) @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3095,plain,
! [SV928: $i,SV314: $i] :
( ( ! [SY2954: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV928 @ SY2954 @ SV314 ) @ SY2954 @ SV314 )
= SV928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3096,plain,
! [SV929: $i,SV315: $i] :
( ( ! [SY2955: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV315 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV315 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV929 @ SY2955 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV929 @ SV315 ) @ SY2955 @ SV315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3097,plain,
! [SV930: $i,SV316: $i] :
( ( ! [SY2956: $i,SY2957: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SY2956 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SY2957 @ SY2956 @ SV316 ) @ SV316 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SY2957 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3098,plain,
! [SV931: $i,SV317: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV317 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV317 )
| ( ( c_HOL_Ozero__class_Ozero @ SV317 )
= ( c_HOL_Oinverse__class_Odivide @ SV931 @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3099,plain,
! [SV318: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV318 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV318 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(3100,plain,
! [SV932: $i,SV319: $i] :
( ( ! [SY2958: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV319 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV319 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV932 @ SY2958 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SY2958 @ SV932 @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3101,plain,
! [SV933: $i,SV320: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV320 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ SV933 @ SV320 )
= ( c_HOL_Ozero__class_Ozero @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3102,plain,
! [SV934: $i,SV321: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV321 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV321 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV934 @ ( c_HOL_Ozero__class_Ozero @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3103,plain,
! [SV935: $i,SV322: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV322 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV322 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV322 ) @ SV322 )
= ( c_HOL_Ozero__class_Ozero @ SV322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3104,plain,
! [SV936: $i,SV323: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV323 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV936 @ SV323 )
= ( c_HOL_Ozero__class_Ozero @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3105,plain,
! [SV937: $i,SV324: $i] :
( ( ! [SY2959: $i,SY2960: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV324 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SY2959 @ SV324 ) @ SY2960 @ SV324 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV937 @ SY2960 @ SV324 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2959 @ SY2960 @ SV324 ) @ SV324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3106,plain,
! [SV938: $i,SV325: $i] :
( ( ! [SY2961: $i,SY2962: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV325 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SY2961 @ SV325 ) @ SY2962 @ SV325 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV938 @ SY2962 @ SV325 ) @ ( c_HOL_Oinverse__class_Odivide @ SY2961 @ SY2962 @ SV325 ) @ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3107,plain,
! [SV939: $i,SV326: $i] :
( ( ( c_lessequals @ SV326 @ SV939 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV326 ) @ ( c_Suc @ SV939 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3108,plain,
! [SV940: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV327 ) @ ( c_Suc @ SV940 ) @ tc_nat )
| ~ ( c_lessequals @ SV327 @ SV940 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3109,plain,
! [SV328: $i] :
( ( c_lessequals @ ( c_Suc @ SV328 ) @ SV328 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(3110,plain,
! [SV941: $i,SV329: $i] :
( ( ( c_lessequals @ SV329 @ SV941 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV329 ) @ SV941 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3111,plain,
! [SV942: $i,SV330: $i] :
( ( ( c_lessequals @ SV330 @ ( c_Suc @ SV942 ) @ tc_nat )
| ~ ( c_lessequals @ SV330 @ SV942 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3112,plain,
! [SV943: $i,SV331: $i] :
( ( ( c_lessequals @ SV331 @ SV943 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV331 @ SV943 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3113,plain,
! [SV944: $i,SV332: $i] :
( ( ( c_lessequals @ SV332 @ SV944 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV332 @ SV944 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3114,plain,
! [SV945: $i,SV333: $i] :
( ( c_lessequals @ SV333 @ ( c_HOL_Oplus__class_Oplus @ SV333 @ SV945 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3115,plain,
! [SV946: $i,SV334: $i] :
( ( c_lessequals @ SV334 @ ( c_HOL_Oplus__class_Oplus @ SV946 @ SV334 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3116,plain,
! [SV947: $i,SV335: $i] :
( ( c_lessequals @ SV335 @ ( c_HOL_Oplus__class_Oplus @ SV335 @ SV947 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3117,plain,
! [SV948: $i,SV336: $i] :
( ( c_lessequals @ SV336 @ ( c_HOL_Oplus__class_Oplus @ SV336 @ SV948 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3118,plain,
! [SV949: $i,SV337: $i] :
( ( ! [SY2963: $i,SY2964: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2963 @ SY2964 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV949 @ SY2964 @ tc_nat )
| ~ ( c_lessequals @ SV337 @ SY2963 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3119,plain,
! [SV950: $i,SV338: $i] :
( ( ( SV338
= ( c_Suc @ SV950 ) )
| ( c_lessequals @ SV338 @ SV950 @ tc_nat )
| ~ ( c_lessequals @ SV338 @ ( c_Suc @ SV950 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3120,plain,
! [SV951: $i,SV339: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV339 @ SV951 @ tc_nat )
| ( SV339 = SV951 )
| ~ ( c_lessequals @ SV339 @ SV951 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3121,plain,
! [SV952: $i,SV340: $i] :
( ( ( SV340 = SV952 )
| ( c_HOL_Oord__class_Oless @ SV340 @ SV952 @ tc_nat )
| ~ ( c_lessequals @ SV340 @ SV952 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3122,plain,
! [SV953: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV341 @ SV953 @ tc_nat )
| ( SV341 = SV953 )
| ~ ( c_lessequals @ SV341 @ SV953 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3123,plain,
! [SV954: $i,SV342: $i] :
( ( ! [SY2965: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV342 @ SV954 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2965 @ SV954 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV342 @ SY2965 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3124,plain,
! [SV955: $i,SV343: $i] :
( ( ! [SY2966: $i] :
( ( c_lessequals @ SV343 @ SV955 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2966 @ SV343 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2966 @ SV955 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3125,plain,
! [SV956: $i,SV344: $i] :
( ( ! [SY2967: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV956 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SY2967 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV956 @ SY2967 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3126,plain,
! [SV345: $i] :
( ( ( SV345
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV345 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(3127,plain,
! [SV957: $i,SV346: $i] :
( ( ! [SY2968: $i] :
( ( c_lessequals @ SV346 @ ( c_HOL_Oplus__class_Oplus @ SV957 @ SY2968 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV346 @ SV957 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3128,plain,
! [SV958: $i,SV347: $i] :
( ( ! [SY2969: $i] :
( ( c_lessequals @ SV347 @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SY2969 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV347 @ SY2969 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3129,plain,
! [SV959: $i,SV348: $i] :
( ( ! [SY2970: $i] :
( ( c_lessequals @ SV348 @ SV959 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV348 @ SY2970 @ tc_nat ) @ SV959 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3130,plain,
! [SV960: $i,SV349: $i] :
( ( ! [SY2971: $i] :
( ( c_lessequals @ SV349 @ SV960 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY2971 @ SV349 @ tc_nat ) @ SV960 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3131,plain,
! [SV961: $i,SV350: $i] :
( ( ! [SY2972: $i] :
( ( c_lessequals @ SV350 @ ( c_HOL_Oplus__class_Oplus @ SV961 @ SY2972 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SV961 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3132,plain,
! [SV962: $i,SV351: $i] :
( ( ! [SY2973: $i] :
( ( c_lessequals @ SV351 @ ( c_HOL_Oplus__class_Oplus @ SV962 @ SY2973 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV351 @ SY2973 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3133,plain,
! [SV963: $i,SV353: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV353 ) @ SV963 @ tc_nat )
| ( c_lessequals @ SV963 @ SV353 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3134,plain,
! [SV964: $i,SV354: $i] :
( ( ~ ( c_lessequals @ SV354 @ SV964 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV964 ) @ SV354 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3135,plain,
! [SV965: $i,SV355: $i] :
( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV355 @ SV965 @ tc_nat ) @ SV355 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3136,plain,
! [SV966: $i,SV357: $i] :
( ( ! [SY2974: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV357 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV966 @ SY2974 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV357 @ SY2974 @ tc_nat ) @ ( c_Suc @ SV966 ) @ tc_nat ) )
| ~ ( c_lessequals @ SY2974 @ SV966 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3137,plain,
! [SV967: $i,SV358: $i] :
( ( ! [SY2975: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV967 @ tc_nat ) ) @ SY2975 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV358 ) @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SY2975 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV967 @ SV358 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3138,plain,
! [SV968: $i,SV359: $i] :
( ( ! [SY2976: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV968 @ tc_nat ) @ SY2976 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SY2976 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3139,plain,
! [SV969: $i,SV360: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV360 ) @ ( c_Suc @ SV969 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV360 @ SV969 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3140,plain,
! [SV970: $i,SV361: $i] :
( ( ! [SY2977: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV970 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SY2977 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2977 @ SV361 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2977 @ SV970 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3141,plain,
! [SV971: $i,SV362: $i] :
( ( ! [SY2978: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV362 @ SV971 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV362 @ SY2978 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV971 @ SY2978 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3142,plain,
! [SV972: $i,SV363: $i] :
( ( ! [SY2979: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV363 @ SV972 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2979 @ SV972 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV363 @ SY2979 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3143,plain,
! [SV973: $i,SV364: $i] :
( ( ! [SY2980: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV364 ) @ SV973 @ tc_nat ) @ ( c_Suc @ SY2980 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV364 @ SV973 @ tc_nat ) @ SY2980 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3144,plain,
! [SV974: $i,SV365: $i] :
( ( ! [SY2981: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SV974 @ SY2981 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SY2981 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV974 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3145,plain,
! [SV975: $i,SV368: $i] :
( ( ! [SY2982: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV368 @ SV975 @ tc_nat ) @ SY2982 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV368 @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SY2982 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3146,plain,
! [SV976: $i,SV370: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV370 @ SV976 @ tc_nat ) @ SV370 @ tc_nat )
= SV976 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(3147,plain,
! [SV977: $i,SV371: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV371 @ SV977 @ tc_nat ) @ SV977 @ tc_nat )
= SV371 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3148,plain,
! [SV372: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV372 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(3149,plain,
! [SV978: $i,SV373: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV373 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3150,plain,
! [SV374: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV374 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ ( c_HOL_Oone__class_Oone @ SV374 ) @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(3151,plain,
! [SV979: $i,SV375: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV375 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3152,plain,
! [SV980: $i,SV376: $i] :
( ( ! [SY2983: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV376 )
| ( c_lessequals @ SV980 @ SY2983 @ SV376 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV980 @ SY2983 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3153,plain,
! [SV981: $i,SV377: $i] :
( ( ! [SY2984: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV377 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV981 @ SY2984 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
| ~ ( c_lessequals @ SV981 @ SY2984 @ SV377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3154,plain,
! [SV982: $i,SV378: $i] :
( ( ! [SY2985: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV378 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SV982 @ SY2985 @ SV378 ) @ SV378 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SV982 @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3155,plain,
! [SV983: $i,SV379: $i] :
( ( ! [SY2986: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV379 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SV983 @ SY2986 @ SV379 ) @ SV379 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SV983 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3156,plain,
! [SV984: $i,SV380: $i] :
( ( ! [SY2987: $i,SY2988: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV380 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SY2987 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SY2988 @ SY2987 @ SV380 ) @ SV380 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
| ~ ( c_lessequals @ SV984 @ SY2988 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3157,plain,
! [SV985: $i,SV381: $i] :
( ( ! [SY2989: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV381 )
| ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
| ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SY2989 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3158,plain,
! [SV986: $i,SV382: $i] :
( ( ! [SY2990: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV382 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SY2990 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SY2990 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3159,plain,
! [SV987: $i,SV383: $i] :
( ( ! [SY2991: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV383 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SY2991 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SY2991 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3160,plain,
! [SV988: $i,SV384: $i] :
( ( ! [SY2992: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV384 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SV988 @ SY2992 @ SV384 ) @ SV384 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SV988 @ SV384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3161,plain,
! [SV385: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV385 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV385 ) @ ( c_HOL_Ozero__class_Ozero @ SV385 ) @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(3162,plain,
! [SV989: $i,SV386: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV386 @ SV989 @ tc_nat ) @ tc_nat )
| ( SV989
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3163,plain,
! [SV990: $i,SV387: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV387 @ SV990 @ tc_nat ) @ tc_nat )
| ( SV387
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3164,plain,
! [SV991: $i,SV388: $i] :
( ( ! [SY2993: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV388 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV991 @ SY2993 @ SV388 ) @ SV388 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV991 @ SV388 ) @ SY2993 @ SV388 ) )
| ( SV991
= ( c_HOL_Ozero__class_Ozero @ SV388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3165,plain,
! [SV992: $i,SV389: $i] :
( ( ! [SY2994: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ SV389 @ ( c_GCD_Ogcd__class_Ogcd @ SV992 @ SY2994 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV992 @ ( c_GCD_Ogcd__class_Ogcd @ SV389 @ SY2994 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3166,plain,
! [SV993: $i,SV390: $i] :
( ( ! [SY2995: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV390 @ SV993 @ tc_nat ) @ SY2995 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV390 @ ( c_GCD_Ogcd__class_Ogcd @ SV993 @ SY2995 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3167,plain,
! [SV994: $i,SV391: $i] :
( ( ! [SY2996: $i] :
( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV391 @ SV994 @ tc_nat ) @ SY2996 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV391 @ ( c_GCD_Ogcd__class_Ogcd @ SV994 @ SY2996 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3168,plain,
! [SV995: $i,SV392: $i] :
( ( ( SV392 = SV995 )
| ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV995 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV392 @ SV995 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3169,plain,
! [SV996: $i,SV393: $i] :
( ( ( SV393 = SV996 )
| ~ ( c_HOL_Oord__class_Oless @ SV996 @ ( c_Suc @ SV393 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV996 @ SV393 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3170,plain,
! [SV997: $i,SV394: $i] :
( ( ( SV394 = SV997 )
| ( c_HOL_Oord__class_Oless @ SV394 @ SV997 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ ( c_Suc @ SV997 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3171,plain,
! [SV998: $i,SV396: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV396 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV998 @ ( c_HOL_Ozero__class_Ozero @ SV396 ) @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3172,plain,
! [SV999: $i,SV398: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV398 )
| ( ( c_Divides_Odiv__class_Omod @ SV999 @ ( c_HOL_Oone__class_Oone @ SV398 ) @ SV398 )
= ( c_HOL_Ozero__class_Ozero @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3173,plain,
! [SV1000: $i,SV399: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ ( c_HOL_Oplus__class_Oplus @ SV1000 @ SV399 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ SV1000 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3174,plain,
! [SV1001: $i,SV400: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ SV1001 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ ( c_HOL_Oplus__class_Oplus @ SV1001 @ SV400 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3175,plain,
! [SV1002: $i,SV401: $i] :
( ( ~ ( class_Orderings_Oorder @ SV401 )
| ~ ( c_HOL_Oord__class_Oless @ SV1002 @ SV1002 @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3176,plain,
! [SV402: $i] :
( ( c_HOL_Oord__class_Oless @ SV402 @ SV402 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(3177,plain,
! [SV403: $i] :
( ( c_HOL_Oord__class_Oless @ SV403 @ SV403 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(3178,plain,
! [SV1003: $i,SV404: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV404 )
| ~ ( c_HOL_Oord__class_Oless @ SV1003 @ SV1003 @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3179,plain,
! [SV1004: $i,SV405: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ SV1004 @ SV1004 @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3180,plain,
! [SV1005: $i,SV406: $i] :
( ( ! [SY2997: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SY2997 @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SY2997 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3181,plain,
! [SV1006: $i,SV407: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV407 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3182,plain,
! [SV1007: $i,SV408: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV408 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3183,plain,
! [SV1008: $i,SV409: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV409 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1008 @ SV409 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3184,plain,
! [SV1009: $i,SV410: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SV1009 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1009 @ SV410 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1009 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3185,plain,
! [SV1010: $i,SV411: $i] :
( ( ! [SY2998: $i,SY2999: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY2998 @ SY2999 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SY2999 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SY2998 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3186,plain,
! [SV1011: $i,SV412: $i] :
( ( ! [SY3000: $i,SY3001: $i,SY3002: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SY3000 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SY3001 @ SY3002 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SY3000 @ SY3002 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SY3001 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3187,plain,
! [SV1012: $i,SV413: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV413 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3188,plain,
! [SV1013: $i,SV414: $i] :
( ( ! [SY3003: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1013 @ SY3003 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ SY3003 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3189,plain,
! [SV1014: $i,SV415: $i] :
( ( ! [SY3004: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
| ( c_HOL_Oord__class_Oless @ SV1014 @ SY3004 @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1014 @ SY3004 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3190,plain,
! [SV1015: $i,SV416: $i] :
( ( ! [SY3005: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 )
| ( c_HOL_Oord__class_Oless @ SV1015 @ SY3005 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3005 @ SV416 ) @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3191,plain,
! [SV1016: $i,SV417: $i] :
( ( ! [SY3006: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3006 @ SV417 ) @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1016 @ SY3006 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3192,plain,
! [SV418: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV418 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ ( c_HOL_Oone__class_Oone @ SV418 ) @ SV418 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(3193,plain,
! [SV1017: $i,SV419: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV419 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1017 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1017 @ SV419 ) @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3194,plain,
! [SV1018: $i,SV420: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV420 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV420 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1018 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1018 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3195,plain,
! [SV421: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV421 @ tc_nat )
= $true )
| ( ( SV421
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(3196,plain,
! [SV1019: $i,SV422: $i] :
( ( ! [SY3007: $i,SY3008: $i] :
( ~ ( class_Divides_Osemiring__div @ SV422 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SY3007 @ SV422 ) @ SY3008 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SY3008 @ SV422 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3008 @ SY3007 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3197,plain,
! [SV1020: $i,SV423: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV423 )
| ( c_lessequals @ SV1020 @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1020 @ SV1020 @ SV423 ) @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3198,plain,
! [SV1021: $i,SV424: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV424 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1021 @ SV1021 @ SV424 ) @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
| ~ ( c_lessequals @ SV1021 @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3199,plain,
! [SV1022: $i,SV425: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV425 @ SV1022 @ tc_nat ) @ SV1022 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3200,plain,
! [SV1023: $i,SV426: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV426 @ SV1023 @ tc_nat ) @ SV426 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3201,plain,
! [SV1024: $i,SV427: $i] :
( ( ! [SY3009: $i] :
( ( c_HOL_Oord__class_Oless @ SV427 @ ( c_HOL_Ominus__class_Ominus @ SV1024 @ SY3009 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV427 @ SY3009 @ tc_nat ) @ SV1024 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3202,plain,
! [SV1025: $i,SV428: $i] :
( ( ! [SY3010: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV428 @ SV1025 @ tc_nat ) @ SY3010 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV428 @ ( c_HOL_Ominus__class_Ominus @ SY3010 @ SV1025 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3203,plain,
! [SV1026: $i,SV429: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV429 @ SV1026 @ tc_nat )
= SV1026 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1026 @ SV429 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3204,plain,
! [SV1027: $i,SV430: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV430 @ SV1027 @ tc_nat )
= SV430 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV430 @ SV1027 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3205,plain,
! [SV1028: $i,SV431: $i] :
( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV431 ) @ SV1028 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV431 @ SV1028 @ tc_nat ) ) @ SV1028 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3206,plain,
! [SV1029: $i,SV432: $i] :
( ( ! [SY3011: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV432 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SY3011 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SY3011 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3207,plain,
! [SV1030: $i,SV433: $i] :
( ( ! [SY3012: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV433 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SY3012 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ SY3012 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3208,plain,
! [SV1031: $i,SV434: $i] :
( ( ! [SY3013: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV434 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SY3013 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SY3013 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3209,plain,
! [SV1032: $i,SV435: $i] :
( ( ! [SY3014: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV435 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SY3014 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SY3014 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3210,plain,
! [SV1033: $i,SV436: $i] :
( ( ! [SY3015: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1033 @ ( c_Power_Opower__class_Opower @ SV1033 @ SY3015 @ SV436 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3015 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3211,plain,
! [SV1034: $i,SV437: $i] :
( ( ! [SY3016: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV1034 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3016 @ SV1034 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV437 @ SY3016 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3212,plain,
! [SV1035: $i,SV438: $i] :
( ( ! [SY3017: $i] :
( ( c_HOL_Oord__class_Oless @ SV438 @ SV1035 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3017 @ SV438 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SY3017 @ SV1035 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3213,plain,
! [SV1036: $i,SV439: $i] :
( ( ! [SY3018: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1036 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SY3018 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1036 @ SY3018 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3214,plain,
! [SV1037: $i,SV440: $i] :
( ( ! [SY3019: $i,SY3020: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
| ( c_HOL_Oord__class_Oless @ SV1037 @ SY3019 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3020 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SY3020 @ SY3019 @ SV440 ) @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3215,plain,
! [SV1038: $i,SV441: $i] :
( ( ! [SY3021: $i,SY3022: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SY3021 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SY3022 @ SV441 ) @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SY3021 @ SY3022 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3216,plain,
! [SV1039: $i,SV442: $i] :
( ( ! [SY3023: $i,SY3024: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SY3023 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SY3024 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SY3023 @ SY3024 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3217,plain,
! [SV1040: $i,SV443: $i] :
( ( ! [SY3025: $i,SY3026: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
| ( c_HOL_Oord__class_Oless @ SV1040 @ SY3025 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SY3026 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SY3025 @ SY3026 @ SV443 ) @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3218,plain,
! [SV1041: $i,SV444: $i] :
( ( ! [SY3027: $i,SY3028: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SY3027 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SY3028 @ SY3027 @ SV444 ) @ SV444 )
| ~ ( c_HOL_Oord__class_Oless @ SV1041 @ SY3028 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3219,plain,
! [SV1042: $i,SV445: $i] :
( ( ! [SY3029: $i,SY3030: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SY3029 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SY3030 @ SY3029 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SY3030 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3220,plain,
! [SV1043: $i,SV446: $i] :
( ( ! [SY3031: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SY3031 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SY3031 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3221,plain,
! [SV1044: $i,SV447: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV447 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3222,plain,
! [SV1045: $i,SV448: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV448 @ SV1045 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1045 @ SV448 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3223,plain,
! [SV1046: $i,SV449: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV449 @ SV1046 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1046 @ SV449 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3224,plain,
! [SV1047: $i,SV450: $i] :
( ( ( SV450 = SV1047 )
| ~ ( c_HOL_Oord__class_Oless @ SV450 @ ( c_Suc @ SV1047 ) @ tc_nat )
| ~ ( c_lessequals @ SV1047 @ SV450 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3225,plain,
! [SV1048: $i,SV451: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV451 @ SV1048 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1048 @ ( c_Divides_Odiv__class_Omod @ SV451 @ SV1048 @ tc_nat ) @ tc_nat ) )
| ( SV1048
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3226,plain,
! [SV1049: $i,SV452: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV452 @ SV1049 @ tc_nat ) @ SV452 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV452 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1049 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3227,plain,
! [SV1050: $i,SV453: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV453 @ ( c_HOL_Ominus__class_Ominus @ SV1050 @ SV453 @ tc_nat ) @ tc_nat )
= SV1050 )
| ( c_HOL_Oord__class_Oless @ SV1050 @ SV453 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3228,plain,
! [SV1051: $i,SV454: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV454 @ ( c_Suc @ SV1051 ) @ tc_nat ) @ SV454 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV454 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3229,plain,
! [SV1052: $i,SV455: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV455 @ ( c_GCD_Ogcd__class_Ogcd @ SV455 @ SV1052 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV455 @ SV1052 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3230,plain,
! [SV1053: $i,SV456: $i] :
( ( ( c_lessequals @ SV456 @ SV1053 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1053 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV456 @ SV1053 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3231,plain,
! [SV1054: $i,SV457: $i] :
( ( ! [SY3032: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV457 @ SV1054 @ tc_nat ) @ SY3032 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3032 @ SV457 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV457 @ SY3032 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3232,plain,
! [SV1055: $i,SV458: $i] :
( ( ! [SY3033: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV458 @ SV1055 @ tc_nat ) @ SY3033 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3033 @ SV1055 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1055 @ SY3033 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3233,plain,
! [SV1056: $i,SV459: $i] :
( ( ! [SY3034: $i] :
( ~ ( class_Orderings_Opreorder @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SV1056 @ SY3034 @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SY3034 @ SV1056 @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3234,plain,
! [SV1057: $i,SV460: $i] :
( ( ! [SY3035: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3035 @ SV1057 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3035 @ SV460 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SY3035 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3235,plain,
! [SV1058: $i,SV461: $i] :
( ( ! [SY3036: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SY3036 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3036 @ SV1058 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SY3036 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3236,plain,
! [SV1059: $i,SV462: $i] :
( ( ! [SY3037: $i] :
( ~ ( class_Orderings_Opreorder @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1059 @ SY3037 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SY3037 @ SV1059 @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3237,plain,
! [SV1060: $i,SV463: $i] :
( ( ! [SY3038: $i] :
( ~ ( class_Orderings_Olinorder @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SV1060 @ SY3038 @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SY3038 @ SV1060 @ SV463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3238,plain,
! [SV1061: $i,SV464: $i] :
( ( ! [SY3039: $i] :
( ~ ( class_Orderings_Oorder @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SY3039 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SY3039 @ SV1061 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3239,plain,
! [SV1062: $i,SV465: $i] :
( ( ! [SY3040: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV465 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
| ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY3040 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3240,plain,
! [SV1063: $i,SV466: $i] :
( ( ! [SY3041: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV466 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
| ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SY3041 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SY3041 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3241,plain,
! [SV1064: $i,SV467: $i] :
( ( ! [SY3042: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV467 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SY3042 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY3042 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3242,plain,
! [SV1065: $i,SV468: $i] :
( ( ! [SY3043: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV468 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
| ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SY3043 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3243,plain,
! [SV1066: $i,SV469: $i] :
( ( ! [SY3044: $i,SY3045: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV469 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SY3044 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3045 @ SY3044 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SY3044 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SY3045 @ SV1066 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3244,plain,
! [SV1067: $i,SV470: $i] :
( ( ! [SY3046: $i,SY3047: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV470 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SY3046 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3047 @ SY3046 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SY3046 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SY3047 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3245,plain,
! [SV1068: $i,SV471: $i] :
( ( ! [SY3048: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV471 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SY3048 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SY3048 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3246,plain,
! [SV1069: $i,SV472: $i] :
( ( ! [SY3049: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV472 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SY3049 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SY3049 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3247,plain,
! [SV1070: $i,SV473: $i] :
( ( ! [SY3050: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV473 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
| ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3050 @ SV1070 @ SV473 ) @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3248,plain,
! [SV1071: $i,SV474: $i] :
( ( ! [SY3051: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV474 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
| ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SY3051 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SY3051 @ SV474 ) @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3249,plain,
! [SV1072: $i,SV475: $i] :
( ( ! [SY3052: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV475 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
| ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SY3052 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3052 @ SV1072 @ SV475 ) @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3250,plain,
! [SV1073: $i,SV476: $i] :
( ( ! [SY3053: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV476 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
| ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SY3053 @ SV476 ) @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3251,plain,
! [SV1074: $i,SV477: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV477 )
| ( ( c_Power_Opower__class_Opower @ SV1074 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV477 )
= ( c_HOL_Oone__class_Oone @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3252,plain,
! [SV1075: $i,SV478: $i] :
( ( ~ ( class_Power_Opower @ SV478 )
| ( ( c_Power_Opower__class_Opower @ SV1075 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV478 )
= ( c_HOL_Oone__class_Oone @ SV478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3253,plain,
! [SV1076: $i,SV479: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV479 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV479 ) @ SV1076 @ SV479 ) @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3254,plain,
! [SV1077: $i,SV480: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV480 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1077 @ SV480 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV480 ) @ SV1077 @ SV480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3255,plain,
! [SV1078: $i,SV481: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV481 )
| ~ ( class_Int_Onumber__ring @ SV481 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1078 @ SV481 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV481 ) @ SV1078 @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3256,plain,
! [SV1079: $i,SV482: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV482 )
| ( SV1079
= ( c_HOL_Ozero__class_Ozero @ SV482 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1079 @ SV1079 @ SV482 )
= ( c_HOL_Oone__class_Oone @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3257,plain,
! [SV1080: $i,SV483: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV483 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1080 @ SV1080 @ SV483 )
= ( c_HOL_Oone__class_Oone @ SV483 ) )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3258,plain,
! [SV1081: $i,SV484: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV484 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV484 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1081 @ SV1081 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
| ( SV1081
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3259,plain,
! [SV1082: $i,SV485: $i] :
( ( ! [SY3054: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV485 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1082 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3054 @ SV485 ) @ SV485 )
| ~ ( c_lessequals @ SV1082 @ SY3054 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3260,plain,
! [SV1083: $i,SV486: $i] :
( ( ! [SY3055: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV486 )
| ( c_lessequals @ SV1083 @ SY3055 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1083 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3055 @ SV486 ) @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3261,plain,
! [SV1084: $i,SV487: $i] :
( ( ! [SY3056: $i] :
( ~ ( class_SEQ_Obanach @ SV487 )
| ~ ( class_RealVector_Oreal__normed__field @ SV487 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SV1084 @ SY3056 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SV1084 @ SV487 ) @ ( c_Transcendental_Oexp @ SY3056 @ SV487 ) @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3262,plain,
! [SV1085: $i,SV488: $i] :
( ( ! [SY3057: $i,SY3058: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1085 @ SY3057 @ SV488 ) @ SY3058 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1085 @ SY3058 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SY3057 @ SY3058 @ SV488 ) @ SV488 ) )
| ( SY3057
= ( c_HOL_Ozero__class_Ozero @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3263,plain,
! [SV1086: $i,SV489: $i] :
( ( ! [SY3059: $i,SY3060: $i,SY3061: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SY3059 @ SV489 ) @ SY3060 @ SV489 )
| ~ ( c_lessequals @ SY3059 @ SY3061 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SY3061 @ SV489 ) @ SY3060 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3264,plain,
! [SV1087: $i,SV490: $i] :
( ( ! [SY3062: $i,SY3063: $i,SY3064: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SY3062 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SY3063 @ SY3064 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SY3062 @ SY3064 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SY3063 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3265,plain,
! [SV1088: $i,SV491: $i] :
( ( ! [SY3065: $i,SY3066: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SY3065 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SY3066 @ SV491 ) @ SV491 )
| ~ ( c_lessequals @ SY3065 @ SY3066 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3266,plain,
! [SV1089: $i,SV492: $i] :
( ( ! [SY3067: $i,SY3068: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV492 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SY3067 @ SY3068 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SY3068 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SY3067 @ SV492 ) @ SV492 ) )
| ~ ( c_lessequals @ SY3068 @ SY3067 @ tc_nat )
| ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3267,plain,
! [SV1090: $i,SV493: $i] :
( ( ! [SY3069: $i] :
( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SY3069 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SY3069 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3069 @ SV1090 @ tc_nat )
| ~ ( c_lessequals @ SY3069 @ SV493 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3268,plain,
! [SV1091: $i,SV494: $i] :
( ( ! [SY3070: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3070 @ SV1091 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ SY3070 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SY3070 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3269,plain,
! [SV1092: $i,SV495: $i] :
( ( ! [SY3071: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV495 @ ( c_HOL_Ominus__class_Ominus @ SV1092 @ SY3071 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV495 @ SV1092 @ tc_nat ) @ SY3071 @ tc_nat ) )
| ~ ( c_lessequals @ SY3071 @ SV1092 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3270,plain,
! [SV1093: $i,SV496: $i] :
( ( ! [SY3072: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV496 @ SV1093 @ tc_nat ) @ SY3072 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV496 @ SY3072 @ tc_nat ) @ SV1093 @ tc_nat ) )
| ~ ( c_lessequals @ SV1093 @ SV496 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3271,plain,
! [SV1094: $i,SV497: $i] :
( ( ~ ( c_lessequals @ SV497 @ SV1094 @ tc_nat )
| ( SV1094
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1094 @ SV497 @ tc_nat ) @ SV497 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3272,plain,
! [SV1095: $i,SV498: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV498 @ ( c_HOL_Ominus__class_Ominus @ SV1095 @ SV498 @ tc_nat ) @ tc_nat )
= SV1095 )
| ~ ( c_lessequals @ SV498 @ SV1095 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3273,plain,
! [SV1096: $i,SV499: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV499 @ SV1096 @ tc_nat ) @ SV1096 @ tc_nat )
= SV499 )
| ~ ( c_lessequals @ SV1096 @ SV499 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3274,plain,
! [SV1097: $i,SV500: $i] :
( ( ~ ( c_lessequals @ SV500 @ ( c_HOL_Oplus__class_Oplus @ SV1097 @ SV500 @ tc_nat ) @ tc_nat )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1097 @ SV500 @ tc_nat ) @ SV500 @ tc_nat )
= SV1097 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3275,plain,
! [SV1098: $i,SV501: $i] :
( ( ! [SY3073: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV501 @ ( c_HOL_Ominus__class_Ominus @ SV1098 @ SY3073 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SY3073 @ tc_nat ) @ SV1098 @ tc_nat ) )
| ~ ( c_lessequals @ SY3073 @ SV1098 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3276,plain,
! [SV1099: $i,SV502: $i] :
( ( ! [SY3074: $i] :
( ( c_lessequals @ SV502 @ ( c_HOL_Oplus__class_Oplus @ SV1099 @ SY3074 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV502 @ SY3074 @ tc_nat ) @ SV1099 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(3277,plain,
! [SV1100: $i,SV503: $i] :
( ( ! [SY3075: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV503 @ SV1100 @ tc_nat ) @ SY3075 @ tc_nat )
| ~ ( c_lessequals @ SV503 @ ( c_HOL_Oplus__class_Oplus @ SY3075 @ SV1100 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3278,plain,
! [SV1101: $i,SV504: $i] :
( ( ! [SY3076: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
| ~ ( c_lessequals @ SY3076 @ SV1101 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SY3076 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SY3076 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3279,plain,
! [SV1102: $i,SV505: $i] :
( ( ! [SY3077: $i] :
( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
| ~ ( c_lessequals @ SV1102 @ SY3077 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SY3077 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SY3077 @ SV1102 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3280,plain,
! [SV1103: $i,SV506: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV506 @ SV1103 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV506 @ SV1103 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3281,plain,
! [SV1104: $i,SV507: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV507 @ SV1104 @ tc_nat ) @ SV1104 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV507 @ SV1104 @ tc_nat ) )
| ~ ( c_lessequals @ SV1104 @ SV507 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3282,plain,
! [SV1105: $i,SV508: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV508 @ SV1105 @ tc_nat ) @ SV508 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1105 @ SV508 @ tc_nat ) )
| ~ ( c_lessequals @ SV1105 @ SV508 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3283,plain,
! [SV1106: $i,SV509: $i] :
( ( ! [SY3078: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV509 @ SV1106 @ tc_nat ) @ SY3078 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ominus__class_Ominus @ SV1106 @ SY3078 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SY3078 @ SV1106 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3284,plain,
! [SV1107: $i,SV510: $i] :
( ( ! [SY3079: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV510 @ SV1107 @ tc_nat ) @ SY3079 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV510 @ SY3079 @ tc_nat ) @ SV1107 @ tc_nat ) )
| ~ ( c_lessequals @ SY3079 @ SV510 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3285,plain,
! [SV1108: $i,SV511: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV511 @ SV1108 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV511 @ SV1108 @ tc_nat ) @ SV1108 @ tc_nat ) )
| ~ ( c_lessequals @ SV1108 @ SV511 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3286,plain,
! [SV1109: $i,SV512: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV512 ) @ SV1109 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV512 @ SV1109 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV1109 @ SV512 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3287,plain,
! [SV1110: $i,SV513: $i] :
( ( ! [SY3080: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SV1110 @ tc_nat ) @ SY3080 @ tc_nat )
| ~ ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SY3080 @ SV1110 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1110 @ SY3080 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3288,plain,
! [SV1111: $i,SV514: $i] :
( ( ! [SY3081: $i] :
( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SV1111 @ SY3081 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SY3081 @ tc_nat ) @ SV1111 @ tc_nat )
| ~ ( c_lessequals @ SY3081 @ SV1111 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3289,plain,
! [SV1112: $i,SV515: $i] :
( ( ! [SY3082: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV1112 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3082 @ SV1112 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1112 @ SV515 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV515 @ SY3082 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3290,plain,
! [SV1113: $i,SV516: $i] :
( ( ! [SY3083: $i] :
( ( c_lessequals @ SV516 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1113 @ SV516 @ tc_nat ) @ SY3083 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3083 @ SV1113 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3291,plain,
! [SV1114: $i,SV517: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV517 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
| ~ ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3292,plain,
! [SV1115: $i,SV518: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV518 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
| ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3293,plain,
! [SV1116: $i,SV519: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV519 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3294,plain,
! [SV1117: $i,SV520: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV520 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3295,plain,
! [SV1118: $i,SV521: $i] :
( ( ! [SY3084: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV521 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SY3084 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1118 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3084 @ SV521 ) @ SV521 ) )
| ~ ( c_lessequals @ SY3084 @ SV1118 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3296,plain,
! [SV1119: $i,SV522: $i] :
( ( ! [SY3085: $i,SY3086: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV522 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SY3085 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SY3086 @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SY3086 @ SY3085 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3297,plain,
! [SV1120: $i,SV523: $i] :
( ( ! [SY3087: $i,SY3088: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV523 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SY3087 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SY3088 @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SY3087 @ SY3088 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3298,plain,
! [SV1121: $i,SV524: $i] :
( ( ! [SY3089: $i,SY3090: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV524 )
| ( c_lessequals @ SV1121 @ SY3089 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3090 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SY3090 @ SY3089 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SY3090 @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3299,plain,
! [SV1122: $i,SV525: $i] :
( ( ! [SY3091: $i,SY3092: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV525 )
| ( c_lessequals @ SV1122 @ SY3091 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3092 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SY3092 @ SY3091 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SY3092 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3300,plain,
! [SV1123: $i,SV526: $i] :
( ( ! [SY3093: $i,SY3094: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV526 )
| ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SY3093 @ SY3094 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SY3093 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SY3094 @ SV526 ) @ SV526 ) )
| ~ ( c_lessequals @ SY3094 @ SY3093 @ tc_nat )
| ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3301,plain,
! [SV1124: $i,SV527: $i] :
( ( ( c_lessequals @ SV527 @ SV1124 @ tc_nat )
| ( c_lessequals @ SV1124 @ SV527 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3302,plain,
! [SV1125: $i,SV528: $i] :
( ( ! [SY3095: $i] :
( ~ ( class_Orderings_Olinorder @ SV528 )
| ( c_lessequals @ SV1125 @ SY3095 @ SV528 )
| ( c_lessequals @ SY3095 @ SV1125 @ SV528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3303,plain,
! [SV1126: $i,SV529: $i] :
( ( ! [SY3096: $i,SY3097: $i] :
( ~ ( class_Orderings_Oorder @ SV529 )
| ( c_lessequals @ SV1126 @ SY3096 @ SV529 )
| ~ ( c_lessequals @ SV1126 @ SY3097 @ SV529 )
| ~ ( c_lessequals @ SY3097 @ SY3096 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3304,plain,
! [SV1127: $i,SV530: $i] :
( ( ! [SY3098: $i,SY3099: $i] :
( ~ ( class_Orderings_Opreorder @ SV530 )
| ( c_lessequals @ SV1127 @ SY3098 @ SV530 )
| ~ ( c_lessequals @ SY3099 @ SY3098 @ SV530 )
| ~ ( c_lessequals @ SV1127 @ SY3099 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3305,plain,
! [SV1128: $i,SV532: $i] :
( ( ! [SY3100: $i] :
( ( c_lessequals @ SV532 @ SV1128 @ tc_nat )
| ~ ( c_lessequals @ SY3100 @ SV1128 @ tc_nat )
| ~ ( c_lessequals @ SV532 @ SY3100 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3306,plain,
! [SV1129: $i,SV534: $i] :
( ( ~ ( class_Orderings_Oorder @ SV534 )
| ( c_lessequals @ SV1129 @ SV1129 @ SV534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3307,plain,
! [SV1130: $i,SV535: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV535 )
| ( c_lessequals @ SV1130 @ SV1130 @ SV535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3308,plain,
! [SV1131: $i,SV536: $i] :
( ( ! [SY3101: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SV1131 @ SY3101 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SV1131 @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3309,plain,
! [SV1132: $i,SV537: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV537 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV537 ) @ SV1132 @ SV537 )
= ( c_HOL_Oone__class_Oone @ SV537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3310,plain,
! [SV1133: $i,SV538: $i] :
( ( ! [SY3102: $i,SY3103: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV538 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SY3102 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SY3103 @ SV538 ) @ SV538 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
| ~ ( c_lessequals @ SY3102 @ SY3103 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3311,plain,
! [SV1134: $i,SV539: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV539 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1134 @ ( c_HOL_Oone__class_Oone @ SV539 ) @ SV539 )
= SV1134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3312,plain,
! [SV1135: $i,SV540: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV540 @ SV1135 @ tc_nat ) @ tc_nat )
= SV1135 )
| ~ ( c_lessequals @ SV1135 @ SV540 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3313,plain,
! [SV1136: $i,SV541: $i] :
( ( ! [SY3104: $i] :
( ~ ( class_Orderings_Oorder @ SV541 )
| ( SV1136 = SY3104 )
| ~ ( c_lessequals @ SV1136 @ SY3104 @ SV541 )
| ~ ( c_lessequals @ SY3104 @ SV1136 @ SV541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3314,plain,
! [SV1137: $i,SV542: $i] :
( ( ( SV542 = SV1137 )
| ~ ( c_lessequals @ SV1137 @ SV542 @ tc_nat )
| ~ ( c_lessequals @ SV542 @ SV1137 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3315,plain,
! [SV1138: $i,SV543: $i] :
( ( ! [SY3105: $i] :
( ~ ( class_Orderings_Oorder @ SV543 )
| ( SV1138 = SY3105 )
| ~ ( c_lessequals @ SY3105 @ SV1138 @ SV543 )
| ~ ( c_lessequals @ SV1138 @ SY3105 @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3316,plain,
! [SV1139: $i,SV544: $i] :
( ( ! [SY3106: $i] :
( ~ ( class_Orderings_Oorder @ SV544 )
| ( SV1139 = SY3106 )
| ~ ( c_lessequals @ SY3106 @ SV1139 @ SV544 )
| ~ ( c_lessequals @ SV1139 @ SY3106 @ SV544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3317,plain,
! [SV1140: $i,SV545: $i] :
( ( ! [SY3107: $i,SY3108: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV545 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SY3107 @ SV545 ) @ SY3108 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SY3108 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SY3107 @ SY3108 @ SV545 ) @ SV545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3318,plain,
! [SV1141: $i,SV546: $i] :
( ( ! [SY3109: $i,SY3110: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV546 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1141 @ SY3109 @ SV546 ) @ SY3110 @ SV546 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1141 @ SY3110 @ SV546 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3109 @ SY3110 @ SV546 ) @ SV546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3319,plain,
! [SV1142: $i,SV547: $i] :
( ( ! [SY3111: $i,SY3112: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV547 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1142 @ SY3111 @ SV547 ) @ SY3112 @ SV547 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1142 @ SY3112 @ SV547 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3111 @ SY3112 @ SV547 ) @ SV547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3320,plain,
! [SV1143: $i,SV548: $i] :
( ( ! [SY3113: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV548 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV548 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SV1143 @ SY3113 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SV1143 @ SV548 ) @ SY3113 @ SV548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3321,plain,
! [SV1144: $i,SV549: $i] :
( ( ! [SY3114: $i] :
( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SY3114 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SY3114 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3114 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ SY3114 @ SV549 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3322,plain,
! [SV1145: $i,SV550: $i] :
( ( ! [SY3115: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3115 @ SV1145 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV550 @ SY3115 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SY3115 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3323,plain,
! [SV1146: $i,SV551: $i] :
( ( ! [SY3116: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV551 @ SV1146 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3116 @ SV1146 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV551 @ SY3116 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3324,plain,
! [SV1147: $i,SV552: $i] :
( ( ! [SY3117: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1147 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SY3117 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3117 @ SV1147 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3325,plain,
! [SV1148: $i,SV553: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV553 @ SV1148 @ tc_nat ) @ SV553 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3326,plain,
! [SV1149: $i,SV554: $i] :
( ( ! [SY3118: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV554 @ SV1149 @ tc_nat ) @ SY3118 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV554 @ SY3118 @ tc_nat ) @ SV1149 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3327,plain,
! [SV1150: $i,SV555: $i] :
( ( ! [SY3119: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1150 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3119 @ SV1150 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SY3119 @ tc_nat ) )
| ~ ( c_lessequals @ SV1150 @ SY3119 @ tc_nat )
| ~ ( c_lessequals @ SV1150 @ SV555 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3328,plain,
! [SV556: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV556 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2699]) ).
thf(3329,plain,
! [SV557: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV557 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV557 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(3330,plain,
! [SV558: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV558 ) )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV558 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(3331,plain,
! [SV559: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV559 ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(3332,plain,
! [SV560: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV560 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(3333,plain,
! [SV561: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV561 ) )
= $true )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV561 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2704]) ).
thf(3334,plain,
! [SV562: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV562 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(3335,plain,
! [SV563: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV563 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(3336,plain,
! [SV564: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV564 ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV564 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(3337,plain,
! [SV565: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV565 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(3338,plain,
! [SV566: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV566 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(3339,plain,
! [SV567: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV567 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV567 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2710]) ).
thf(3340,plain,
! [SV568: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV568 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(3341,plain,
! [SV569: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV569 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(3342,plain,
! [SV570: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV570 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__mult @ SV570 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(3343,plain,
! [SV571: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV571 ) )
= $true )
| ( ( class_OrderedGroup_Omonoid__add @ SV571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(3344,plain,
! [SV572: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV572 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV572 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(3345,plain,
! [SV573: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV573 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV573 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(3346,plain,
! [SV574: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV574 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV574 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(3347,plain,
! [SV575: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV575 ) )
= $true )
| ( ( class_Power_Opower @ SV575 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(3348,plain,
! [SV1151: $i,SV576: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV576 @ SV1151 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV576
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3349,plain,
! [SV1152: $i,SV577: $i] :
( ( ! [SY3120: $i,SY3121: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SY3120 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SY3121 @ SV577 ) )
| ( SY3120 = SY3121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3350,plain,
! [SV1153: $i,SV578: $i] :
( ( ! [SY3122: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 )
| ( ( c_Power_Opower__class_Opower @ SV1153 @ SY3122 @ SV578 )
!= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3351,plain,
! [SV1154: $i,SV579: $i] :
( ( ! [SY3123: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV579 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1154 @ SY3123 @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
| ( SV1154 = SY3123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3352,plain,
! [SV1155: $i,SV580: $i] :
( ( ( ( c_Suc @ SV580 )
!= ( c_Suc @ SV1155 ) )
| ( SV580 = SV1155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3353,plain,
! [SV581: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV581 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(3354,plain,
! [SV1156: $i,SV582: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV1156 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV582
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3355,plain,
! [SV1157: $i,SV583: $i] :
( ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV583 @ SV1157 @ tc_nat ) )
!= SV1157 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV583 ) @ SV1157 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3356,plain,
! [SV1158: $i,SV584: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV584 @ SV1158 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1158
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1158
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3357,plain,
! [SV585: $i] :
( ( SV585
= ( c_Suc @ SV585 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(3358,plain,
! [SV1159: $i,SV586: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV586 @ SV1159 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1159
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3359,plain,
! [SV1160: $i,SV587: $i] :
( ( ~ ( class_SEQ_Obanach @ SV587 )
| ~ ( class_RealVector_Oreal__normed__field @ SV587 )
| ( ( c_Transcendental_Oexp @ SV1160 @ SV587 )
!= ( c_HOL_Ozero__class_Ozero @ SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3360,plain,
! [SV1161: $i,SV588: $i] :
( ( ! [SY3124: $i,SY3125: $i,SY3126: $i,SY3127: $i] :
( ~ ( class_Divides_Osemiring__div @ SV588 )
| ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SY3124 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY3125 @ SY3124 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3126 @ SY3124 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY3127 @ SY3124 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3126 @ SV1161 @ SV588 ) @ SY3124 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3127 @ SY3125 @ SV588 ) @ SY3124 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3361,plain,
! [SV589: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV589 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(3362,plain,
! [SV1162: $i,SV590: $i] :
( ( ! [SY3128: $i,SY3129: $i,SY3130: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SY3128 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SY3129 @ SY3130 @ SV590 ) )
| ( c_lessequals @ SY3130 @ SY3129 @ SV590 )
| ~ ( c_lessequals @ SY3128 @ SV1162 @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3363,plain,
! [SV1163: $i,SV591: $i] :
( ( ( SV591
!= ( c_HOL_Oplus__class_Oplus @ SV591 @ SV1163 @ tc_nat ) )
| ( SV1163
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3364,plain,
! [SV1164: $i,SV592: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV592 @ SV1164 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1164
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3365,plain,
! [SV1165: $i,SV593: $i] :
( ( ! [SY3131: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV593 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY3131 @ SV593 ) )
| ( SV1165 = SY3131 )
| ( SY3131
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3366,plain,
! [SV1166: $i,SV594: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV594 @ SV1166 @ tc_nat ) )
| ( SV1166
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1166
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3367,plain,
! [SV1167: $i,SV595: $i] :
( ( ! [SY3132: $i,SY3133: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SY3132 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SY3133 @ SY3132 @ SV595 ) )
| ( SV1167 = SY3133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3368,plain,
! [SV1168: $i,SV596: $i] :
( ( ! [SY3134: $i,SY3135: $i,SY3136: $i,SY3137: $i] :
( ~ ( class_Divides_Oring__div @ SV596 )
| ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SY3134 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY3135 @ SY3134 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3136 @ SY3134 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY3137 @ SY3134 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3136 @ SV1168 @ SV596 ) @ SY3134 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3137 @ SY3135 @ SV596 ) @ SY3134 @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3369,plain,
! [SV1169: $i,SV597: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV597 @ SV1169 @ tc_nat )
!= SV597 )
| ( SV1169
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3370,plain,
! [SV1170: $i,SV598: $i] :
( ( ! [SY3138: $i,SY3139: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV598 )
| ( ( c_Power_Opower__class_Opower @ SV1170 @ SY3138 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SY3139 @ SY3138 @ SV598 ) )
| ( SV1170 = SY3139 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3138 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SY3139 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3371,plain,
! [SV1171: $i,SV599: $i] :
( ( ! [SY3140: $i,SY3141: $i,SY3142: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SY3140 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SY3141 @ SY3142 @ SV599 ) )
| ( c_lessequals @ SY3140 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SY3142 @ SY3141 @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3372,plain,
! [SV1172: $i,SV600: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV600 @ SV1172 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV600
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3373,plain,
! [SV1173: $i,SV601: $i] :
( ( ! [SY3143: $i,SY3144: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY3143 @ SY3144 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3143 @ SV1173 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV601 @ SY3144 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3374,plain,
! [SV1174: $i,SV602: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV602 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
| ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3375,plain,
! [SV1175: $i,SV603: $i] :
( ( ! [SY3145: $i,SY3146: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV603 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SY3145 @ SY3146 @ SV603 ) )
| ( SY3145 = SY3146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3376,plain,
! [SV1176: $i,SV604: $i] :
( ( ! [SY3147: $i,SY3148: $i,SY3149: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV604 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SY3147 @ SY3148 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SY3147 @ SY3149 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SY3148 @ SV604 )
= SY3149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3377,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
!= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3378,plain,
! [SV1177: $i,SV605: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV605 @ SV1177 @ tc_nat ) )
| ( SV605
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV605
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3379,plain,
! [SV1178: $i,SV606: $i] :
( ( ! [SY3150: $i] :
( ~ ( class_Divides_Osemiring__div @ SV606 )
| ( ( c_Divides_Odiv__class_Omod @ SV1178 @ SY3150 @ SV606 )
!= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SY3150 @ SV1178 @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3380,plain,
! [SV1179: $i,SV607: $i] :
( ( ! [SY3151: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1179 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV607 @ SY3151 @ tc_nat ) )
| ( SV1179 = SY3151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3381,plain,
! [SV1180: $i,SV608: $i] :
( ( ! [SY3152: $i,SY3153: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SY3152 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SY3153 @ SV608 ) )
| ( SY3152 = SY3153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3382,plain,
! [SV609: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV609 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV609 )
!= ( c_HOL_Ozero__class_Ozero @ SV609 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(3383,plain,
! [SV1181: $i,SV610: $i] :
( ( ! [SY3154: $i,SY3155: $i,SY3156: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SY3154 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SY3155 @ SY3156 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SY3155 @ SY3156 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SY3154 @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3384,plain,
! [SV1182: $i,SV611: $i] :
( ( ! [SY3157: $i] :
( ~ ( class_Ring__and__Field_Odivision__ring @ SV611 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SY3157 @ SV611 ) )
| ( SV1182 = SY3157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3385,plain,
! [SV1183: $i,SV612: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV612 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1183 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1183
= ( c_HOL_Ozero__class_Ozero @ SV612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3386,plain,
( ( ( class_Ring__and__Field_Ofield @ t_a )
= $false )
| ( ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(3387,plain,
! [SV1184: $i,SV613: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1184 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV613 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1184 = SV613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3388,plain,
! [SV1185: $i,SV614: $i] :
( ( ! [SY3158: $i,SY3159: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV614 )
| ( ( c_Power_Opower__class_Opower @ SV1185 @ SY3158 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SV1185 @ SY3159 @ SV614 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SY3158 = SY3159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3389,plain,
! [SV615: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV615 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV615 )
!= ( c_HOL_Oone__class_Oone @ SV615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(3390,plain,
! [SV1186: $i,SV616: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ SV1186 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV616 @ SV1186 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3391,plain,
! [SV1187: $i,SV617: $i] :
( ( ! [SY3160: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV617 )
| ~ ( class_Int_Onumber__ring @ SV617 )
| ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SY3160 @ SV617 ) )
| ( SY3160
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3392,plain,
! [SV1188: $i,SV618: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV618 @ SV1188 @ tc_nat ) )
| ( SV1188
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV618
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3393,plain,
! [SV1189: $i,SV619: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV619 @ SV1189 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1189
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3394,plain,
! [SV1190: $i,SV620: $i] :
( ( ! [SY3161: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV620 )
| ~ ( class_Int_Onumber__ring @ SV620 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SY3161 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SV1190 = SY3161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3395,plain,
! [SV621: $i] :
( ( ( c_Suc @ SV621 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(3396,plain,
! [SV1191: $i,SV622: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV622 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1191 @ SV1191 @ SV622 )
!= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
| ( SV1191
= ( c_HOL_Ozero__class_Ozero @ SV622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3397,plain,
! [SV1192: $i,SV623: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV623 @ SV1192 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1192
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3398,plain,
! [SV1193: $i,SV624: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV624 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3399,plain,
! [SV1194: $i,SV625: $i] :
( ( ! [SY3162: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV625 @ SV1194 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SY3162 @ SV1194 @ tc_nat ) )
| ( SV625 = SY3162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3400,plain,
! [SV626: $i] :
( ( ( c_Suc @ SV626 )
= SV626 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(3401,plain,
( ( ( class_Ring__and__Field_Ofield @ t_a )
= $false )
| ( ( v_a
!= ( c_HOL_Ozero__class_Ozero @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(3402,plain,
! [SV1195: $i,SV627: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV627 @ SV1195 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3403,plain,
! [SV1196: $i,SV628: $i] :
( ( ! [SY3163: $i,SY3164: $i,SY3165: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SY3163 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SY3164 @ SY3165 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV1196 @ SY3163 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SY3164 @ SY3165 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3404,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
= $false )
| ( ( ~ ( c_lessequals @ v_n @ v_m @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(3405,plain,
! [SV1197: $i,SV629: $i] :
( ( ( ( c_Suc @ SV629 )
!= ( c_Suc @ SV1197 ) )
| ( SV629 = SV1197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3406,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
= $false )
| ( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(3407,plain,
! [SV1198: $i,SV630: $i] :
( ( ! [SY3166: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV630 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1198 @ SY3166 @ SV630 )
!= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
| ( SV1198 = SY3166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3408,plain,
! [SV1199: $i,SV631: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV631 @ SV1199 @ tc_nat )
!= SV631 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV631 @ SV1199 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3409,plain,
! [SV1200: $i,SV632: $i] :
( ( ! [SY3167: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SY3167 @ SV632 )
!= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SY3167 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SY3167
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3410,plain,
! [SV1201: $i,SV633: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV633 )
| ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3411,plain,
! [SV1202: $i,SV634: $i] :
( ( ! [SY3168: $i,SY3169: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV634 )
| ~ ( class_Int_Onumber__ring @ SV634 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SY3168 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SY3169 @ SV634 ) )
| ( SY3168 = SY3169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3412,plain,
! [SV1203: $i,SV635: $i] :
( ( ! [SY3170: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY3170 @ SV1203 @ tc_nat ) )
| ~ ( c_lessequals @ SV1203 @ SY3170 @ tc_nat )
| ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
| ( SV635 = SY3170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3413,plain,
! [SV1204: $i,SV636: $i] :
( ( ! [SY3171: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1204 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV636 @ SY3171 @ tc_nat ) )
| ( SV1204 = SY3171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3414,plain,
! [SV1205: $i,SV637: $i] :
( ( ! [SY3172: $i,SY3173: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV637 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SY3172 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SY3173 @ SY3173 @ SV637 ) )
| ( SV1205 = SY3172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3415,plain,
! [SV1206: $i,SV638: $i] :
( ( ! [SY3174: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SY3174 @ SV638 )
!= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SY3174 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3416,plain,
! [SV1207: $i,SV639: $i] :
( ( ! [SY3175: $i,SY3176: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SY3175 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SY3176 @ ( c_Suc @ SY3175 ) @ SV639 ) )
| ( SV1207 = SY3176 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SY3176 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3417,plain,
! [SV1208: $i,SV640: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV640 @ SV1208 @ tc_nat ) )
| ( SV640
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1208
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3418,plain,
! [SV1209: $i,SV641: $i] :
( ( ! [SY3177: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SY3177 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3419,plain,
! [SV642: $i] :
( ( ( c_Suc @ SV642 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3420,plain,
! [SV1210: $i,SV643: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV643 @ SV1210 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1210
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3421,plain,
! [SV1211: $i,SV644: $i] :
( ( ! [SY3178: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV644 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SY3178 @ SV644 )
!= ( c_HOL_Oone__class_Oone @ SV644 ) )
| ( SY3178
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SV1211 = SY3178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3422,plain,
! [SV1212: $i,SV645: $i] :
( ( ! [SY3179: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV645 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV645 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY3179 @ SV645 ) )
| ( SV1212 = SY3179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3423,plain,
! [SV1213: $i,SV646: $i,SV1: $i] :
( ( ! [SY3180: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV1 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV646 @ SV1213 @ SV1 ) @ SY3180 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV646 @ ( c_HOL_Oplus__class_Oplus @ SV1213 @ SY3180 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3424,plain,
! [SV1214: $i,SV647: $i,SV2: $i] :
( ( ! [SY3181: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Oplus__class_Oplus @ SV647 @ ( c_HOL_Oplus__class_Oplus @ SV1214 @ SY3181 @ SV2 ) @ SV2 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV647 @ SV1214 @ SV2 ) @ SY3181 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3425,plain,
! [SV1215: $i,SV648: $i,SV3: $i] :
( ( ! [SY3182: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV3 )
| ( ( c_HOL_Oplus__class_Oplus @ SV648 @ ( c_HOL_Oplus__class_Oplus @ SV1215 @ SY3182 @ SV3 ) @ SV3 )
= ( c_HOL_Oplus__class_Oplus @ SV1215 @ ( c_HOL_Oplus__class_Oplus @ SV648 @ SY3182 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3426,plain,
! [SV1216: $i,SV649: $i,SV4: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV4 @ SV649 @ tc_nat ) @ SV1216 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV4 @ ( c_HOL_Oplus__class_Oplus @ SV649 @ SV1216 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3427,plain,
! [SV1217: $i,SV650: $i,SV5: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV5 @ ( c_HOL_Oplus__class_Oplus @ SV650 @ SV1217 @ tc_nat ) @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV650 @ ( c_HOL_Oplus__class_Oplus @ SV5 @ SV1217 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3428,plain,
! [SV1218: $i,SV651: $i,SV6: $i] :
( ( ! [SY3183: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV6 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV1218 @ SV6 ) @ SY3183 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ SV651 @ ( c_HOL_Oplus__class_Oplus @ SV1218 @ SY3183 @ SV6 ) @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3429,plain,
! [SV1219: $i,SV652: $i,SV7: $i] :
( ( ! [SY3184: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
| ( ( c_HOL_Oplus__class_Oplus @ SV652 @ ( c_HOL_Oplus__class_Oplus @ SV1219 @ SY3184 @ SV7 ) @ SV7 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV652 @ SV1219 @ SV7 ) @ SY3184 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3430,plain,
! [SV1220: $i,SV653: $i,SV8: $i] :
( ( ! [SY3185: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV8 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1220 @ SV8 ) @ SY3185 @ SV8 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SY3185 @ SV8 ) @ SV1220 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3431,plain,
! [SV1221: $i,SV654: $i,SV9: $i] :
( ( ! [SY3186: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( c_HOL_Oplus__class_Oplus @ SV654 @ ( c_HOL_Oplus__class_Oplus @ SV1221 @ SY3186 @ SV9 ) @ SV9 )
= ( c_HOL_Oplus__class_Oplus @ SV1221 @ ( c_HOL_Oplus__class_Oplus @ SV654 @ SY3186 @ SV9 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3432,plain,
! [SV1222: $i,SV655: $i,SV10: $i] :
( ( ! [SY3187: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV10 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV655 @ SV1222 @ SV10 ) @ SY3187 @ SV10 )
= ( c_HOL_Oplus__class_Oplus @ SV655 @ ( c_HOL_Oplus__class_Oplus @ SV1222 @ SY3187 @ SV10 ) @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3433,plain,
! [SV656: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV11 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV656 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV656 @ SV11 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3434,plain,
! [SV1223: $i,SV657: $i,SV13: $i] :
( ( ! [SY3188: $i] :
( ~ ( class_Divides_Osemiring__div @ SV13 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ SV1223 @ SV13 ) @ SY3188 @ SV13 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ ( c_Divides_Odiv__class_Omod @ SV1223 @ SY3188 @ SV13 ) @ SV13 ) @ SY3188 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3435,plain,
! [SV1224: $i,SV658: $i,SV14: $i] :
( ( ! [SY3189: $i] :
( ~ ( class_Divides_Osemiring__div @ SV14 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV658 @ SV1224 @ SV14 ) @ SY3189 @ SV14 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV658 @ SY3189 @ SV14 ) @ SV1224 @ SV14 ) @ SY3189 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3436,plain,
! [SV1225: $i,SV659: $i,SV15: $i] :
( ( ! [SY3190: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SY3190 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SY3190 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3437,plain,
! [SV1226: $i,SV661: $i,SV17: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 )
| ( c_HOL_Oord__class_Oless @ SV661 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV661 @ SV1226 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3438,plain,
! [SV18: $i] :
( ( ( SV18
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV18 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat ) )
= $true )
| ( ( SV18
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2811]) ).
thf(3439,plain,
! [SV662: $i,SV21: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV21 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(3440,plain,
! [SV1227: $i,SV663: $i,SV22: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV22 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3441,plain,
! [SV1228: $i,SV666: $i,SV25: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3442,plain,
! [SV1229: $i,SV667: $i,SV26: $i] :
( ( ! [SY3191: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SY3191 @ SV1229 @ SV26 ) @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SY3191 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3443,plain,
! [SV668: $i,SV27: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV27 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
| ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(3444,plain,
! [SV669: $i,SV28: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV28 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2819]) ).
thf(3445,plain,
! [SV670: $i,SV29: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV29 ) @ SV670 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV29 )
= SV670 )
| ~ ( c_HOL_Oord__class_Oless @ SV29 @ SV670 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(3446,plain,
! [SV671: $i,SV30: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV30 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
| ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(3447,plain,
! [SV672: $i,SV31: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV31 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV672 @ SV31 ) @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV672 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(3448,plain,
! [SV673: $i,SV32: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV32 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(3449,plain,
! [SV674: $i,SV33: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV33 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3450,plain,
! [SV675: $i,SV34: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV34 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV675 @ SV34 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(3451,plain,
! [SV1230: $i,SV676: $i,SV35: $i] :
( ( ! [SY3192: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SV676 @ ( c_HOL_Oplus__class_Oplus @ SV1230 @ SY3192 @ SV35 ) @ SV35 )
= ( c_HOL_Oplus__class_Oplus @ SV1230 @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SY3192 @ SV35 ) @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3452,plain,
! [SV1231: $i,SV677: $i,SV36: $i] :
( ( ! [SY3193: $i] :
( ~ ( class_Orderings_Opreorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SY3193 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SY3193 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3453,plain,
! [SV1232: $i,SV678: $i,SV37: $i] :
( ( ! [SY3194: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SY3194 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SY3194 @ SV1232 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3454,plain,
! [SV679: $i,SV38: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV38 ) )
= $true )
| ( ( ( SV679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV679 @ SV38 ) @ SV38 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(3455,plain,
! [SV1233: $i,SV680: $i,SV39: $i] :
( ( ! [SY3195: $i] :
( ~ ( class_Divides_Osemiring__div @ SV39 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV1233 @ SV39 ) @ SY3195 @ SV39 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV680 @ SY3195 @ SV39 ) @ ( c_Divides_Odiv__class_Omod @ SV1233 @ SY3195 @ SV39 ) @ SV39 ) @ SY3195 @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3456,plain,
! [SV40: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV40 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ ( c_HOL_Ozero__class_Ozero @ SV40 ) @ SV40 )
= ( c_HOL_Ozero__class_Ozero @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3457,plain,
! [SV41: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(3458,plain,
! [SV681: $i,SV42: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV42 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV42 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV42 ) @ SV42 )
= SV681 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(3459,plain,
! [SV682: $i,SV43: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV43 ) @ SV682 @ tc_nat )
= ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV43 @ SV682 @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV43 @ SV682 @ tc_nat ) )
= SV682 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3460,plain,
! [SV44: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV44 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV44
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(3461,plain,
! [SV683: $i,SV45: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV45 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ SV683 @ SV45 )
= ( c_HOL_Ozero__class_Ozero @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(3462,plain,
! [SV684: $i,SV46: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV46 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV46 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Suc @ SV684 ) @ SV46 )
= ( c_HOL_Ozero__class_Ozero @ SV46 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(3463,plain,
! [SV1234: $i,SV688: $i,SV50: $i] :
( ( ! [SY3196: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SY3196 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SY3196 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3464,plain,
! [SV1235: $i,SV689: $i,SV51: $i] :
( ( ! [SY3197: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
| ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SY3197 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SY3197 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3465,plain,
! [SV690: $i,SV52: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV52 @ SV690 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV52 ) @ SV690 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3466,plain,
! [SV691: $i,SV53: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV53 ) @ SV691 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV53 @ SV691 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3467,plain,
! [SV692: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV692 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV54 ) @ SV692 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3468,plain,
! [SV693: $i,SV55: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV55 ) @ SV693 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SV693 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(3469,plain,
! [SV1236: $i,SV694: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ ( c_HOL_Oplus__class_Oplus @ SV694 @ SV1236 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV1236 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3470,plain,
! [SV1237: $i,SV695: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1237 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV695 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3471,plain,
! [SV1238: $i,SV696: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV58 @ SV696 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV58 @ SV1238 @ tc_nat ) @ SV696 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3472,plain,
! [SV1239: $i,SV697: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1239 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV1239 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3473,plain,
! [SV1240: $i,SV698: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV60 @ ( c_HOL_Oplus__class_Oplus @ SV698 @ SV1240 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV60 @ SV698 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3474,plain,
! [SV1241: $i,SV699: $i,SV61: $i] :
( ( ! [SY3198: $i] :
( ~ ( class_Divides_Osemiring__div @ SV61 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SY3198 @ SV61 ) @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SY3198 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3475,plain,
! [SV1242: $i,SV700: $i,SV62: $i] :
( ( ! [SY3199: $i] :
( ~ ( class_Divides_Osemiring__div @ SV62 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SY3199 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SY3199 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3476,plain,
! [SV1243: $i,SV701: $i,SV63: $i] :
( ( ! [SY3200: $i] :
( ~ ( class_Divides_Osemiring__div @ SV63 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SY3200 @ SV63 ) @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SY3200 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3477,plain,
! [SV1244: $i,SV702: $i,SV64: $i] :
( ( ! [SY3201: $i] :
( ~ ( class_Divides_Osemiring__div @ SV64 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SY3201 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SY3201 @ SV64 ) @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3478,plain,
! [SV703: $i,SV65: $i] :
( ( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV65 @ SV703 @ tc_nat ) @ SV703 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV703 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2856]) ).
thf(3479,plain,
! [SV705: $i,SV67: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV67 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV705 @ SV705 @ SV67 ) @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
| ~ ( c_HOL_Oord__class_Oless @ SV705 @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3480,plain,
! [SV706: $i,SV68: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV68 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV706 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV706 @ SV706 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(3481,plain,
! [SV707: $i,SV69: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV69 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV707 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV707 @ SV707 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(3482,plain,
! [SV708: $i,SV70: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV70 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV708 @ SV708 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ SV708 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(3483,plain,
! [SV1245: $i,SV709: $i,SV72: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3484,plain,
! [SV1246: $i,SV710: $i,SV73: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3485,plain,
! [SV711: $i,SV74: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV74 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
| ~ ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(3486,plain,
! [SV712: $i,SV75: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV75 @ SV712 @ tc_nat )
= SV75 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV75 @ SV712 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(3487,plain,
! [SV1247: $i,SV713: $i,SV76: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV713 @ SV1247 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV1247 @ SV713 @ SV76 )
| ( SV1247 = SV713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3488,plain,
! [SV714: $i,SV77: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV77 @ SV714 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV714 @ SV77 @ tc_nat )
| ( SV714 = SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3489,plain,
! [SV715: $i,SV78: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV78 @ SV715 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV715 @ SV78 @ tc_nat )
| ( SV715 = SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3490,plain,
! [SV716: $i,SV79: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV79 @ SV716 @ tc_nat ) )
= $true )
| ( ( ( SV716 = SV79 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV716 @ SV79 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(3491,plain,
! [SV717: $i,SV80: $i] :
( ( ( SV80 = SV717 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV80 @ SV717 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV80 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2870]) ).
thf(3492,plain,
! [SV718: $i,SV81: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV81 @ SV718 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV718 @ SV81 @ tc_nat )
| ( SV718 = SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(3493,plain,
! [SV719: $i,SV82: $i] :
( ( ( SV82 = SV719 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV719 @ SV82 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV82 @ SV719 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2872]) ).
thf(3494,plain,
! [SV720: $i,SV83: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV83 @ SV720 @ tc_nat ) )
= $true )
| ( ( ( SV720 = SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV720 @ SV83 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3495,plain,
! [SV721: $i,SV84: $i] :
( ( ( SV84 = SV721 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV721 @ SV84 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV84 @ SV721 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3496,plain,
! [SV722: $i,SV85: $i] :
( ( ( SV85 = SV722 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV85 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV85 @ SV722 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3497,plain,
! [SV1248: $i,SV723: $i,SV86: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV723 @ SV1248 @ SV86 )
| ( SV1248 = SV723 )
| ( c_HOL_Oord__class_Oless @ SV1248 @ SV723 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3498,plain,
! [SV1249: $i,SV724: $i,SV87: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV87 )
| ( SV724 = SV1249 )
| ( c_HOL_Oord__class_Oless @ SV724 @ SV1249 @ SV87 )
| ( c_HOL_Oord__class_Oless @ SV1249 @ SV724 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3499,plain,
! [SV1250: $i,SV725: $i,SV88: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV88 )
| ( SV725 = SV1250 )
| ( c_HOL_Oord__class_Oless @ SV1250 @ SV725 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SV1250 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3500,plain,
! [SV1251: $i,SV726: $i,SV89: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV726 @ SV1251 @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV1251 @ SV726 @ SV89 )
| ( SV1251 = SV726 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3501,plain,
! [SV1252: $i,SV727: $i,SV90: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ SV727 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ ( c_GCD_Ogcd__class_Ogcd @ SV1252 @ SV727 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3502,plain,
! [SV1253: $i,SV728: $i,SV91: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ SV728 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ ( c_GCD_Ogcd__class_Ogcd @ SV728 @ SV1253 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3503,plain,
! [SV1254: $i,SV729: $i,SV92: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ SV729 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ ( c_GCD_Ogcd__class_Ogcd @ SV729 @ SV1254 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3504,plain,
! [SV1255: $i,SV730: $i,SV93: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ SV730 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ ( c_GCD_Ogcd__class_Ogcd @ SV1255 @ SV730 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3505,plain,
! [SV1256: $i,SV731: $i,SV94: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV94 @ SV731 @ tc_nat ) @ SV1256 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV1256 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3506,plain,
! [SV1257: $i,SV732: $i,SV95: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV95 @ SV732 @ tc_nat ) @ SV1257 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV732 @ SV1257 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3507,plain,
! [SV1258: $i,SV733: $i,SV96: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ SV733 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ ( c_GCD_Ogcd__class_Ogcd @ SV733 @ SV1258 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3508,plain,
! [SV1259: $i,SV734: $i,SV97: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ SV734 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ ( c_GCD_Ogcd__class_Ogcd @ SV1259 @ SV734 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3509,plain,
! [SV1260: $i,SV735: $i,SV98: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV735 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1260 @ SV735 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV1260 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3510,plain,
! [SV1261: $i,SV736: $i,SV99: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3511,plain,
! [SV737: $i,SV100: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV100 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV100 @ SV737 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV737 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(3512,plain,
! [SV738: $i,SV102: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV102 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV738 @ SV738 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3513,plain,
! [SV1262: $i,SV739: $i,SV103: $i] :
( ( ! [SY3202: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3202 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SY3202 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3514,plain,
! [SV1263: $i,SV740: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SV740 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1263 @ SV740 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV1263 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3515,plain,
! [SV741: $i,SV107: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV107 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV741 @ ( c_HOL_Oplus__class_Oplus @ SV741 @ ( c_HOL_Oone__class_Oone @ SV107 ) @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2894]) ).
thf(3516,plain,
! [SV742: $i,SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV108 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2895]) ).
thf(3517,plain,
! [SV743: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV109 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV109 )
| ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3518,plain,
! [SV744: $i,SV110: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV110 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV110 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV744 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3519,plain,
! [SV1264: $i,SV745: $i,SV111: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV111 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1264 @ SV111 ) @ SV745 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ SV1264 @ SV745 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3520,plain,
! [SV1265: $i,SV746: $i,SV112: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV112 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV746 @ SV1265 @ SV112 ) @ SV1265 @ SV112 )
= ( c_Divides_Odiv__class_Omod @ SV746 @ SV1265 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3521,plain,
! [SV1266: $i,SV747: $i,SV113: $i] :
( ( ! [SY3203: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SY3203 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY3203 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3522,plain,
! [SV748: $i,SV114: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV114 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
| ( SV748
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV748 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(3523,plain,
! [SV749: $i,SV115: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV115 @ SV749 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV115 @ SV749 @ tc_nat ) @ SV749 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV115 @ SV749 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(3524,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV116 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3525,plain,
! [SV1268: $i,SV751: $i,SV117: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV117 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
| ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3526,plain,
! [SV1269: $i,SV752: $i,SV118: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV118 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
| ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3527,plain,
! [SV1270: $i,SV753: $i,SV119: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV119 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3528,plain,
! [SV1271: $i,SV754: $i,SV120: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV120 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3529,plain,
! [SV1272: $i,SV755: $i,SV121: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV121 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3530,plain,
! [SV1273: $i,SV756: $i,SV122: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV122 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3531,plain,
! [SV123: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV123 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV123
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(3532,plain,
! [SV757: $i,SV124: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV124 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV757 @ SV124 ) @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(3533,plain,
! [SV758: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV125 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV758 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3534,plain,
! [SV759: $i,SV126: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV126 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV126 ) @ SV126 )
= SV759 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3535,plain,
! [SV760: $i,SV127: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV127 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV127 ) @ SV760 @ SV127 )
= SV760 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3536,plain,
! [SV761: $i,SV128: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV128 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 )
= SV761 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3537,plain,
! [SV762: $i,SV129: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV129 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV129 )
| ( SV762
= ( c_HOL_Oplus__class_Oplus @ SV762 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2916]) ).
thf(3538,plain,
! [SV763: $i,SV130: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV130 ) @ SV763 @ SV130 )
= SV763 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2917]) ).
thf(3539,plain,
! [SV764: $i,SV131: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV131 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV131 ) @ SV764 @ SV131 )
= SV764 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(3540,plain,
! [SV765: $i,SV135: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV765 @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= SV765 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(3541,plain,
! [SV766: $i,SV136: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV136 ) @ SV766 @ SV136 )
= SV766 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(3542,plain,
! [SV1274: $i,SV767: $i,SV137: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SV767 @ SV1274 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV1274 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV767 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3543,plain,
! [SV1275: $i,SV768: $i,SV138: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SV768 @ SV1275 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SV1275 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1275 @ SV138 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3544,plain,
! [SV1276: $i,SV769: $i,SV139: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SV769 @ SV1276 @ tc_nat ) @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SV769 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV769 @ SV139 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3545,plain,
! [SV1277: $i,SV770: $i,SV140: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SV770 @ SV1277 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV1277 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV770 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3546,plain,
! [SV1278: $i,SV771: $i,SV141: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SV771 @ SV1278 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV1278 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV771 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3547,plain,
! [SV1279: $i,SV778: $i,SV148: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SV778 @ SV1279 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV1279 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV778 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3548,plain,
! [SV1280: $i,SV779: $i,SV149: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SV779 @ SV1280 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV1280 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV779 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3549,plain,
! [SV1281: $i,SV780: $i,SV150: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SV780 @ SV1281 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV1281 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV780 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3550,plain,
! [SV1282: $i,SV781: $i,SV151: $i] :
( ( ! [SY3204: $i,SY3205: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SY3204 @ SY3205 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SV1282 @ SY3205 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SY3204 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3551,plain,
! [SV1283: $i,SV782: $i,SV152: $i] :
( ( ! [SY3206: $i,SY3207: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SY3206 @ SY3207 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SY3207 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SY3206 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3552,plain,
! [SV783: $i,SV153: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV153 ) @ ( c_Suc @ SV783 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV153 @ SV783 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3553,plain,
! [SV784: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV154 @ SV784 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV154 ) @ ( c_Suc @ SV784 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3554,plain,
! [SV785: $i,SV155: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV155 ) @ ( c_Suc @ SV785 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV155 @ SV785 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3555,plain,
! [SV1284: $i,SV786: $i,SV156: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3556,plain,
! [SV1285: $i,SV787: $i,SV157: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3557,plain,
! [SV1286: $i,SV788: $i,SV158: $i] :
( ( ! [SY3208: $i] :
( ~ ( class_Orderings_Oorder @ SV158 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
| ~ ( c_lessequals @ SV788 @ SY3208 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SY3208 @ SV1286 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3558,plain,
! [SV1287: $i,SV789: $i,SV159: $i] :
( ( ! [SY3209: $i] :
( ~ ( class_Orderings_Oorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV789 @ SY3209 @ SV159 )
| ~ ( c_lessequals @ SY3209 @ SV1287 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3559,plain,
! [SV1288: $i,SV790: $i,SV160: $i] :
( ( ! [SY3210: $i,SY3211: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
| ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SY3210 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SY3211 @ SY3210 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SY3211 @ SV160 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3560,plain,
! [SV1289: $i,SV791: $i,SV161: $i] :
( ( ! [SY3212: $i] :
( ~ ( class_Orderings_Opreorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
| ~ ( c_lessequals @ SY3212 @ SV1289 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV791 @ SY3212 @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3561,plain,
! [SV1290: $i,SV792: $i,SV162: $i] :
( ( ! [SY3213: $i] :
( ~ ( class_Orderings_Opreorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SY3213 @ SV1290 @ SV162 )
| ~ ( c_lessequals @ SV792 @ SY3213 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3562,plain,
! [SV1291: $i,SV793: $i,SV163: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV163 )
| ( c_lessequals @ SV793 @ SV1291 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV1291 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3563,plain,
! [SV1292: $i,SV794: $i,SV164: $i] :
( ( ~ ( class_Orderings_Oorder @ SV164 )
| ( c_lessequals @ SV794 @ SV1292 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV1292 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3564,plain,
! [SV1293: $i,SV795: $i,SV165: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV165 )
| ( c_HOL_Oord__class_Oless @ SV795 @ SV1293 @ SV165 )
| ( c_lessequals @ SV1293 @ SV795 @ SV165 )
| ~ ( c_lessequals @ SV795 @ SV1293 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3565,plain,
! [SV1294: $i,SV796: $i,SV166: $i] :
( ( ! [SY3214: $i,SY3215: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SY3214 @ SY3215 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SV1294 @ SY3215 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SY3214 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3566,plain,
! [SV1295: $i,SV797: $i,SV167: $i] :
( ( ~ ( class_Orderings_Oorder @ SV167 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SV1295 @ SV167 )
| ( SV1295 = SV797 )
| ~ ( c_lessequals @ SV797 @ SV1295 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3567,plain,
! [SV1296: $i,SV798: $i,SV168: $i] :
( ( ~ ( class_Orderings_Oorder @ SV168 )
| ( c_HOL_Oord__class_Oless @ SV798 @ SV1296 @ SV168 )
| ~ ( c_lessequals @ SV798 @ SV1296 @ SV168 )
| ( SV1296 = SV798 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3568,plain,
! [SV1297: $i,SV799: $i,SV169: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV169 )
| ( SV799 = SV1297 )
| ( c_HOL_Oord__class_Oless @ SV799 @ SV1297 @ SV169 )
| ~ ( c_lessequals @ SV799 @ SV1297 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3569,plain,
! [SV1298: $i,SV800: $i,SV170: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV170 )
| ( SV800 = SV1298 )
| ~ ( c_lessequals @ SV800 @ SV1298 @ SV170 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1298 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3570,plain,
! [SV1299: $i,SV801: $i,SV171: $i] :
( ( ~ ( class_Orderings_Oorder @ SV171 )
| ( c_HOL_Oord__class_Oless @ SV801 @ SV1299 @ SV171 )
| ~ ( c_lessequals @ SV801 @ SV1299 @ SV171 )
| ( SV801 = SV1299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3571,plain,
! [SV1300: $i,SV802: $i,SV172: $i] :
( ( ~ ( class_Orderings_Oorder @ SV172 )
| ( c_HOL_Oord__class_Oless @ SV802 @ SV1300 @ SV172 )
| ( SV802 = SV1300 )
| ~ ( c_lessequals @ SV802 @ SV1300 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3572,plain,
! [SV1301: $i,SV803: $i,SV173: $i] :
( ( ~ ( class_Orderings_Oorder @ SV173 )
| ( SV803 = SV1301 )
| ( c_HOL_Oord__class_Oless @ SV803 @ SV1301 @ SV173 )
| ~ ( c_lessequals @ SV803 @ SV1301 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3573,plain,
! [SV1302: $i,SV804: $i,SV174: $i] :
( ( ~ ( class_Orderings_Oorder @ SV174 )
| ( c_HOL_Oord__class_Oless @ SV804 @ SV1302 @ SV174 )
| ( SV804 = SV1302 )
| ~ ( c_lessequals @ SV804 @ SV1302 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3574,plain,
! [SV1303: $i,SV805: $i,SV175: $i] :
( ( ! [SY3216: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SV1303 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SY3216 @ SV1303 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV805 @ SY3216 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3575,plain,
! [SV1304: $i,SV806: $i,SV176: $i] :
( ( ! [SY3217: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
| ( c_lessequals @ SV806 @ SV1304 @ SV176 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SY3217 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SV1304 @ SY3217 @ SV176 ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3576,plain,
! [SV1305: $i,SV807: $i,SV177: $i] :
( ( ! [SY3218: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1305 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SY3218 @ SV177 ) @ SV177 )
| ~ ( c_lessequals @ SV1305 @ SY3218 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3577,plain,
! [SV1306: $i,SV808: $i,SV178: $i] :
( ( ! [SY3219: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
| ( c_lessequals @ SV808 @ SV1306 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SY3219 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SY3219 @ SV1306 @ SV178 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3578,plain,
! [SV1307: $i,SV809: $i,SV179: $i] :
( ( ! [SY3220: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SV1307 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SY3220 @ SV1307 @ SV179 ) @ SV179 )
| ~ ( c_lessequals @ SV809 @ SY3220 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3579,plain,
! [SV1308: $i,SV810: $i,SV180: $i] :
( ( ! [SY3221: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1308 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SY3221 @ SV180 ) @ SV180 )
| ~ ( c_lessequals @ SV1308 @ SY3221 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3580,plain,
! [SV1309: $i,SV811: $i,SV181: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV181 )
| ~ ( c_lessequals @ SV811 @ SV1309 @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ SV1309 @ SV811 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3581,plain,
! [SV1310: $i,SV812: $i,SV182: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV182 )
| ( c_HOL_Oord__class_Oless @ SV812 @ SV1310 @ SV182 )
| ( c_lessequals @ SV1310 @ SV812 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3582,plain,
! [SV813: $i,SV183: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV183 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV813 @ SV813 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV813 @ SV813 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3583,plain,
! [SV814: $i,SV184: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV184 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV814 @ SV814 @ SV184 )
| ( c_lessequals @ SV814 @ SV814 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3584,plain,
! [SV1311: $i,SV815: $i,SV185: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV815 @ SV1311 @ SV185 )
| ~ ( c_lessequals @ SV1311 @ SV815 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3585,plain,
! [SV1312: $i,SV816: $i,SV186: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV186 )
| ( c_lessequals @ SV816 @ SV1312 @ SV186 )
| ( c_HOL_Oord__class_Oless @ SV1312 @ SV816 @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3586,plain,
! [SV1313: $i,SV817: $i,SV187: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV187 )
| ( c_HOL_Oord__class_Oless @ SV817 @ SV1313 @ SV187 )
| ( c_lessequals @ SV1313 @ SV817 @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3587,plain,
! [SV1314: $i,SV818: $i,SV188: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV188 )
| ~ ( c_lessequals @ SV818 @ SV1314 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV1314 @ SV818 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3588,plain,
! [SV819: $i,SV189: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV189 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
| ~ ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3589,plain,
! [SV820: $i,SV190: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV190 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
| ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3590,plain,
! [SV1315: $i,SV821: $i,SV191: $i] :
( ( ! [SY3222: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SV821 @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SY3222 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SY3222 ) @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3591,plain,
! [SV822: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV192 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV822 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV192 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3592,plain,
! [SV1316: $i,SV823: $i,SV193: $i] :
( ( ! [SY3223: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SY3223 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SY3223 @ SV193 ) @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3593,plain,
! [SV1317: $i,SV824: $i,SV194: $i] :
( ( ! [SY3224: $i,SY3225: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV194 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3224 @ SY3225 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SY3225 @ SV1317 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY3225 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SY3224 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3594,plain,
! [SV1318: $i,SV825: $i,SV195: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV195 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
| ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3595,plain,
! [SV1319: $i,SV826: $i,SV196: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV196 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3596,plain,
! [SV1320: $i,SV827: $i,SV197: $i] :
( ( ! [SY3226: $i,SY3227: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV197 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3226 @ SY3227 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SY3227 @ SV1320 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY3227 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SY3226 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3597,plain,
! [SV1321: $i,SV828: $i,SV198: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV198 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 )
| ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3598,plain,
! [SV1322: $i,SV829: $i,SV199: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV199 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3599,plain,
! [SV1323: $i,SV830: $i,SV200: $i] :
( ( ! [SY3228: $i,SY3229: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3228 @ SY3229 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SY3229 @ SV1323 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SY3229 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SY3228 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3600,plain,
! [SV1324: $i,SV831: $i,SV201: $i] :
( ( ! [SY3230: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV201 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
| ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SY3230 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SY3230 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SY3230 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3601,plain,
! [SV1325: $i,SV832: $i,SV202: $i] :
( ( ! [SY3231: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SY3231 @ SV1325 @ SV202 ) @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3602,plain,
! [SV1326: $i,SV833: $i,SV203: $i] :
( ( ! [SY3232: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SY3232 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SY3232 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3603,plain,
! [SV1327: $i,SV834: $i,SV204: $i] :
( ( ! [SY3233: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV204 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SY3233 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3604,plain,
! [SV205: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV205 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV205 ) @ SV205 )
= ( c_HOL_Oone__class_Oone @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3605,plain,
! [SV206: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV206 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV206 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= ( c_HOL_Oone__class_Oone @ SV206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3606,plain,
! [SV835: $i,SV207: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV207 ) @ SV835 @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2991]) ).
thf(3607,plain,
! [SV1328: $i,SV836: $i,SV208: $i] :
( ( ! [SY3234: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV208 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SY3234 @ SV208 ) @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ SV1328 @ SY3234 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3608,plain,
! [SV1329: $i,SV837: $i,SV209: $i] :
( ( ! [SY3235: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV209 )
| ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3235 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SY3235 @ SV1329 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SY3235 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3609,plain,
! [SV1330: $i,SV838: $i,SV210: $i] :
( ( ! [SY3236: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV210 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SY3236 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SY3236 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3610,plain,
! [SV1331: $i,SV839: $i,SV211: $i] :
( ( ! [SY3237: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV211 )
| ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3237 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SY3237 @ SV1331 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SY3237 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3611,plain,
! [SV1332: $i,SV840: $i,SV212: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV212 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV840 @ ( c_Suc @ SV1332 ) @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SV840 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3612,plain,
! [SV1333: $i,SV841: $i,SV213: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV213 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
| ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3613,plain,
! [SV842: $i,SV214: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV214 @ SV842 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV842 @ SV214 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2998]) ).
thf(3614,plain,
! [SV843: $i,SV215: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV215 @ SV843 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV843 @ SV215 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3615,plain,
! [SV844: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV216 @ ( c_Suc @ SV844 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV216 @ SV844 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3616,plain,
! [SV845: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV217 @ SV845 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV217 ) @ SV845 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3617,plain,
! [SV218: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV218 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV218 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3618,plain,
! [SV219: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV219 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV219 )
= ( c_HOL_Ozero__class_Ozero @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3619,plain,
! [SV220: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV220 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV220 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3620,plain,
! [SV1334: $i,SV846: $i,SV221: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV221 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV846 @ SV1334 @ tc_nat ) @ SV221 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV846 @ SV221 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1334 @ SV221 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3621,plain,
! [SV1335: $i,SV847: $i,SV222: $i] :
( ( ! [SY3238: $i] :
( ~ ( class_Divides_Osemiring__div @ SV222 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ ( c_Divides_Odiv__class_Omod @ SV1335 @ SY3238 @ SV222 ) @ SV222 ) @ SY3238 @ SV222 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ SV1335 @ SV222 ) @ SY3238 @ SV222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3622,plain,
! [SV1336: $i,SV848: $i,SV223: $i] :
( ( ! [SY3239: $i] :
( ~ ( class_Divides_Osemiring__div @ SV223 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV848 @ SV1336 @ SV223 ) @ SY3239 @ SV223 ) @ SV1336 @ SV223 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV848 @ SY3239 @ SV223 ) @ SV1336 @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3623,plain,
! [SV849: $i,SV224: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV224 @ SV849 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV849 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3624,plain,
! [SV850: $i,SV225: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV225 @ SV850 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV225 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3625,plain,
! [SV851: $i,SV226: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV226 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV851 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ ( c_HOL_Oplus__class_Oplus @ SV851 @ SV851 @ SV226 ) @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3626,plain,
! [SV852: $i,SV227: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV227 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV852 @ SV852 @ SV227 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV852 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3627,plain,
! [SV853: $i,SV228: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV228 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
| ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3628,plain,
! [SV854: $i,SV229: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV229 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV854 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV229 ) @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3629,plain,
! [SV230: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV230 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV230 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV230 ) @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3630,plain,
! [SV1337: $i,SV855: $i,SV231: $i] :
( ( ! [SY3240: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV231 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SY3240 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3631,plain,
! [SV1338: $i,SV856: $i,SV232: $i] :
( ( ! [SY3241: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV232 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SY3241 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SY3241 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3016]) ).
thf(3632,plain,
! [SV1339: $i,SV857: $i,SV233: $i] :
( ( ! [SY3242: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV233 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SY3242 @ SV1339 @ SV233 ) @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3633,plain,
! [SV1340: $i,SV858: $i,SV234: $i] :
( ( ! [SY3243: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV234 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SY3243 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SY3243 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SY3243 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3634,plain,
! [SV859: $i,SV235: $i] :
( ( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ SV235 @ SV859 @ tc_nat ) @ SV859 @ tc_nat )
= $true )
| ( ( SV859
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3635,plain,
! [SV860: $i,SV236: $i] :
( ( ( c_lessequals @ ( c_GCD_Ogcd__class_Ogcd @ SV236 @ SV860 @ tc_nat ) @ SV236 @ tc_nat )
= $true )
| ( ( SV236
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3636,plain,
! [SV861: $i,SV238: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV238 @ SV861 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_Suc @ SV238 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3637,plain,
! [SV862: $i,SV239: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV239 @ ( c_Suc @ SV862 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV862 @ SV239 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3638,plain,
! [SV1341: $i,SV863: $i,SV240: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV240 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3639,plain,
! [SV1342: $i,SV864: $i,SV241: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV241 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3640,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV242 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3641,plain,
! [SV1344: $i,SV866: $i,SV243: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV243 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3642,plain,
! [SV867: $i,SV244: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV244 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
| ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3643,plain,
! [SV1345: $i,SV868: $i,SV245: $i] :
( ( ! [SY3244: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SY3244 @ SV245 ) @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SY3244 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3644,plain,
! [SV1346: $i,SV869: $i,SV246: $i] :
( ( ! [SY3245: $i,SY3246: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1346 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SY3245 @ SY3246 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SY3245 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1346 @ SY3246 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3645,plain,
! [SV1347: $i,SV870: $i,SV247: $i] :
( ( ! [SY3247: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV247 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3247 @ SV1347 @ SV247 ) @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ SY3247 @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3646,plain,
! [SV1348: $i,SV871: $i,SV248: $i] :
( ( ! [SY3248: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV248 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3248 @ SV1348 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SY3248 @ SV871 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3647,plain,
! [SV1349: $i,SV872: $i,SV249: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3648,plain,
! [SV1350: $i,SV873: $i,SV250: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3649,plain,
! [SV1351: $i,SV874: $i,SV251: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV251 )
| ( ( c_Divides_Odiv__class_Omod @ SV874 @ SV1351 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1351 @ SV874 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3650,plain,
! [SV875: $i,SV252: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV252 ) )
= $true )
| ( ( ( SV875
= ( c_HOL_Ozero__class_Ozero @ SV252 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV875 @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3651,plain,
! [SV876: $i,SV253: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV253 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV876 @ SV253 ) @ SV253 )
= SV876 )
| ( SV876
= ( c_HOL_Ozero__class_Ozero @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3652,plain,
! [SV254: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV254 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV254 )
= ( c_HOL_Ozero__class_Ozero @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3653,plain,
! [SV878: $i,SV256: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV256 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV878 ) @ SV256 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV256 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV878 @ SV256 ) @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3654,plain,
! [SV1352: $i,SV879: $i,SV257: $i] :
( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3655,plain,
! [SV880: $i,SV258: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV258 @ SV880 @ tc_nat ) @ SV880 @ 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)],[3042]) ).
thf(3656,plain,
! [SV881: $i,SV259: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV259 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV881 @ SV259 )
| ( SV881
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV881 @ SV259 ) @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3657,plain,
! [SV1353: $i,SV882: $i,SV262: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV262 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3658,plain,
! [SV1354: $i,SV883: $i,SV263: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV263 )
| ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3659,plain,
! [SV1355: $i,SV884: $i,SV264: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV264 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3660,plain,
! [SV1356: $i,SV885: $i,SV265: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV265 )
| ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3661,plain,
! [SV1357: $i,SV886: $i,SV266: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV266 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3662,plain,
! [SV1358: $i,SV887: $i,SV267: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3663,plain,
! [SV269: $i] :
( ( ( class_SEQ_Obanach @ SV269 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__field @ SV269 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= ( c_HOL_Oone__class_Oone @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3664,plain,
! [SV889: $i,SV270: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Suc @ SV889 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV270 @ SV889 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3665,plain,
! [SV890: $i,SV271: $i] :
( ( ( c_lessequals @ SV271 @ SV890 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV271 @ ( c_Suc @ SV890 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3055]) ).
thf(3666,plain,
! [SV272: $i] :
( ( ( c_lessequals @ SV272 @ SV272 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV272 @ ( c_Suc @ SV272 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3667,plain,
! [SV891: $i,SV273: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV273 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3668,plain,
! [SV892: $i,SV274: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV274 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3669,plain,
! [SV893: $i,SV275: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV275 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ SV893 @ SV275 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ ( c_HOL_Oplus__class_Oplus @ SV893 @ SV893 @ SV275 ) @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3059]) ).
thf(3670,plain,
! [SV894: $i,SV276: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV276 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ ( c_HOL_Oplus__class_Oplus @ SV894 @ SV894 @ SV276 ) @ SV276 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV894 @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3671,plain,
! [SV1359: $i,SV895: $i,SV279: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV279 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV895 @ SV1359 @ SV279 ) @ SV1359 @ SV279 )
= ( c_Divides_Odiv__class_Omod @ SV895 @ SV1359 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3672,plain,
! [SV1360: $i,SV896: $i,SV280: $i] :
( ( ! [SY3249: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
| ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SY3249 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SY3249 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3673,plain,
! [SV1361: $i,SV899: $i,SV284: $i] :
( ( ! [SY3250: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV284 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SY3250 @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SY3250 @ SV1361 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3674,plain,
! [SV900: $i,SV285: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV285 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV900 @ ( c_HOL_Ozero__class_Ozero @ SV285 ) @ SV285 )
= SV900 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3675,plain,
! [SV901: $i,SV286: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV286 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV901 @ SV901 @ SV286 )
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3676,plain,
! [SV1362: $i,SV902: $i,SV287: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV287 )
| ( ( c_HOL_Oplus__class_Oplus @ SV902 @ SV1362 @ SV287 )
= ( c_HOL_Oplus__class_Oplus @ SV1362 @ SV902 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3677,plain,
! [SV1363: $i,SV904: $i,SV289: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV289 )
| ( ( c_HOL_Oplus__class_Oplus @ SV904 @ SV1363 @ SV289 )
= ( c_HOL_Oplus__class_Oplus @ SV1363 @ SV904 @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3070]) ).
thf(3678,plain,
! [SV1364: $i,SV905: $i,SV290: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV290 )
| ( ( c_HOL_Oplus__class_Oplus @ SV905 @ SV1364 @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SV1364 @ SV905 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3679,plain,
! [SV1365: $i,SV906: $i,SV291: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV291 )
| ( c_lessequals @ SV906 @ SV1365 @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3680,plain,
! [SV1366: $i,SV907: $i,SV292: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV292 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 )
| ~ ( c_lessequals @ SV1366 @ SV907 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3681,plain,
! [SV1367: $i,SV908: $i,SV293: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV293 )
| ( c_lessequals @ SV908 @ SV1367 @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3682,plain,
! [SV1368: $i,SV909: $i,SV294: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV294 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
| ~ ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
| ~ ( c_lessequals @ SV1368 @ SV909 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3683,plain,
! [SV295: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV295 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV295 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV295 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV295 )
= ( c_HOL_Oone__class_Oone @ SV295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3684,plain,
! [SV910: $i,SV296: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV296 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3685,plain,
! [SV911: $i,SV297: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV297 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3686,plain,
! [SV912: $i,SV298: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV298 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3687,plain,
! [SV913: $i,SV299: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV299 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
| ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3688,plain,
! [SV1369: $i,SV914: $i,SV300: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV300 )
| ( c_HOL_Oord__class_Oless @ SV914 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV914 @ SV1369 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1369 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3689,plain,
! [SV1370: $i,SV915: $i,SV301: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV301 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV915 @ SV1370 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SV1370 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV915 @ SV1370 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3690,plain,
! [SV916: $i,SV302: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV302 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV916 @ SV302 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV302 ) @ SV916 @ SV302 ) )
| ( SV916
= ( c_HOL_Ozero__class_Ozero @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3691,plain,
! [SV1371: $i,SV917: $i,SV303: $i] :
( ( ! [SY3251: $i] :
( ~ ( class_Divides_Oring__div @ SV303 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ SV1371 @ SV303 ) @ SY3251 @ SV303 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ ( c_Divides_Odiv__class_Omod @ SV1371 @ SY3251 @ SV303 ) @ SV303 ) @ SY3251 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3692,plain,
! [SV1372: $i,SV918: $i,SV304: $i] :
( ( ! [SY3252: $i] :
( ~ ( class_Divides_Oring__div @ SV304 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1372 @ SV304 ) @ SY3252 @ SV304 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV918 @ SY3252 @ SV304 ) @ SV1372 @ SV304 ) @ SY3252 @ SV304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3693,plain,
! [SV1373: $i,SV919: $i,SV305: $i] :
( ( ! [SY3253: $i] :
( ~ ( class_Divides_Oring__div @ SV305 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV919 @ SV1373 @ SV305 ) @ SY3253 @ SV305 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV919 @ SY3253 @ SV305 ) @ ( c_Divides_Odiv__class_Omod @ SV1373 @ SY3253 @ SV305 ) @ SV305 ) @ SY3253 @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3694,plain,
! [SV1374: $i,SV920: $i,SV306: $i] :
( ( ! [SY3254: $i] :
( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SY3254 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SY3254 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3695,plain,
! [SV921: $i,SV307: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV307 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV921 @ SV921 @ SV307 )
= ( c_HOL_Ozero__class_Ozero @ SV307 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3696,plain,
! [SV922: $i,SV308: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV308 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV922 @ SV922 @ SV308 )
= ( c_HOL_Ozero__class_Ozero @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3697,plain,
! [SV923: $i,SV309: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV309 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV923 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 )
= SV923 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3698,plain,
! [SV924: $i,SV310: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV310 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV924 @ SV924 @ SV310 )
= ( c_HOL_Ozero__class_Ozero @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3699,plain,
! [SV925: $i,SV311: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV311 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV311 )
| ( ( c_HOL_Ominus__class_Ominus @ SV925 @ SV925 @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ SV311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3700,plain,
! [SV1375: $i,SV926: $i,SV312: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV312 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV926 @ SV1375 @ SV312 ) @ SV1375 @ SV312 )
= SV926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3701,plain,
! [SV1376: $i,SV927: $i,SV313: $i] :
( ( ! [SY3255: $i,SY3256: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV313 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV927 @ SV1376 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SY3255 @ SY3256 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV927 @ SY3255 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SV1376 @ SY3256 @ SV313 ) @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3702,plain,
! [SV1377: $i,SV928: $i,SV314: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV314 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV928 @ SV1377 @ SV314 ) @ SV1377 @ SV314 )
= SV928 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3703,plain,
! [SV1378: $i,SV929: $i,SV315: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV315 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV315 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV929 @ SV1378 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV929 @ SV315 ) @ SV1378 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3704,plain,
! [SV1379: $i,SV930: $i,SV316: $i] :
( ( ! [SY3257: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SV1379 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SY3257 @ SV1379 @ SV316 ) @ SV316 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SY3257 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3705,plain,
! [SV931: $i,SV317: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV317 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV317 )
| ( ( c_HOL_Ozero__class_Ozero @ SV317 )
= ( c_HOL_Oinverse__class_Odivide @ SV931 @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3706,plain,
! [SV318: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV318 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV318 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= ( c_HOL_Ozero__class_Ozero @ SV318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3707,plain,
! [SV1380: $i,SV932: $i,SV319: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV319 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV319 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV932 @ SV1380 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SV1380 @ SV932 @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3708,plain,
! [SV933: $i,SV320: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV320 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ SV933 @ SV320 )
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3101]) ).
thf(3709,plain,
! [SV934: $i,SV321: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV321 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV321 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV934 @ ( c_HOL_Ozero__class_Ozero @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3710,plain,
! [SV935: $i,SV322: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV322 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV322 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV322 ) @ SV322 )
= ( c_HOL_Ozero__class_Ozero @ SV322 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3711,plain,
! [SV936: $i,SV323: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV323 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV936 @ SV323 )
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3712,plain,
! [SV1381: $i,SV937: $i,SV324: $i] :
( ( ! [SY3258: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV324 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV1381 @ SV324 ) @ SY3258 @ SV324 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV937 @ SY3258 @ SV324 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1381 @ SY3258 @ SV324 ) @ SV324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3713,plain,
! [SV1382: $i,SV938: $i,SV325: $i] :
( ( ! [SY3259: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV325 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV1382 @ SV325 ) @ SY3259 @ SV325 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV938 @ SY3259 @ SV325 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1382 @ SY3259 @ SV325 ) @ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3714,plain,
! [SV939: $i,SV326: $i] :
( ( ( c_lessequals @ SV326 @ SV939 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV326 ) @ ( c_Suc @ SV939 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3107]) ).
thf(3715,plain,
! [SV940: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV327 ) @ ( c_Suc @ SV940 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV327 @ SV940 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3716,plain,
! [SV941: $i,SV329: $i] :
( ( ( c_lessequals @ SV329 @ SV941 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV329 ) @ SV941 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3717,plain,
! [SV942: $i,SV330: $i] :
( ( ( c_lessequals @ SV330 @ ( c_Suc @ SV942 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV330 @ SV942 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3718,plain,
! [SV943: $i,SV331: $i] :
( ( ( c_lessequals @ SV331 @ SV943 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV331 @ SV943 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3719,plain,
! [SV944: $i,SV332: $i] :
( ( ( c_lessequals @ SV332 @ SV944 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV332 @ SV944 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3720,plain,
! [SV1383: $i,SV949: $i,SV337: $i] :
( ( ! [SY3260: $i] :
( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1383 @ SY3260 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV949 @ SY3260 @ tc_nat )
| ~ ( c_lessequals @ SV337 @ SV1383 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3721,plain,
! [SV950: $i,SV338: $i] :
( ( ( SV338
= ( c_Suc @ SV950 ) )
= $true )
| ( ( ( c_lessequals @ SV338 @ SV950 @ tc_nat )
| ~ ( c_lessequals @ SV338 @ ( c_Suc @ SV950 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3722,plain,
! [SV951: $i,SV339: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV339 @ SV951 @ tc_nat )
= $true )
| ( ( ( SV339 = SV951 )
| ~ ( c_lessequals @ SV339 @ SV951 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3120]) ).
thf(3723,plain,
! [SV952: $i,SV340: $i] :
( ( ( SV340 = SV952 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV340 @ SV952 @ tc_nat )
| ~ ( c_lessequals @ SV340 @ SV952 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3121]) ).
thf(3724,plain,
! [SV953: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV341 @ SV953 @ tc_nat )
= $true )
| ( ( ( SV341 = SV953 )
| ~ ( c_lessequals @ SV341 @ SV953 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3122]) ).
thf(3725,plain,
! [SV1384: $i,SV954: $i,SV342: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV342 @ SV954 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV954 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV342 @ SV1384 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3726,plain,
! [SV1385: $i,SV955: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ SV955 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV343 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV955 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3727,plain,
! [SV1386: $i,SV956: $i,SV344: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV956 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV1386 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV956 @ SV1386 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3728,plain,
! [SV345: $i] :
( ( ( c_lessequals @ SV345 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV345
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3729,plain,
! [SV1387: $i,SV957: $i,SV346: $i] :
( ( ( c_lessequals @ SV346 @ ( c_HOL_Oplus__class_Oplus @ SV957 @ SV1387 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV346 @ SV957 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3730,plain,
! [SV1388: $i,SV958: $i,SV347: $i] :
( ( ( c_lessequals @ SV347 @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV1388 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV347 @ SV1388 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3731,plain,
! [SV1389: $i,SV959: $i,SV348: $i] :
( ( ( c_lessequals @ SV348 @ SV959 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV348 @ SV1389 @ tc_nat ) @ SV959 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3732,plain,
! [SV1390: $i,SV960: $i,SV349: $i] :
( ( ( c_lessequals @ SV349 @ SV960 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1390 @ SV349 @ tc_nat ) @ SV960 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3733,plain,
! [SV1391: $i,SV961: $i,SV350: $i] :
( ( ( c_lessequals @ SV350 @ ( c_HOL_Oplus__class_Oplus @ SV961 @ SV1391 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV350 @ SV961 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3734,plain,
! [SV1392: $i,SV962: $i,SV351: $i] :
( ( ( c_lessequals @ SV351 @ ( c_HOL_Oplus__class_Oplus @ SV962 @ SV1392 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV351 @ SV1392 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3735,plain,
! [SV963: $i,SV353: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV353 ) @ SV963 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV963 @ SV353 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3736,plain,
! [SV964: $i,SV354: $i] :
( ( ( ~ ( c_lessequals @ SV354 @ SV964 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV964 ) @ SV354 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3134]) ).
thf(3737,plain,
! [SV1393: $i,SV966: $i,SV357: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV357 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV966 @ SV1393 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV357 @ SV1393 @ tc_nat ) @ ( c_Suc @ SV966 ) @ tc_nat ) )
| ~ ( c_lessequals @ SV1393 @ SV966 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3738,plain,
! [SV1394: $i,SV967: $i,SV358: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV967 @ tc_nat ) ) @ SV1394 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV358 ) @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1394 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV967 @ SV358 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(3739,plain,
! [SV1395: $i,SV968: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV968 @ tc_nat ) @ SV1395 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV359 @ SV1395 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3740,plain,
! [SV1396: $i,SV970: $i,SV361: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV970 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV1396 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV361 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV970 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3741,plain,
! [SV1397: $i,SV971: $i,SV362: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV362 @ SV971 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV362 @ SV1397 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV971 @ SV1397 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3742,plain,
! [SV1398: $i,SV972: $i,SV363: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV363 @ SV972 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1398 @ SV972 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV363 @ SV1398 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3743,plain,
! [SV1399: $i,SV973: $i,SV364: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV364 ) @ SV973 @ tc_nat ) @ ( c_Suc @ SV1399 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV364 @ SV973 @ tc_nat ) @ SV1399 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3744,plain,
! [SV1400: $i,SV974: $i,SV365: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SV974 @ SV1400 @ tc_nat ) @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV1400 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV974 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3745,plain,
! [SV1401: $i,SV975: $i,SV368: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV368 @ SV975 @ tc_nat ) @ SV1401 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV368 @ ( c_HOL_Oplus__class_Oplus @ SV975 @ SV1401 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3746,plain,
! [SV372: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV372 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3747,plain,
! [SV978: $i,SV373: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV373 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3149]) ).
thf(3748,plain,
! [SV374: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV374 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ ( c_HOL_Oone__class_Oone @ SV374 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3749,plain,
! [SV979: $i,SV375: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV375 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3750,plain,
! [SV1402: $i,SV980: $i,SV376: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV376 )
| ( c_lessequals @ SV980 @ SV1402 @ SV376 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV980 @ SV1402 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3751,plain,
! [SV1403: $i,SV981: $i,SV377: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV377 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV981 @ SV1403 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
| ~ ( c_lessequals @ SV981 @ SV1403 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3752,plain,
! [SV1404: $i,SV982: $i,SV378: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV378 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SV982 @ SV1404 @ SV378 ) @ SV378 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SV982 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3753,plain,
! [SV1405: $i,SV983: $i,SV379: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV379 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SV983 @ SV1405 @ SV379 ) @ SV379 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SV983 @ SV379 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3754,plain,
! [SV1406: $i,SV984: $i,SV380: $i] :
( ( ! [SY3261: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV380 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SY3261 @ SV1406 @ SV380 ) @ SV380 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
| ~ ( c_lessequals @ SV984 @ SY3261 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3755,plain,
! [SV1407: $i,SV985: $i,SV381: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV381 )
| ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
| ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SV1407 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3756,plain,
! [SV1408: $i,SV986: $i,SV382: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV382 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3757,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV383 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3758,plain,
! [SV1410: $i,SV988: $i,SV384: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV384 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SV988 @ SV1410 @ SV384 ) @ SV384 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SV988 @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3759,plain,
! [SV385: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV385 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV385 ) @ ( c_HOL_Ozero__class_Ozero @ SV385 ) @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3760,plain,
! [SV989: $i,SV386: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV386 @ SV989 @ tc_nat ) @ tc_nat )
= $true )
| ( ( SV989
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3761,plain,
! [SV990: $i,SV387: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_GCD_Ogcd__class_Ogcd @ SV387 @ SV990 @ tc_nat ) @ tc_nat )
= $true )
| ( ( SV387
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3762,plain,
! [SV1411: $i,SV991: $i,SV388: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV388 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV991 @ SV1411 @ SV388 ) @ SV388 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV991 @ SV388 ) @ SV1411 @ SV388 ) )
| ( SV991
= ( c_HOL_Ozero__class_Ozero @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3763,plain,
! [SV1412: $i,SV992: $i,SV389: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ SV389 @ ( c_GCD_Ogcd__class_Ogcd @ SV992 @ SV1412 @ tc_nat ) @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV992 @ ( c_GCD_Ogcd__class_Ogcd @ SV389 @ SV1412 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3764,plain,
! [SV1413: $i,SV993: $i,SV390: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV390 @ SV993 @ tc_nat ) @ SV1413 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV390 @ ( c_GCD_Ogcd__class_Ogcd @ SV993 @ SV1413 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3765,plain,
! [SV1414: $i,SV994: $i,SV391: $i] :
( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_GCD_Ogcd__class_Ogcd @ SV391 @ SV994 @ tc_nat ) @ SV1414 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV391 @ ( c_GCD_Ogcd__class_Ogcd @ SV994 @ SV1414 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3766,plain,
! [SV995: $i,SV392: $i] :
( ( ( SV392 = SV995 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV995 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV392 @ SV995 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3767,plain,
! [SV996: $i,SV393: $i] :
( ( ( SV393 = SV996 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV996 @ ( c_Suc @ SV393 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV996 @ SV393 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3768,plain,
! [SV997: $i,SV394: $i] :
( ( ( SV394 = SV997 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV394 @ SV997 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV394 @ ( c_Suc @ SV997 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3769,plain,
! [SV998: $i,SV396: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV396 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV998 @ ( c_HOL_Ozero__class_Ozero @ SV396 ) @ SV396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3770,plain,
! [SV999: $i,SV398: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV398 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV999 @ ( c_HOL_Oone__class_Oone @ SV398 ) @ SV398 )
= ( c_HOL_Ozero__class_Ozero @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3771,plain,
! [SV1000: $i,SV399: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ ( c_HOL_Oplus__class_Oplus @ SV1000 @ SV399 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ SV1000 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3772,plain,
! [SV1001: $i,SV400: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ SV1001 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ ( c_HOL_Oplus__class_Oplus @ SV1001 @ SV400 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3773,plain,
! [SV1002: $i,SV401: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV401 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1002 @ SV1002 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3774,plain,
! [SV1003: $i,SV404: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV404 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1003 @ SV1003 @ SV404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3178]) ).
thf(3775,plain,
! [SV1004: $i,SV405: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV405 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1004 @ SV1004 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3776,plain,
! [SV1415: $i,SV1005: $i,SV406: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3777,plain,
! [SV1006: $i,SV407: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV407 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3778,plain,
! [SV1007: $i,SV408: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV408 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3182]) ).
thf(3779,plain,
! [SV1008: $i,SV409: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV409 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1008 @ SV409 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3183]) ).
thf(3780,plain,
! [SV1009: $i,SV410: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SV1009 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1009 @ SV410 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1009 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3781,plain,
! [SV1416: $i,SV1010: $i,SV411: $i] :
( ( ! [SY3262: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1416 @ SY3262 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SY3262 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1416 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3782,plain,
! [SV1417: $i,SV1011: $i,SV412: $i] :
( ( ! [SY3263: $i,SY3264: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SY3263 @ SY3264 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SY3264 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SY3263 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3783,plain,
! [SV1012: $i,SV413: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV413 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3784,plain,
! [SV1418: $i,SV1013: $i,SV414: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1013 @ SV1418 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ SV1418 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3785,plain,
! [SV1419: $i,SV1014: $i,SV415: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
| ( c_HOL_Oord__class_Oless @ SV1014 @ SV1419 @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1014 @ SV1419 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3786,plain,
! [SV1420: $i,SV1015: $i,SV416: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 )
| ( c_HOL_Oord__class_Oless @ SV1015 @ SV1420 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1420 @ SV416 ) @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3787,plain,
! [SV1421: $i,SV1016: $i,SV417: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1421 @ SV417 ) @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1016 @ SV1421 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3788,plain,
! [SV418: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV418 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ ( c_HOL_Oone__class_Oone @ SV418 ) @ SV418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3789,plain,
! [SV1017: $i,SV419: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV419 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1017 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1017 @ SV419 ) @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3790,plain,
! [SV1018: $i,SV420: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV420 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV420 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1018 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1018 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3791,plain,
! [SV1422: $i,SV1019: $i,SV422: $i] :
( ( ! [SY3265: $i] :
( ~ ( class_Divides_Osemiring__div @ SV422 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1422 @ SV422 ) @ SY3265 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SY3265 @ SV422 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SY3265 @ SV1422 @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3792,plain,
! [SV1020: $i,SV423: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV423 ) )
= $true )
| ( ( ( c_lessequals @ SV1020 @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1020 @ SV1020 @ SV423 ) @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3793,plain,
! [SV1021: $i,SV424: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV424 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1021 @ SV1021 @ SV424 ) @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
| ~ ( c_lessequals @ SV1021 @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3794,plain,
! [SV1022: $i,SV425: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV425 @ SV1022 @ tc_nat ) @ SV1022 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3795,plain,
! [SV1023: $i,SV426: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV426 @ SV1023 @ tc_nat ) @ SV426 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3796,plain,
! [SV1423: $i,SV1024: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV427 @ ( c_HOL_Ominus__class_Ominus @ SV1024 @ SV1423 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV427 @ SV1423 @ tc_nat ) @ SV1024 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3797,plain,
! [SV1424: $i,SV1025: $i,SV428: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV428 @ SV1025 @ tc_nat ) @ SV1424 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV428 @ ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1025 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3798,plain,
! [SV1026: $i,SV429: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV429 @ SV1026 @ tc_nat )
= SV1026 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1026 @ SV429 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3799,plain,
! [SV1027: $i,SV430: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV430 @ SV1027 @ tc_nat )
= SV430 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV430 @ SV1027 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3800,plain,
! [SV1425: $i,SV1029: $i,SV432: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV432 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3801,plain,
! [SV1426: $i,SV1030: $i,SV433: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV433 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3802,plain,
! [SV1427: $i,SV1031: $i,SV434: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV434 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3803,plain,
! [SV1428: $i,SV1032: $i,SV435: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV435 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3804,plain,
! [SV1429: $i,SV1033: $i,SV436: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1033 @ ( c_Power_Opower__class_Opower @ SV1033 @ SV1429 @ SV436 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1429 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3805,plain,
! [SV1430: $i,SV1034: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV1034 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1430 @ SV1034 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV437 @ SV1430 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3806,plain,
! [SV1431: $i,SV1035: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV438 @ SV1035 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1431 @ SV438 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1431 @ SV1035 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3807,plain,
! [SV1432: $i,SV1036: $i,SV439: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1036 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1432 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1036 @ SV1432 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3808,plain,
! [SV1433: $i,SV1037: $i,SV440: $i] :
( ( ! [SY3266: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
| ( c_HOL_Oord__class_Oless @ SV1037 @ SV1433 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SY3266 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SY3266 @ SV1433 @ SV440 ) @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3809,plain,
! [SV1434: $i,SV1038: $i,SV441: $i] :
( ( ! [SY3267: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1434 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SY3267 @ SV441 ) @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SY3267 @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3810,plain,
! [SV1435: $i,SV1039: $i,SV442: $i] :
( ( ! [SY3268: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1435 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SY3268 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1435 @ SY3268 @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3811,plain,
! [SV1436: $i,SV1040: $i,SV443: $i] :
( ( ! [SY3269: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
| ( c_HOL_Oord__class_Oless @ SV1040 @ SV1436 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SY3269 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SV1436 @ SY3269 @ SV443 ) @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3812,plain,
! [SV1437: $i,SV1041: $i,SV444: $i] :
( ( ! [SY3270: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SV1437 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SY3270 @ SV1437 @ SV444 ) @ SV444 )
| ~ ( c_HOL_Oord__class_Oless @ SV1041 @ SY3270 @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3813,plain,
! [SV1438: $i,SV1042: $i,SV445: $i] :
( ( ! [SY3271: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SV1438 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SY3271 @ SV1438 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SY3271 @ SV445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3814,plain,
! [SV1439: $i,SV1043: $i,SV446: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3815,plain,
! [SV1044: $i,SV447: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV447 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3221]) ).
thf(3816,plain,
! [SV1047: $i,SV450: $i] :
( ( ( SV450 = SV1047 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV450 @ ( c_Suc @ SV1047 ) @ tc_nat )
| ~ ( c_lessequals @ SV1047 @ SV450 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3224]) ).
thf(3817,plain,
! [SV1048: $i,SV451: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV451 @ SV1048 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1048 @ ( c_Divides_Odiv__class_Omod @ SV451 @ SV1048 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( SV1048
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3818,plain,
! [SV1049: $i,SV452: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV452 @ SV1049 @ tc_nat ) @ SV452 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV452 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1049 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3226]) ).
thf(3819,plain,
! [SV1050: $i,SV453: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV453 @ ( c_HOL_Ominus__class_Ominus @ SV1050 @ SV453 @ tc_nat ) @ tc_nat )
= SV1050 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1050 @ SV453 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3820,plain,
! [SV1051: $i,SV454: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV454 @ ( c_Suc @ SV1051 ) @ tc_nat ) @ SV454 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV454 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3821,plain,
! [SV1053: $i,SV456: $i] :
( ( ( c_lessequals @ SV456 @ SV1053 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1053 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV456 @ SV1053 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3822,plain,
! [SV1440: $i,SV1054: $i,SV457: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV457 @ SV1054 @ tc_nat ) @ SV1440 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1440 @ SV457 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV457 @ SV1440 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3823,plain,
! [SV1441: $i,SV1055: $i,SV458: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV458 @ SV1055 @ tc_nat ) @ SV1441 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1441 @ SV1055 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1055 @ SV1441 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3824,plain,
! [SV1442: $i,SV1056: $i,SV459: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SV1056 @ SV1442 @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SV1442 @ SV1056 @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3825,plain,
! [SV1443: $i,SV1057: $i,SV460: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV1057 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV460 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1443 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3826,plain,
! [SV1444: $i,SV1058: $i,SV461: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SV1444 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1444 @ SV1058 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1444 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3827,plain,
! [SV1445: $i,SV1059: $i,SV462: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1059 @ SV1445 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1445 @ SV1059 @ SV462 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3828,plain,
! [SV1446: $i,SV1060: $i,SV463: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SV1060 @ SV1446 @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SV1446 @ SV1060 @ SV463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3829,plain,
! [SV1447: $i,SV1061: $i,SV464: $i] :
( ( ~ ( class_Orderings_Oorder @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1447 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SV1447 @ SV1061 @ SV464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3830,plain,
! [SV1448: $i,SV1062: $i,SV465: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV465 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
| ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3831,plain,
! [SV1449: $i,SV1063: $i,SV466: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV466 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
| ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3832,plain,
! [SV1450: $i,SV1064: $i,SV467: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV467 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3833,plain,
! [SV1451: $i,SV1065: $i,SV468: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV468 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
| ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3834,plain,
! [SV1452: $i,SV1066: $i,SV469: $i] :
( ( ! [SY3272: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV469 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3272 @ SV1452 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SY3272 @ SV1066 @ SV469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3835,plain,
! [SV1453: $i,SV1067: $i,SV470: $i] :
( ( ! [SY3273: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV470 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SY3273 @ SV1453 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SY3273 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3836,plain,
! [SV1454: $i,SV1068: $i,SV471: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV471 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3837,plain,
! [SV1455: $i,SV1069: $i,SV472: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV472 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3838,plain,
! [SV1456: $i,SV1070: $i,SV473: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV473 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
| ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3839,plain,
! [SV1457: $i,SV1071: $i,SV474: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV474 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
| ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3840,plain,
! [SV1458: $i,SV1072: $i,SV475: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV475 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
| ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3841,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV476 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
| ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3842,plain,
! [SV1074: $i,SV477: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV477 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1074 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV477 )
= ( c_HOL_Oone__class_Oone @ SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3251]) ).
thf(3843,plain,
! [SV1075: $i,SV478: $i] :
( ( ( ~ ( class_Power_Opower @ SV478 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1075 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV478 )
= ( c_HOL_Oone__class_Oone @ SV478 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3844,plain,
! [SV1076: $i,SV479: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV479 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV479 ) @ SV1076 @ SV479 ) @ SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3253]) ).
thf(3845,plain,
! [SV1077: $i,SV480: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV480 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1077 @ SV480 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV480 ) @ SV1077 @ SV480 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3254]) ).
thf(3846,plain,
! [SV1078: $i,SV481: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV481 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV481 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1078 @ SV481 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV481 ) @ SV1078 @ SV481 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3255]) ).
thf(3847,plain,
! [SV1079: $i,SV482: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV482 ) )
= $true )
| ( ( ( SV1079
= ( c_HOL_Ozero__class_Ozero @ SV482 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1079 @ SV1079 @ SV482 )
= ( c_HOL_Oone__class_Oone @ SV482 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3848,plain,
! [SV1080: $i,SV483: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV483 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1080 @ SV1080 @ SV483 )
= ( c_HOL_Oone__class_Oone @ SV483 ) )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV483 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3849,plain,
! [SV1081: $i,SV484: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV484 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV484 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1081 @ SV1081 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
| ( SV1081
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3258]) ).
thf(3850,plain,
! [SV1460: $i,SV1082: $i,SV485: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV485 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1082 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1460 @ SV485 ) @ SV485 )
| ~ ( c_lessequals @ SV1082 @ SV1460 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3851,plain,
! [SV1461: $i,SV1083: $i,SV486: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV486 )
| ( c_lessequals @ SV1083 @ SV1461 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1083 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1461 @ SV486 ) @ SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(3852,plain,
! [SV1462: $i,SV1084: $i,SV487: $i] :
( ( ~ ( class_SEQ_Obanach @ SV487 )
| ~ ( class_RealVector_Oreal__normed__field @ SV487 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SV1084 @ SV1462 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SV1084 @ SV487 ) @ ( c_Transcendental_Oexp @ SV1462 @ SV487 ) @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(3853,plain,
! [SV1463: $i,SV1085: $i,SV488: $i] :
( ( ! [SY3274: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1085 @ SV1463 @ SV488 ) @ SY3274 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1085 @ SY3274 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SV1463 @ SY3274 @ SV488 ) @ SV488 ) )
| ( SV1463
= ( c_HOL_Ozero__class_Ozero @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3854,plain,
! [SV1464: $i,SV1086: $i,SV489: $i] :
( ( ! [SY3275: $i,SY3276: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SY3275 @ SV489 )
| ~ ( c_lessequals @ SV1464 @ SY3276 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SY3276 @ SV489 ) @ SY3275 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3855,plain,
! [SV1465: $i,SV1087: $i,SV490: $i] :
( ( ! [SY3277: $i,SY3278: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SY3277 @ SY3278 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SV1465 @ SY3278 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SY3277 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3856,plain,
! [SV1466: $i,SV1088: $i,SV491: $i] :
( ( ! [SY3279: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1466 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SY3279 @ SV491 ) @ SV491 )
| ~ ( c_lessequals @ SV1466 @ SY3279 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3857,plain,
! [SV1467: $i,SV1089: $i,SV492: $i] :
( ( ! [SY3280: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV492 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SY3280 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SY3280 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
| ~ ( c_lessequals @ SY3280 @ SV1467 @ tc_nat )
| ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3858,plain,
! [SV1468: $i,SV1090: $i,SV493: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1468 @ SV1090 @ tc_nat )
| ~ ( c_lessequals @ SV1468 @ SV493 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3859,plain,
! [SV1469: $i,SV1091: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV1469 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3860,plain,
! [SV1470: $i,SV1092: $i,SV495: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV495 @ ( c_HOL_Ominus__class_Ominus @ SV1092 @ SV1470 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV495 @ SV1092 @ tc_nat ) @ SV1470 @ tc_nat ) )
| ~ ( c_lessequals @ SV1470 @ SV1092 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3861,plain,
! [SV1471: $i,SV1093: $i,SV496: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV496 @ SV1093 @ tc_nat ) @ SV1471 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV496 @ SV1471 @ tc_nat ) @ SV1093 @ tc_nat ) )
| ~ ( c_lessequals @ SV1093 @ SV496 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3270]) ).
thf(3862,plain,
! [SV1094: $i,SV497: $i] :
( ( ( ~ ( c_lessequals @ SV497 @ SV1094 @ tc_nat ) )
= $true )
| ( ( SV1094
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1094 @ SV497 @ tc_nat ) @ SV497 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3863,plain,
! [SV1095: $i,SV498: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV498 @ ( c_HOL_Ominus__class_Ominus @ SV1095 @ SV498 @ tc_nat ) @ tc_nat )
= SV1095 )
= $true )
| ( ( ~ ( c_lessequals @ SV498 @ SV1095 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3864,plain,
! [SV1096: $i,SV499: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV499 @ SV1096 @ tc_nat ) @ SV1096 @ tc_nat )
= SV499 )
= $true )
| ( ( ~ ( c_lessequals @ SV1096 @ SV499 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3273]) ).
thf(3865,plain,
! [SV1097: $i,SV500: $i] :
( ( ( ~ ( c_lessequals @ SV500 @ ( c_HOL_Oplus__class_Oplus @ SV1097 @ SV500 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1097 @ SV500 @ tc_nat ) @ SV500 @ tc_nat )
= SV1097 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3866,plain,
! [SV1472: $i,SV1098: $i,SV501: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV501 @ ( c_HOL_Ominus__class_Ominus @ SV1098 @ SV1472 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV1472 @ tc_nat ) @ SV1098 @ tc_nat ) )
| ~ ( c_lessequals @ SV1472 @ SV1098 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3867,plain,
! [SV1473: $i,SV1099: $i,SV502: $i] :
( ( ( c_lessequals @ SV502 @ ( c_HOL_Oplus__class_Oplus @ SV1099 @ SV1473 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV502 @ SV1473 @ tc_nat ) @ SV1099 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(3868,plain,
! [SV1474: $i,SV1100: $i,SV503: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV503 @ SV1100 @ tc_nat ) @ SV1474 @ tc_nat )
| ~ ( c_lessequals @ SV503 @ ( c_HOL_Oplus__class_Oplus @ SV1474 @ SV1100 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3869,plain,
! [SV1475: $i,SV1101: $i,SV504: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
| ~ ( c_lessequals @ SV1475 @ SV1101 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3870,plain,
! [SV1476: $i,SV1102: $i,SV505: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
| ~ ( c_lessequals @ SV1102 @ SV1476 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3871,plain,
! [SV1103: $i,SV506: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV506 @ SV1103 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV506 @ SV1103 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3872,plain,
! [SV1104: $i,SV507: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV507 @ SV1104 @ tc_nat ) @ SV1104 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV507 @ SV1104 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1104 @ SV507 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3873,plain,
! [SV1105: $i,SV508: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV508 @ SV1105 @ tc_nat ) @ SV508 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1105 @ SV508 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1105 @ SV508 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3874,plain,
! [SV1477: $i,SV1106: $i,SV509: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV509 @ SV1106 @ tc_nat ) @ SV1477 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ominus__class_Ominus @ SV1106 @ SV1477 @ tc_nat ) @ tc_nat ) )
| ~ ( c_lessequals @ SV1477 @ SV1106 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(3875,plain,
! [SV1478: $i,SV1107: $i,SV510: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV510 @ SV1107 @ tc_nat ) @ SV1478 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV510 @ SV1478 @ tc_nat ) @ SV1107 @ tc_nat ) )
| ~ ( c_lessequals @ SV1478 @ SV510 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3284]) ).
thf(3876,plain,
! [SV1108: $i,SV511: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV511 @ SV1108 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV511 @ SV1108 @ tc_nat ) @ SV1108 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1108 @ SV511 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3877,plain,
! [SV1109: $i,SV512: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV512 ) @ SV1109 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV512 @ SV1109 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1109 @ SV512 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3878,plain,
! [SV1479: $i,SV1110: $i,SV513: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SV1110 @ tc_nat ) @ SV1479 @ tc_nat )
| ~ ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SV1479 @ SV1110 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1110 @ SV1479 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(3879,plain,
! [SV1480: $i,SV1111: $i,SV514: $i] :
( ( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SV1111 @ SV1480 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SV1480 @ tc_nat ) @ SV1111 @ tc_nat )
| ~ ( c_lessequals @ SV1480 @ SV1111 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3880,plain,
! [SV1481: $i,SV1112: $i,SV515: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV1112 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ SV1112 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1112 @ SV515 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV515 @ SV1481 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3881,plain,
! [SV1482: $i,SV1113: $i,SV516: $i] :
( ( ( c_lessequals @ SV516 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1113 @ SV516 @ tc_nat ) @ SV1482 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1482 @ SV1113 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3290]) ).
thf(3882,plain,
! [SV1114: $i,SV517: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV517 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
| ~ ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3883,plain,
! [SV1115: $i,SV518: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV518 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
| ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3884,plain,
! [SV1116: $i,SV519: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV519 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3885,plain,
! [SV1117: $i,SV520: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV520 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3886,plain,
! [SV1483: $i,SV1118: $i,SV521: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV521 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1483 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1118 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1483 @ SV521 ) @ SV521 ) )
| ~ ( c_lessequals @ SV1483 @ SV1118 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3295]) ).
thf(3887,plain,
! [SV1484: $i,SV1119: $i,SV522: $i] :
( ( ! [SY3281: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV522 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SY3281 @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SY3281 @ SV1484 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3888,plain,
! [SV1485: $i,SV1120: $i,SV523: $i] :
( ( ! [SY3282: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV523 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SY3282 @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1485 @ SY3282 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(3889,plain,
! [SV1486: $i,SV1121: $i,SV524: $i] :
( ( ! [SY3283: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV524 )
| ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3283 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SY3283 @ SV1486 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SY3283 @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3298]) ).
thf(3890,plain,
! [SV1487: $i,SV1122: $i,SV525: $i] :
( ( ! [SY3284: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV525 )
| ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3284 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SY3284 @ SV1487 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SY3284 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3891,plain,
! [SV1488: $i,SV1123: $i,SV526: $i] :
( ( ! [SY3285: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV526 )
| ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SY3285 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SY3285 @ SV526 ) @ SV526 ) )
| ~ ( c_lessequals @ SY3285 @ SV1488 @ tc_nat )
| ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3300]) ).
thf(3892,plain,
! [SV1124: $i,SV527: $i] :
( ( ( c_lessequals @ SV527 @ SV1124 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV1124 @ SV527 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3893,plain,
! [SV1489: $i,SV1125: $i,SV528: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV528 )
| ( c_lessequals @ SV1125 @ SV1489 @ SV528 )
| ( c_lessequals @ SV1489 @ SV1125 @ SV528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3894,plain,
! [SV1490: $i,SV1126: $i,SV529: $i] :
( ( ! [SY3286: $i] :
( ~ ( class_Orderings_Oorder @ SV529 )
| ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
| ~ ( c_lessequals @ SV1126 @ SY3286 @ SV529 )
| ~ ( c_lessequals @ SY3286 @ SV1490 @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3895,plain,
! [SV1491: $i,SV1127: $i,SV530: $i] :
( ( ! [SY3287: $i] :
( ~ ( class_Orderings_Opreorder @ SV530 )
| ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SY3287 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1127 @ SY3287 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3896,plain,
! [SV1492: $i,SV1128: $i,SV532: $i] :
( ( ( c_lessequals @ SV532 @ SV1128 @ tc_nat )
| ~ ( c_lessequals @ SV1492 @ SV1128 @ tc_nat )
| ~ ( c_lessequals @ SV532 @ SV1492 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3897,plain,
! [SV1129: $i,SV534: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV534 ) )
= $true )
| ( ( c_lessequals @ SV1129 @ SV1129 @ SV534 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(3898,plain,
! [SV1130: $i,SV535: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV535 ) )
= $true )
| ( ( c_lessequals @ SV1130 @ SV1130 @ SV535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3899,plain,
! [SV1493: $i,SV1131: $i,SV536: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SV1131 @ SV1493 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SV1131 @ SV536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3900,plain,
! [SV1132: $i,SV537: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV537 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV537 ) @ SV1132 @ SV537 )
= ( c_HOL_Oone__class_Oone @ SV537 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3901,plain,
! [SV1494: $i,SV1133: $i,SV538: $i] :
( ( ! [SY3288: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV538 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SY3288 @ SV538 ) @ SV538 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
| ~ ( c_lessequals @ SV1494 @ SY3288 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3902,plain,
! [SV1134: $i,SV539: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV539 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV1134 @ ( c_HOL_Oone__class_Oone @ SV539 ) @ SV539 )
= SV1134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3903,plain,
! [SV1135: $i,SV540: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV540 @ SV1135 @ tc_nat ) @ tc_nat )
= SV1135 )
= $true )
| ( ( ~ ( c_lessequals @ SV1135 @ SV540 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3312]) ).
thf(3904,plain,
! [SV1495: $i,SV1136: $i,SV541: $i] :
( ( ~ ( class_Orderings_Oorder @ SV541 )
| ( SV1136 = SV1495 )
| ~ ( c_lessequals @ SV1136 @ SV1495 @ SV541 )
| ~ ( c_lessequals @ SV1495 @ SV1136 @ SV541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3905,plain,
! [SV1137: $i,SV542: $i] :
( ( ( SV542 = SV1137 )
= $true )
| ( ( ~ ( c_lessequals @ SV1137 @ SV542 @ tc_nat )
| ~ ( c_lessequals @ SV542 @ SV1137 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3314]) ).
thf(3906,plain,
! [SV1496: $i,SV1138: $i,SV543: $i] :
( ( ~ ( class_Orderings_Oorder @ SV543 )
| ( SV1138 = SV1496 )
| ~ ( c_lessequals @ SV1496 @ SV1138 @ SV543 )
| ~ ( c_lessequals @ SV1138 @ SV1496 @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3907,plain,
! [SV1497: $i,SV1139: $i,SV544: $i] :
( ( ~ ( class_Orderings_Oorder @ SV544 )
| ( SV1139 = SV1497 )
| ~ ( c_lessequals @ SV1497 @ SV1139 @ SV544 )
| ~ ( c_lessequals @ SV1139 @ SV1497 @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3908,plain,
! [SV1498: $i,SV1140: $i,SV545: $i] :
( ( ! [SY3289: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV545 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SV1498 @ SV545 ) @ SY3289 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SY3289 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SV1498 @ SY3289 @ SV545 ) @ SV545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3909,plain,
! [SV1499: $i,SV1141: $i,SV546: $i] :
( ( ! [SY3290: $i] :
( ~ ( class_Ring__and__Field_Ofield @ SV546 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1141 @ SV1499 @ SV546 ) @ SY3290 @ SV546 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1141 @ SY3290 @ SV546 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1499 @ SY3290 @ SV546 ) @ SV546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3910,plain,
! [SV1500: $i,SV1142: $i,SV547: $i] :
( ( ! [SY3291: $i] :
( ~ ( class_RealVector_Oreal__normed__field @ SV547 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1142 @ SV1500 @ SV547 ) @ SY3291 @ SV547 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1142 @ SY3291 @ SV547 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1500 @ SY3291 @ SV547 ) @ SV547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3911,plain,
! [SV1501: $i,SV1143: $i,SV548: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV548 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV548 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SV1143 @ SV1501 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SV1143 @ SV548 ) @ SV1501 @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3912,plain,
! [SV1502: $i,SV1144: $i,SV549: $i] :
( ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1502 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ SV1502 @ SV549 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3913,plain,
! [SV1503: $i,SV1145: $i,SV550: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV550 @ SV1503 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV1503 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3914,plain,
! [SV1504: $i,SV1146: $i,SV551: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV551 @ SV1146 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ SV1146 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV551 @ SV1504 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3915,plain,
! [SV1505: $i,SV1147: $i,SV552: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1147 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1505 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1505 @ SV1147 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3916,plain,
! [SV1506: $i,SV1149: $i,SV554: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV554 @ SV1149 @ tc_nat ) @ SV1506 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV554 @ SV1506 @ tc_nat ) @ SV1149 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3326]) ).
thf(3917,plain,
! [SV1507: $i,SV1150: $i,SV555: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1150 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1507 @ SV1150 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1507 @ tc_nat ) )
| ~ ( c_lessequals @ SV1150 @ SV1507 @ tc_nat )
| ~ ( c_lessequals @ SV1150 @ SV555 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3327]) ).
thf(3918,plain,
! [SV556: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV556 )
= $false )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3919,plain,
! [SV557: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV557 )
= $false )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3920,plain,
! [SV558: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV558 )
= $false )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV558 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3921,plain,
! [SV559: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV559 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3922,plain,
! [SV560: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV560 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV560 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3923,plain,
! [SV561: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV561 )
= $false )
| ( ( class_OrderedGroup_Oab__semigroup__add @ SV561 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3924,plain,
! [SV562: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV562 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3925,plain,
! [SV563: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV563 )
= $false )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3926,plain,
! [SV564: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV564 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV564 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3927,plain,
! [SV565: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV565 )
= $false )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3928,plain,
! [SV566: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV566 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__1 @ SV566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3929,plain,
! [SV567: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV567 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV567 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3930,plain,
! [SV568: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV568 )
= $false )
| ( ( class_OrderedGroup_Oab__group__add @ SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3931,plain,
! [SV569: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV569 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3932,plain,
! [SV570: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV570 )
= $false )
| ( ( class_OrderedGroup_Omonoid__mult @ SV570 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3342]) ).
thf(3933,plain,
! [SV571: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV571 )
= $false )
| ( ( class_OrderedGroup_Omonoid__add @ SV571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3343]) ).
thf(3934,plain,
! [SV572: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV572 )
= $false )
| ( ( class_OrderedGroup_Ogroup__add @ SV572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3935,plain,
! [SV573: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV573 )
= $false )
| ( ( class_Ring__and__Field_Oring__1 @ SV573 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3936,plain,
! [SV574: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV574 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV574 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3937,plain,
! [SV575: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV575 )
= $false )
| ( ( class_Power_Opower @ SV575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3938,plain,
! [SV1151: $i,SV576: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV576 @ SV1151 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV576
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3348]) ).
thf(3939,plain,
! [SV1508: $i,SV1152: $i,SV577: $i] :
( ( ! [SY3292: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1508 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SY3292 @ SV577 ) )
| ( SV1508 = SY3292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3940,plain,
! [SV1509: $i,SV1153: $i,SV578: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 )
| ( ( c_Power_Opower__class_Opower @ SV1153 @ SV1509 @ SV578 )
!= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3941,plain,
! [SV1510: $i,SV1154: $i,SV579: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV579 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1154 @ SV1510 @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
| ( SV1154 = SV1510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3942,plain,
! [SV1155: $i,SV580: $i] :
( ( ( ( c_Suc @ SV580 )
!= ( c_Suc @ SV1155 ) )
= $true )
| ( ( SV580 = SV1155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3352]) ).
thf(3943,plain,
! [SV1156: $i,SV582: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV1156 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV582
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3944,plain,
! [SV1157: $i,SV583: $i] :
( ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV583 @ SV1157 @ tc_nat ) )
!= SV1157 )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV583 ) @ SV1157 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3945,plain,
! [SV1158: $i,SV584: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV584 @ SV1158 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1158
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1158
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3946,plain,
! [SV1159: $i,SV586: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV586 @ SV1159 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1159
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3947,plain,
! [SV1160: $i,SV587: $i] :
( ( ( ~ ( class_SEQ_Obanach @ SV587 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__field @ SV587 )
| ( ( c_Transcendental_Oexp @ SV1160 @ SV587 )
!= ( c_HOL_Ozero__class_Ozero @ SV587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3948,plain,
! [SV1511: $i,SV1161: $i,SV588: $i] :
( ( ! [SY3293: $i,SY3294: $i,SY3295: $i] :
( ~ ( class_Divides_Osemiring__div @ SV588 )
| ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY3293 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3294 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY3295 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3294 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3295 @ SY3293 @ SV588 ) @ SV1511 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3949,plain,
! [SV1512: $i,SV1162: $i,SV590: $i] :
( ( ! [SY3296: $i,SY3297: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SY3296 @ SY3297 @ SV590 ) )
| ( c_lessequals @ SY3297 @ SY3296 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3950,plain,
! [SV1163: $i,SV591: $i] :
( ( ( SV591
!= ( c_HOL_Oplus__class_Oplus @ SV591 @ SV1163 @ tc_nat ) )
= $true )
| ( ( SV1163
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3363]) ).
thf(3951,plain,
! [SV1164: $i,SV592: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV592 @ SV1164 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1164
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3952,plain,
! [SV1513: $i,SV1165: $i,SV593: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV593 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
| ( SV1165 = SV1513 )
| ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(3953,plain,
! [SV1166: $i,SV594: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV594 @ SV1166 @ tc_nat ) )
= $true )
| ( ( ( SV1166
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1166
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3954,plain,
! [SV1514: $i,SV1167: $i,SV595: $i] :
( ( ! [SY3298: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SV1514 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SY3298 @ SV1514 @ SV595 ) )
| ( SV1167 = SY3298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3955,plain,
! [SV1515: $i,SV1168: $i,SV596: $i] :
( ( ! [SY3299: $i,SY3300: $i,SY3301: $i] :
( ~ ( class_Divides_Oring__div @ SV596 )
| ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY3299 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3300 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY3301 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3300 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3301 @ SY3299 @ SV596 ) @ SV1515 @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3956,plain,
! [SV1169: $i,SV597: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV597 @ SV1169 @ tc_nat )
!= SV597 )
= $true )
| ( ( SV1169
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3369]) ).
thf(3957,plain,
! [SV1516: $i,SV1170: $i,SV598: $i] :
( ( ! [SY3302: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV598 )
| ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SY3302 @ SV1516 @ SV598 ) )
| ( SV1170 = SY3302 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SY3302 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3958,plain,
! [SV1517: $i,SV1171: $i,SV599: $i] :
( ( ! [SY3303: $i,SY3304: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SY3303 @ SY3304 @ SV599 ) )
| ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SY3304 @ SY3303 @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3959,plain,
! [SV1172: $i,SV600: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV600 @ SV1172 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV600
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3960,plain,
! [SV1518: $i,SV1173: $i,SV601: $i] :
( ( ! [SY3305: $i] :
( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1518 @ SY3305 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV1173 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV601 @ SY3305 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3961,plain,
! [SV1174: $i,SV602: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV602 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
| ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3962,plain,
! [SV1519: $i,SV1175: $i,SV603: $i] :
( ( ! [SY3306: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV603 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SV1519 @ SY3306 @ SV603 ) )
| ( SV1519 = SY3306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3963,plain,
! [SV1520: $i,SV1176: $i,SV604: $i] :
( ( ! [SY3307: $i,SY3308: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV604 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SY3307 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SY3308 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SY3307 @ SV604 )
= SY3308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3964,plain,
( ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ t_a ) @ v_a @ t_a ) @ ( c_HOL_Ominus__class_Ominus @ v_n @ v_m @ tc_nat ) @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3965,plain,
! [SV1177: $i,SV605: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV605 @ SV1177 @ tc_nat ) )
= $true )
| ( ( ( SV605
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV605
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3966,plain,
! [SV1521: $i,SV1178: $i,SV606: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV606 )
| ( ( c_Divides_Odiv__class_Omod @ SV1178 @ SV1521 @ SV606 )
!= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1521 @ SV1178 @ SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3967,plain,
! [SV1522: $i,SV1179: $i,SV607: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1179 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1522 @ tc_nat ) )
| ( SV1179 = SV1522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3968,plain,
! [SV1523: $i,SV1180: $i,SV608: $i] :
( ( ! [SY3309: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1523 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SY3309 @ SV608 ) )
| ( SV1523 = SY3309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3969,plain,
! [SV609: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV609 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV609 )
!= ( c_HOL_Ozero__class_Ozero @ SV609 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3970,plain,
! [SV1524: $i,SV1181: $i,SV610: $i] :
( ( ! [SY3310: $i,SY3311: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SY3310 @ SY3311 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SY3310 @ SY3311 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3971,plain,
! [SV1525: $i,SV1182: $i,SV611: $i] :
( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV611 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
| ( SV1182 = SV1525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3972,plain,
! [SV1183: $i,SV612: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV612 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1183 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1183
= ( c_HOL_Ozero__class_Ozero @ SV612 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3973,plain,
( ( ( v_a
= ( c_HOL_Ozero__class_Ozero @ t_a ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3974,plain,
! [SV1184: $i,SV613: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1184 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV613 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1184 = SV613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3975,plain,
! [SV1526: $i,SV1185: $i,SV614: $i] :
( ( ! [SY3312: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV614 )
| ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SV1185 @ SY3312 @ SV614 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SV1526 = SY3312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3976,plain,
! [SV615: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV615 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV615 )
!= ( c_HOL_Oone__class_Oone @ SV615 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3977,plain,
! [SV1186: $i,SV616: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ SV1186 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV616 @ SV1186 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3978,plain,
! [SV1527: $i,SV1187: $i,SV617: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV617 )
| ~ ( class_Int_Onumber__ring @ SV617 )
| ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
| ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3979,plain,
! [SV1188: $i,SV618: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV618 @ SV1188 @ tc_nat ) )
= $true )
| ( ( ( SV1188
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV618
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3980,plain,
! [SV1189: $i,SV619: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV619 @ SV1189 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1189
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3981,plain,
! [SV1528: $i,SV1190: $i,SV620: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV620 )
| ~ ( class_Int_Onumber__ring @ SV620 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SV1190 = SV1528 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3982,plain,
! [SV1191: $i,SV622: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV622 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1191 @ SV1191 @ SV622 )
!= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
| ( SV1191
= ( c_HOL_Ozero__class_Ozero @ SV622 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3983,plain,
! [SV1192: $i,SV623: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV623 @ SV1192 @ tc_nat )
!= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( SV1192
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3984,plain,
! [SV1193: $i,SV624: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV624 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3985,plain,
! [SV1529: $i,SV1194: $i,SV625: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV625 @ SV1194 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1529 @ SV1194 @ tc_nat ) )
| ( SV625 = SV1529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3986,plain,
( ( ( v_a
= ( c_HOL_Ozero__class_Ozero @ t_a ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ t_a )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(3987,plain,
! [SV1195: $i,SV627: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV627 @ SV1195 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3402]) ).
thf(3988,plain,
! [SV1530: $i,SV1196: $i,SV628: $i] :
( ( ! [SY3313: $i,SY3314: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SY3313 @ SY3314 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SY3313 @ SY3314 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(3989,plain,
( ( ( c_lessequals @ v_n @ v_m @ tc_nat )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ v_a @ v_m @ t_a ) @ ( c_Power_Opower__class_Opower @ v_a @ v_n @ t_a ) @ t_a )
= ( c_Power_Opower__class_Opower @ v_a @ ( c_HOL_Ominus__class_Ominus @ v_m @ v_n @ tc_nat ) @ t_a ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3990,plain,
! [SV1197: $i,SV629: $i] :
( ( ( ( c_Suc @ SV629 )
!= ( c_Suc @ SV1197 ) )
= $true )
| ( ( SV629 = SV1197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3405]) ).
thf(3991,plain,
! [SV1531: $i,SV1198: $i,SV630: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV630 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1198 @ SV1531 @ SV630 )
!= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
| ( SV1198 = SV1531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(3992,plain,
! [SV1199: $i,SV631: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV631 @ SV1199 @ tc_nat )
!= SV631 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV631 @ SV1199 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(3993,plain,
! [SV1532: $i,SV1200: $i,SV632: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
!= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(3994,plain,
! [SV1201: $i,SV633: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV633 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV633 )
| ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3410]) ).
thf(3995,plain,
! [SV1533: $i,SV1202: $i,SV634: $i] :
( ( ! [SY3315: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV634 )
| ~ ( class_Int_Onumber__ring @ SV634 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SY3315 @ SV634 ) )
| ( SV1533 = SY3315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(3996,plain,
! [SV1534: $i,SV1203: $i,SV635: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
| ~ ( c_lessequals @ SV1203 @ SV1534 @ tc_nat )
| ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
| ( SV635 = SV1534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3997,plain,
! [SV1535: $i,SV1204: $i,SV636: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1204 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1535 @ tc_nat ) )
| ( SV1204 = SV1535 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3998,plain,
! [SV1536: $i,SV1205: $i,SV637: $i] :
( ( ! [SY3316: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV637 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SV1536 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SY3316 @ SY3316 @ SV637 ) )
| ( SV1205 = SV1536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(3999,plain,
! [SV1537: $i,SV1206: $i,SV638: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
!= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(4000,plain,
! [SV1538: $i,SV1207: $i,SV639: $i] :
( ( ! [SY3317: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SY3317 @ ( c_Suc @ SV1538 ) @ SV639 ) )
| ( SV1207 = SY3317 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SY3317 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(4001,plain,
! [SV1208: $i,SV640: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
!= ( c_HOL_Oplus__class_Oplus @ SV640 @ SV1208 @ tc_nat ) )
= $true )
| ( ( ( SV640
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1208
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3417]) ).
thf(4002,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4003,plain,
! [SV1210: $i,SV643: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV643 @ SV1210 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1210
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3420]) ).
thf(4004,plain,
! [SV1540: $i,SV1211: $i,SV644: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV644 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SV1540 @ SV644 )
!= ( c_HOL_Oone__class_Oone @ SV644 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SV1211 = SV1540 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4005,plain,
! [SV1541: $i,SV1212: $i,SV645: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV645 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV645 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV645 ) )
| ( SV1212 = SV1541 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(4006,plain,
! [SV1542: $i,SV1213: $i,SV646: $i,SV1: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV1 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV646 @ SV1213 @ SV1 ) @ SV1542 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV646 @ ( c_HOL_Oplus__class_Oplus @ SV1213 @ SV1542 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(4007,plain,
! [SV1543: $i,SV1214: $i,SV647: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
| ( ( c_HOL_Oplus__class_Oplus @ SV647 @ ( c_HOL_Oplus__class_Oplus @ SV1214 @ SV1543 @ SV2 ) @ SV2 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV647 @ SV1214 @ SV2 ) @ SV1543 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(4008,plain,
! [SV1544: $i,SV1215: $i,SV648: $i,SV3: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV3 )
| ( ( c_HOL_Oplus__class_Oplus @ SV648 @ ( c_HOL_Oplus__class_Oplus @ SV1215 @ SV1544 @ SV3 ) @ SV3 )
= ( c_HOL_Oplus__class_Oplus @ SV1215 @ ( c_HOL_Oplus__class_Oplus @ SV648 @ SV1544 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(4009,plain,
! [SV1545: $i,SV1218: $i,SV651: $i,SV6: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV6 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV1218 @ SV6 ) @ SV1545 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ SV651 @ ( c_HOL_Oplus__class_Oplus @ SV1218 @ SV1545 @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4010,plain,
! [SV1546: $i,SV1219: $i,SV652: $i,SV7: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
| ( ( c_HOL_Oplus__class_Oplus @ SV652 @ ( c_HOL_Oplus__class_Oplus @ SV1219 @ SV1546 @ SV7 ) @ SV7 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV652 @ SV1219 @ SV7 ) @ SV1546 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(4011,plain,
! [SV1547: $i,SV1220: $i,SV653: $i,SV8: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV8 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1220 @ SV8 ) @ SV1547 @ SV8 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1547 @ SV8 ) @ SV1220 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(4012,plain,
! [SV1548: $i,SV1221: $i,SV654: $i,SV9: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
| ( ( c_HOL_Oplus__class_Oplus @ SV654 @ ( c_HOL_Oplus__class_Oplus @ SV1221 @ SV1548 @ SV9 ) @ SV9 )
= ( c_HOL_Oplus__class_Oplus @ SV1221 @ ( c_HOL_Oplus__class_Oplus @ SV654 @ SV1548 @ SV9 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(4013,plain,
! [SV1549: $i,SV1222: $i,SV655: $i,SV10: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV10 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV655 @ SV1222 @ SV10 ) @ SV1549 @ SV10 )
= ( c_HOL_Oplus__class_Oplus @ SV655 @ ( c_HOL_Oplus__class_Oplus @ SV1222 @ SV1549 @ SV10 ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(4014,plain,
! [SV11: $i,SV656: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV656 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV656 @ SV11 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV11 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3433]) ).
thf(4015,plain,
! [SV1550: $i,SV1223: $i,SV657: $i,SV13: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV13 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ SV1223 @ SV13 ) @ SV1550 @ SV13 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ ( c_Divides_Odiv__class_Omod @ SV1223 @ SV1550 @ SV13 ) @ SV13 ) @ SV1550 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4016,plain,
! [SV1551: $i,SV1224: $i,SV658: $i,SV14: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV14 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV658 @ SV1224 @ SV14 ) @ SV1551 @ SV14 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV658 @ SV1551 @ SV14 ) @ SV1224 @ SV14 ) @ SV1551 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4017,plain,
! [SV1552: $i,SV1225: $i,SV659: $i,SV15: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4018,plain,
! [SV1226: $i,SV661: $i,SV17: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV17 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV661 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV661 @ SV1226 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(4019,plain,
! [SV18: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV18 @ ( c_Suc @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ tc_nat )
= $false )
| ( ( SV18
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV18
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(4020,plain,
! [SV662: $i,SV21: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV21 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(4021,plain,
! [SV1227: $i,SV663: $i,SV22: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV22 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3440]) ).
thf(4022,plain,
! [SV1228: $i,SV666: $i,SV25: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(4023,plain,
! [SV1553: $i,SV1229: $i,SV667: $i,SV26: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(4024,plain,
! [SV668: $i,SV27: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV27 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
| ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(4025,plain,
! [SV669: $i,SV28: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV28 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
| ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(4026,plain,
! [SV670: $i,SV29: $i] :
( ( ( ( c_Suc @ SV29 )
= SV670 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV29 @ SV670 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV29 ) @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(4027,plain,
! [SV671: $i,SV30: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV30 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
| ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(4028,plain,
! [SV672: $i,SV31: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV31 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV672 @ SV31 ) @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV672 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(4029,plain,
! [SV673: $i,SV32: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV32 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(4030,plain,
! [SV674: $i,SV33: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV33 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3449]) ).
thf(4031,plain,
! [SV675: $i,SV34: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV34 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV675 @ SV34 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3450]) ).
thf(4032,plain,
! [SV1554: $i,SV1230: $i,SV676: $i,SV35: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV35 )
| ( ( c_HOL_Oplus__class_Oplus @ SV676 @ ( c_HOL_Oplus__class_Oplus @ SV1230 @ SV1554 @ SV35 ) @ SV35 )
= ( c_HOL_Oplus__class_Oplus @ SV1230 @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV1554 @ SV35 ) @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4033,plain,
! [SV1555: $i,SV1231: $i,SV677: $i,SV36: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4034,plain,
! [SV1556: $i,SV1232: $i,SV678: $i,SV37: $i] :
( ( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(4035,plain,
! [SV679: $i,SV38: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV38 )
= $false )
| ( ( ( SV679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV679 @ SV38 ) @ SV38 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(4036,plain,
! [SV1557: $i,SV1233: $i,SV680: $i,SV39: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV39 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV1233 @ SV39 ) @ SV1557 @ SV39 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV680 @ SV1557 @ SV39 ) @ ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1557 @ SV39 ) @ SV39 ) @ SV1557 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(4037,plain,
! [SV41: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(4038,plain,
! [SV681: $i,SV42: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV42 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV42 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV42 ) @ SV42 )
= SV681 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(4039,plain,
! [SV683: $i,SV45: $i] :
( ( ( class_Divides_Osemiring__div @ SV45 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ SV683 @ SV45 )
= ( c_HOL_Ozero__class_Ozero @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(4040,plain,
! [SV684: $i,SV46: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV46 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV46 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Suc @ SV684 ) @ SV46 )
= ( c_HOL_Ozero__class_Ozero @ SV46 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(4041,plain,
! [SV1558: $i,SV1234: $i,SV688: $i,SV50: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4042,plain,
! [SV1559: $i,SV1235: $i,SV689: $i,SV51: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
| ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4043,plain,
! [SV690: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV52 ) @ SV690 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV52 @ SV690 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(4044,plain,
! [SV691: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ SV691 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV53 ) @ SV691 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(4045,plain,
! [SV692: $i,SV54: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV692 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV54 @ SV692 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3467]) ).
thf(4046,plain,
! [SV693: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV693 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV55 ) @ SV693 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(4047,plain,
! [SV1236: $i,SV694: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ ( c_HOL_Oplus__class_Oplus @ SV694 @ SV1236 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV1236 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3469]) ).
thf(4048,plain,
! [SV1237: $i,SV695: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1237 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV57 @ SV695 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(4049,plain,
! [SV1238: $i,SV696: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV58 @ SV696 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV58 @ SV1238 @ tc_nat ) @ SV696 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3471]) ).
thf(4050,plain,
! [SV1239: $i,SV697: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1239 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV59 @ SV1239 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3472]) ).
thf(4051,plain,
! [SV1240: $i,SV698: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV60 @ ( c_HOL_Oplus__class_Oplus @ SV698 @ SV1240 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV60 @ SV698 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(4052,plain,
! [SV1560: $i,SV1241: $i,SV699: $i,SV61: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV61 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(4053,plain,
! [SV1561: $i,SV1242: $i,SV700: $i,SV62: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV62 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(4054,plain,
! [SV1562: $i,SV1243: $i,SV701: $i,SV63: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV63 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4055,plain,
! [SV1563: $i,SV1244: $i,SV702: $i,SV64: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV64 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4056,plain,
! [SV65: $i,SV703: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV703 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Divides_Odiv__class_Omod @ SV65 @ SV703 @ tc_nat ) @ SV703 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(4057,plain,
! [SV705: $i,SV67: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV67 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV705 @ SV705 @ SV67 ) @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
| ~ ( c_HOL_Oord__class_Oless @ SV705 @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(4058,plain,
! [SV706: $i,SV68: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV706 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV706 @ SV706 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(4059,plain,
! [SV707: $i,SV69: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV707 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV707 @ SV707 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(4060,plain,
! [SV708: $i,SV70: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV70 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV708 @ SV708 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
| ~ ( c_HOL_Oord__class_Oless @ SV708 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(4061,plain,
! [SV1245: $i,SV709: $i,SV72: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3483]) ).
thf(4062,plain,
! [SV1246: $i,SV710: $i,SV73: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(4063,plain,
! [SV711: $i,SV74: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV74 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
| ~ ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(4064,plain,
! [SV712: $i,SV75: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV75 @ SV712 @ tc_nat )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV75 @ SV712 @ tc_nat )
= SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(4065,plain,
! [SV1247: $i,SV713: $i,SV76: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV76 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV713 @ SV1247 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV1247 @ SV713 @ SV76 )
| ( SV1247 = SV713 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3487]) ).
thf(4066,plain,
! [SV77: $i,SV714: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV714 @ SV77 @ tc_nat )
= $true )
| ( ( SV714 = SV77 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV77 @ SV714 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(4067,plain,
! [SV715: $i,SV78: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV78 @ SV715 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV715 @ SV78 @ tc_nat )
| ( SV715 = SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3489]) ).
thf(4068,plain,
! [SV716: $i,SV79: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV79 @ SV716 @ tc_nat )
= $false )
| ( ( ( SV716 = SV79 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV716 @ SV79 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(4069,plain,
! [SV717: $i,SV80: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV80 @ SV717 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV80 @ tc_nat ) )
= $true )
| ( ( SV80 = SV717 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(4070,plain,
! [SV81: $i,SV718: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV718 @ SV81 @ tc_nat )
= $true )
| ( ( SV718 = SV81 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV81 @ SV718 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(4071,plain,
! [SV82: $i,SV719: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV719 @ SV82 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV82 @ SV719 @ tc_nat ) )
= $true )
| ( ( SV82 = SV719 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(4072,plain,
! [SV720: $i,SV83: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV83 @ SV720 @ tc_nat )
= $false )
| ( ( ( SV720 = SV83 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV720 @ SV83 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(4073,plain,
! [SV84: $i,SV721: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV721 @ SV84 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV84 @ SV721 @ tc_nat ) )
= $true )
| ( ( SV84 = SV721 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3495]) ).
thf(4074,plain,
! [SV85: $i,SV722: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV85 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV85 @ SV722 @ tc_nat ) )
= $true )
| ( ( SV85 = SV722 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3496]) ).
thf(4075,plain,
! [SV1248: $i,SV723: $i,SV86: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV86 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV723 @ SV1248 @ SV86 )
| ( SV1248 = SV723 )
| ( c_HOL_Oord__class_Oless @ SV1248 @ SV723 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3497]) ).
thf(4076,plain,
! [SV1249: $i,SV724: $i,SV87: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV87 ) )
= $true )
| ( ( ( SV724 = SV1249 )
| ( c_HOL_Oord__class_Oless @ SV724 @ SV1249 @ SV87 )
| ( c_HOL_Oord__class_Oless @ SV1249 @ SV724 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3498]) ).
thf(4077,plain,
! [SV1250: $i,SV725: $i,SV88: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV88 ) )
= $true )
| ( ( ( SV725 = SV1250 )
| ( c_HOL_Oord__class_Oless @ SV1250 @ SV725 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SV1250 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3499]) ).
thf(4078,plain,
! [SV1251: $i,SV726: $i,SV89: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV89 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV726 @ SV1251 @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV1251 @ SV726 @ SV89 )
| ( SV1251 = SV726 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(4079,plain,
! [SV1252: $i,SV727: $i,SV90: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ SV727 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ ( c_GCD_Ogcd__class_Ogcd @ SV1252 @ SV727 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(4080,plain,
! [SV1253: $i,SV728: $i,SV91: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ SV728 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ ( c_GCD_Ogcd__class_Ogcd @ SV728 @ SV1253 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(4081,plain,
! [SV1254: $i,SV729: $i,SV92: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ SV729 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ ( c_GCD_Ogcd__class_Ogcd @ SV729 @ SV1254 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(4082,plain,
! [SV1255: $i,SV730: $i,SV93: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ SV730 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ ( c_GCD_Ogcd__class_Ogcd @ SV1255 @ SV730 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3504]) ).
thf(4083,plain,
! [SV1256: $i,SV731: $i,SV94: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV94 @ SV731 @ tc_nat ) @ SV1256 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV1256 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3505]) ).
thf(4084,plain,
! [SV1257: $i,SV732: $i,SV95: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV95 @ SV732 @ tc_nat ) @ SV1257 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV732 @ SV1257 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(4085,plain,
! [SV1258: $i,SV733: $i,SV96: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ SV733 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ ( c_GCD_Ogcd__class_Ogcd @ SV733 @ SV1258 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(4086,plain,
! [SV1259: $i,SV734: $i,SV97: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ SV734 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ ( c_GCD_Ogcd__class_Ogcd @ SV1259 @ SV734 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(4087,plain,
! [SV1260: $i,SV735: $i,SV98: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV735 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1260 @ SV735 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV1260 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(4088,plain,
! [SV1261: $i,SV736: $i,SV99: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3510]) ).
thf(4089,plain,
! [SV737: $i,SV100: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV100 @ SV737 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV737 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV100 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(4090,plain,
! [SV738: $i,SV102: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV102 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV738 @ SV738 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3512]) ).
thf(4091,plain,
! [SV1564: $i,SV1262: $i,SV739: $i,SV103: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4092,plain,
! [SV1263: $i,SV740: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SV740 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1263 @ SV740 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV1263 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(4093,plain,
! [SV741: $i,SV107: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV107 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV741 @ ( c_HOL_Oplus__class_Oplus @ SV741 @ ( c_HOL_Oone__class_Oone @ SV107 ) @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3515]) ).
thf(4094,plain,
! [SV742: $i,SV108: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV108 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(4095,plain,
! [SV743: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV109 )
| ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(4096,plain,
! [SV744: $i,SV110: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV110 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV110 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV744 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(4097,plain,
! [SV1264: $i,SV745: $i,SV111: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV111 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1264 @ SV111 ) @ SV745 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ SV1264 @ SV745 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(4098,plain,
! [SV1265: $i,SV746: $i,SV112: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV112 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV746 @ SV1265 @ SV112 ) @ SV1265 @ SV112 )
= ( c_Divides_Odiv__class_Omod @ SV746 @ SV1265 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(4099,plain,
! [SV1565: $i,SV1266: $i,SV747: $i,SV113: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 )
| ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4100,plain,
! [SV748: $i,SV114: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV114 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
| ( SV748
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV748 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(4101,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV116 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3524]) ).
thf(4102,plain,
! [SV1268: $i,SV751: $i,SV117: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV117 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
| ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3525]) ).
thf(4103,plain,
! [SV1269: $i,SV752: $i,SV118: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV118 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
| ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(4104,plain,
! [SV1270: $i,SV753: $i,SV119: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV119 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(4105,plain,
! [SV1271: $i,SV754: $i,SV120: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV120 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3528]) ).
thf(4106,plain,
! [SV1272: $i,SV755: $i,SV121: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV121 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(4107,plain,
! [SV1273: $i,SV756: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV122 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(4108,plain,
! [SV757: $i,SV124: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV124 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV757 @ SV124 ) @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3532]) ).
thf(4109,plain,
! [SV758: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV125 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV758 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3533]) ).
thf(4110,plain,
! [SV759: $i,SV126: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV126 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV126 ) @ SV126 )
= SV759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(4111,plain,
! [SV760: $i,SV127: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV127 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV127 ) @ SV760 @ SV127 )
= SV760 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(4112,plain,
! [SV761: $i,SV128: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV128 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV128 ) @ SV128 )
= SV761 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(4113,plain,
! [SV762: $i,SV129: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV129 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV129 )
| ( SV762
= ( c_HOL_Oplus__class_Oplus @ SV762 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(4114,plain,
! [SV763: $i,SV130: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV130 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV130 ) @ SV763 @ SV130 )
= SV763 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3538]) ).
thf(4115,plain,
! [SV764: $i,SV131: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV131 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV131 ) @ SV764 @ SV131 )
= SV764 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3539]) ).
thf(4116,plain,
! [SV765: $i,SV135: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV135 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV765 @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ SV135 )
= SV765 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3540]) ).
thf(4117,plain,
! [SV766: $i,SV136: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV136 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV136 ) @ SV766 @ SV136 )
= SV766 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(4118,plain,
! [SV1274: $i,SV767: $i,SV137: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SV767 @ SV1274 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV1274 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV767 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(4119,plain,
! [SV1275: $i,SV768: $i,SV138: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SV768 @ SV1275 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SV1275 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1275 @ SV138 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(4120,plain,
! [SV1276: $i,SV769: $i,SV139: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SV769 @ SV1276 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SV769 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV769 @ SV139 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(4121,plain,
! [SV1277: $i,SV770: $i,SV140: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SV770 @ SV1277 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV1277 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV770 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3545]) ).
thf(4122,plain,
! [SV1278: $i,SV771: $i,SV141: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SV771 @ SV1278 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV1278 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV771 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3546]) ).
thf(4123,plain,
! [SV1279: $i,SV778: $i,SV148: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SV778 @ SV1279 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV1279 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV778 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3547]) ).
thf(4124,plain,
! [SV1280: $i,SV779: $i,SV149: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SV779 @ SV1280 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV1280 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV779 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3548]) ).
thf(4125,plain,
! [SV1281: $i,SV780: $i,SV150: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SV780 @ SV1281 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV1281 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV780 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3549]) ).
thf(4126,plain,
! [SV1566: $i,SV1282: $i,SV781: $i,SV151: $i] :
( ( ! [SY3318: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SY3318 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SV1282 @ SY3318 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4127,plain,
! [SV1567: $i,SV1283: $i,SV782: $i,SV152: $i] :
( ( ! [SY3319: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SY3319 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SY3319 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4128,plain,
! [SV783: $i,SV153: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV153 @ SV783 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV153 ) @ ( c_Suc @ SV783 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(4129,plain,
! [SV784: $i,SV154: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV154 ) @ ( c_Suc @ SV784 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV154 @ SV784 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3553]) ).
thf(4130,plain,
! [SV785: $i,SV155: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV155 @ SV785 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV155 ) @ ( c_Suc @ SV785 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3554]) ).
thf(4131,plain,
! [SV1284: $i,SV786: $i,SV156: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(4132,plain,
! [SV1285: $i,SV787: $i,SV157: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3556]) ).
thf(4133,plain,
! [SV1568: $i,SV1286: $i,SV788: $i,SV158: $i] :
( ( ~ ( class_Orderings_Oorder @ SV158 )
| ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
| ~ ( c_lessequals @ SV788 @ SV1568 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4134,plain,
! [SV1569: $i,SV1287: $i,SV789: $i,SV159: $i] :
( ( ~ ( class_Orderings_Oorder @ SV159 )
| ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 )
| ~ ( c_lessequals @ SV1569 @ SV1287 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4135,plain,
! [SV1570: $i,SV1288: $i,SV790: $i,SV160: $i] :
( ( ! [SY3320: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
| ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SY3320 @ SV1570 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SY3320 @ SV160 ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4136,plain,
! [SV1571: $i,SV1289: $i,SV791: $i,SV161: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV161 )
| ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
| ~ ( c_lessequals @ SV1571 @ SV1289 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(4137,plain,
! [SV1572: $i,SV1290: $i,SV792: $i,SV162: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV162 )
| ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 )
| ~ ( c_lessequals @ SV792 @ SV1572 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(4138,plain,
! [SV1291: $i,SV793: $i,SV163: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV163 ) )
= $true )
| ( ( ( c_lessequals @ SV793 @ SV1291 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV1291 @ SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3562]) ).
thf(4139,plain,
! [SV1292: $i,SV794: $i,SV164: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV164 ) )
= $true )
| ( ( ( c_lessequals @ SV794 @ SV1292 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV1292 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3563]) ).
thf(4140,plain,
! [SV1293: $i,SV795: $i,SV165: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV165 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1293 @ SV165 )
| ( c_lessequals @ SV1293 @ SV795 @ SV165 )
| ~ ( c_lessequals @ SV795 @ SV1293 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(4141,plain,
! [SV1573: $i,SV1294: $i,SV796: $i,SV166: $i] :
( ( ! [SY3321: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SY3321 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SV1294 @ SY3321 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(4142,plain,
! [SV1295: $i,SV797: $i,SV167: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV167 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1295 @ SV167 )
| ( SV1295 = SV797 )
| ~ ( c_lessequals @ SV797 @ SV1295 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(4143,plain,
! [SV1296: $i,SV798: $i,SV168: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV168 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV798 @ SV1296 @ SV168 )
| ~ ( c_lessequals @ SV798 @ SV1296 @ SV168 )
| ( SV1296 = SV798 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3567]) ).
thf(4144,plain,
! [SV1297: $i,SV799: $i,SV169: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV169 ) )
= $true )
| ( ( ( SV799 = SV1297 )
| ( c_HOL_Oord__class_Oless @ SV799 @ SV1297 @ SV169 )
| ~ ( c_lessequals @ SV799 @ SV1297 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(4145,plain,
! [SV1298: $i,SV800: $i,SV170: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV170 ) )
= $true )
| ( ( ( SV800 = SV1298 )
| ~ ( c_lessequals @ SV800 @ SV1298 @ SV170 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1298 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3569]) ).
thf(4146,plain,
! [SV1299: $i,SV801: $i,SV171: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV171 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV801 @ SV1299 @ SV171 )
| ~ ( c_lessequals @ SV801 @ SV1299 @ SV171 )
| ( SV801 = SV1299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(4147,plain,
! [SV1300: $i,SV802: $i,SV172: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV172 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV802 @ SV1300 @ SV172 )
| ( SV802 = SV1300 )
| ~ ( c_lessequals @ SV802 @ SV1300 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3571]) ).
thf(4148,plain,
! [SV1301: $i,SV803: $i,SV173: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV173 ) )
= $true )
| ( ( ( SV803 = SV1301 )
| ( c_HOL_Oord__class_Oless @ SV803 @ SV1301 @ SV173 )
| ~ ( c_lessequals @ SV803 @ SV1301 @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(4149,plain,
! [SV1302: $i,SV804: $i,SV174: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV174 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1302 @ SV174 )
| ( SV804 = SV1302 )
| ~ ( c_lessequals @ SV804 @ SV1302 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(4150,plain,
! [SV1574: $i,SV1303: $i,SV805: $i,SV175: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SV1303 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1574 @ SV1303 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV805 @ SV1574 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4151,plain,
! [SV1575: $i,SV1304: $i,SV806: $i,SV176: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
| ( c_lessequals @ SV806 @ SV1304 @ SV176 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1575 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SV1304 @ SV1575 @ SV176 ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4152,plain,
! [SV1576: $i,SV1305: $i,SV807: $i,SV177: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1305 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1576 @ SV177 ) @ SV177 )
| ~ ( c_lessequals @ SV1305 @ SV1576 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4153,plain,
! [SV1577: $i,SV1306: $i,SV808: $i,SV178: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
| ( c_lessequals @ SV808 @ SV1306 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV1306 @ SV178 ) @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4154,plain,
! [SV1578: $i,SV1307: $i,SV809: $i,SV179: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SV1307 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SV1578 @ SV1307 @ SV179 ) @ SV179 )
| ~ ( c_lessequals @ SV809 @ SV1578 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4155,plain,
! [SV1579: $i,SV1308: $i,SV810: $i,SV180: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1308 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1579 @ SV180 ) @ SV180 )
| ~ ( c_lessequals @ SV1308 @ SV1579 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(4156,plain,
! [SV1309: $i,SV811: $i,SV181: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV181 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV811 @ SV1309 @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ SV1309 @ SV811 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(4157,plain,
! [SV1310: $i,SV812: $i,SV182: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV182 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV812 @ SV1310 @ SV182 )
| ( c_lessequals @ SV1310 @ SV812 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(4158,plain,
! [SV813: $i,SV183: $i] :
( ( ( class_Orderings_Olinorder @ SV183 )
= $false )
| ( ( ~ ( c_lessequals @ SV813 @ SV813 @ SV183 )
| ~ ( c_HOL_Oord__class_Oless @ SV813 @ SV813 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(4159,plain,
! [SV814: $i,SV184: $i] :
( ( ( class_Orderings_Olinorder @ SV184 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV814 @ SV814 @ SV184 )
| ( c_lessequals @ SV814 @ SV814 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(4160,plain,
! [SV1311: $i,SV815: $i,SV185: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV185 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV815 @ SV1311 @ SV185 )
| ~ ( c_lessequals @ SV1311 @ SV815 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(4161,plain,
! [SV1312: $i,SV816: $i,SV186: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV186 ) )
= $true )
| ( ( ( c_lessequals @ SV816 @ SV1312 @ SV186 )
| ( c_HOL_Oord__class_Oless @ SV1312 @ SV816 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3585]) ).
thf(4162,plain,
! [SV1313: $i,SV817: $i,SV187: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV187 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV817 @ SV1313 @ SV187 )
| ( c_lessequals @ SV1313 @ SV817 @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3586]) ).
thf(4163,plain,
! [SV1314: $i,SV818: $i,SV188: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV188 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV818 @ SV1314 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV1314 @ SV818 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(4164,plain,
! [SV819: $i,SV189: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV189 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
| ~ ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(4165,plain,
! [SV820: $i,SV190: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV190 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
| ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(4166,plain,
! [SV1580: $i,SV1315: $i,SV821: $i,SV191: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SV821 @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4167,plain,
! [SV822: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV192 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV822 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV192 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(4168,plain,
! [SV1581: $i,SV1316: $i,SV823: $i,SV193: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(4169,plain,
! [SV1582: $i,SV1317: $i,SV824: $i,SV194: $i] :
( ( ! [SY3322: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV194 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SY3322 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SY3322 @ SV1317 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SY3322 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4170,plain,
! [SV1318: $i,SV825: $i,SV195: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV195 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
| ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4171,plain,
! [SV1319: $i,SV826: $i,SV196: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV196 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4172,plain,
! [SV1583: $i,SV1320: $i,SV827: $i,SV197: $i] :
( ( ! [SY3323: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV197 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SY3323 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SY3323 @ SV1320 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SY3323 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(4173,plain,
! [SV1321: $i,SV828: $i,SV198: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV198 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 )
| ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3597]) ).
thf(4174,plain,
! [SV1322: $i,SV829: $i,SV199: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV199 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(4175,plain,
! [SV1584: $i,SV1323: $i,SV830: $i,SV200: $i] :
( ( ! [SY3324: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SY3324 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SY3324 @ SV1323 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SY3324 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4176,plain,
! [SV1585: $i,SV1324: $i,SV831: $i,SV201: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV201 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
| ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(4177,plain,
! [SV1586: $i,SV1325: $i,SV832: $i,SV202: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV202 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4178,plain,
! [SV1587: $i,SV1326: $i,SV833: $i,SV203: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV203 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4179,plain,
! [SV1588: $i,SV1327: $i,SV834: $i,SV204: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV204 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4180,plain,
! [SV206: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV206 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= ( c_HOL_Oone__class_Oone @ SV206 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3605]) ).
thf(4181,plain,
! [SV835: $i,SV207: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV207 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV207 ) @ SV835 @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(4182,plain,
! [SV1589: $i,SV1328: $i,SV836: $i,SV208: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV208 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4183,plain,
! [SV1590: $i,SV1329: $i,SV837: $i,SV209: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV209 )
| ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4184,plain,
! [SV1591: $i,SV1330: $i,SV838: $i,SV210: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV210 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4185,plain,
! [SV1592: $i,SV1331: $i,SV839: $i,SV211: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV211 )
| ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4186,plain,
! [SV1332: $i,SV840: $i,SV212: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV212 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV840 @ ( c_Suc @ SV1332 ) @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SV840 @ SV212 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3611]) ).
thf(4187,plain,
! [SV1333: $i,SV841: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV213 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
| ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3612]) ).
thf(4188,plain,
! [SV214: $i,SV842: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV842 @ SV214 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV214 @ SV842 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(4189,plain,
! [SV215: $i,SV843: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV843 @ SV215 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV215 @ SV843 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(4190,plain,
! [SV844: $i,SV216: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV216 @ SV844 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV216 @ ( c_Suc @ SV844 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(4191,plain,
! [SV845: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV217 ) @ SV845 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV217 @ SV845 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3616]) ).
thf(4192,plain,
! [SV218: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV218 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3617]) ).
thf(4193,plain,
! [SV1334: $i,SV846: $i,SV221: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV221 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV846 @ SV1334 @ tc_nat ) @ SV221 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV846 @ SV221 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1334 @ SV221 ) @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(4194,plain,
! [SV1593: $i,SV1335: $i,SV847: $i,SV222: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV222 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ ( c_Divides_Odiv__class_Omod @ SV1335 @ SV1593 @ SV222 ) @ SV222 ) @ SV1593 @ SV222 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ SV1335 @ SV222 ) @ SV1593 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(4195,plain,
! [SV1594: $i,SV1336: $i,SV848: $i,SV223: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV223 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV848 @ SV1336 @ SV223 ) @ SV1594 @ SV223 ) @ SV1336 @ SV223 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV848 @ SV1594 @ SV223 ) @ SV1336 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4196,plain,
! [SV224: $i,SV849: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV849 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV224 @ SV849 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(4197,plain,
! [SV850: $i,SV225: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV225 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV225 @ SV850 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(4198,plain,
! [SV851: $i,SV226: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV226 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV851 @ SV226 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ ( c_HOL_Oplus__class_Oplus @ SV851 @ SV851 @ SV226 ) @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(4199,plain,
! [SV852: $i,SV227: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV227 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV852 @ SV852 @ SV227 ) @ SV227 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV852 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3626]) ).
thf(4200,plain,
! [SV853: $i,SV228: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
| ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(4201,plain,
! [SV854: $i,SV229: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV229 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV854 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV229 ) @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(4202,plain,
! [SV1595: $i,SV1337: $i,SV855: $i,SV231: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV231 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(4203,plain,
! [SV1596: $i,SV1338: $i,SV856: $i,SV232: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV232 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3631]) ).
thf(4204,plain,
! [SV1597: $i,SV1339: $i,SV857: $i,SV233: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV233 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4205,plain,
! [SV1598: $i,SV1340: $i,SV858: $i,SV234: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV234 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4206,plain,
! [SV861: $i,SV238: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV238 @ SV861 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV861 @ ( c_Suc @ SV238 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3636]) ).
thf(4207,plain,
! [SV1341: $i,SV863: $i,SV240: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV240 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(4208,plain,
! [SV1342: $i,SV864: $i,SV241: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV241 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3639]) ).
thf(4209,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV242 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3640]) ).
thf(4210,plain,
! [SV1344: $i,SV866: $i,SV243: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV243 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3641]) ).
thf(4211,plain,
! [SV867: $i,SV244: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV244 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
| ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(4212,plain,
! [SV1599: $i,SV1345: $i,SV868: $i,SV245: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4213,plain,
! [SV1600: $i,SV1346: $i,SV869: $i,SV246: $i] :
( ( ! [SY3325: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1346 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SY3325 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1600 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1346 @ SY3325 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(4214,plain,
! [SV1601: $i,SV1347: $i,SV870: $i,SV247: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV247 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4215,plain,
! [SV1602: $i,SV1348: $i,SV871: $i,SV248: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV248 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(4216,plain,
! [SV1349: $i,SV872: $i,SV249: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(4217,plain,
! [SV1350: $i,SV873: $i,SV250: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(4218,plain,
! [SV1351: $i,SV874: $i,SV251: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV251 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV874 @ SV1351 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1351 @ SV874 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(4219,plain,
! [SV875: $i,SV252: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV252 )
= $false )
| ( ( ( SV875
= ( c_HOL_Ozero__class_Ozero @ SV252 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV875 @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3650]) ).
thf(4220,plain,
! [SV876: $i,SV253: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV253 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV876 @ SV253 ) @ SV253 )
= SV876 )
| ( SV876
= ( c_HOL_Ozero__class_Ozero @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(4221,plain,
! [SV878: $i,SV256: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV256 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV878 ) @ SV256 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV256 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV878 @ SV256 ) @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3653]) ).
thf(4222,plain,
! [SV1352: $i,SV879: $i,SV257: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(4223,plain,
! [SV258: $i,SV880: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV880 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Divides_Odiv__class_Omod @ SV258 @ SV880 @ tc_nat ) @ SV880 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(4224,plain,
! [SV881: $i,SV259: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV259 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV881 @ SV259 )
| ( SV881
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV881 @ SV259 ) @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(4225,plain,
! [SV1353: $i,SV882: $i,SV262: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV262 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3657]) ).
thf(4226,plain,
! [SV1354: $i,SV883: $i,SV263: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV263 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3658]) ).
thf(4227,plain,
! [SV1355: $i,SV884: $i,SV264: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV264 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3659]) ).
thf(4228,plain,
! [SV1356: $i,SV885: $i,SV265: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV265 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(4229,plain,
! [SV1357: $i,SV886: $i,SV266: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV266 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3661]) ).
thf(4230,plain,
! [SV1358: $i,SV887: $i,SV267: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(4231,plain,
! [SV269: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV269 ) )
= $true )
| ( ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= ( c_HOL_Oone__class_Oone @ SV269 ) )
= $true )
| ( ( class_SEQ_Obanach @ SV269 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3663]) ).
thf(4232,plain,
! [SV889: $i,SV270: $i] :
( ( ( c_lessequals @ SV270 @ SV889 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV270 @ ( c_Suc @ SV889 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(4233,plain,
! [SV890: $i,SV271: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV271 @ ( c_Suc @ SV890 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV271 @ SV890 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(4234,plain,
! [SV891: $i,SV273: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV273 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(4235,plain,
! [SV892: $i,SV274: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV274 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(4236,plain,
! [SV893: $i,SV275: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV275 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ SV893 @ SV275 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ ( c_HOL_Oplus__class_Oplus @ SV893 @ SV893 @ SV275 ) @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(4237,plain,
! [SV894: $i,SV276: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV276 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ ( c_HOL_Oplus__class_Oplus @ SV894 @ SV894 @ SV276 ) @ SV276 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV894 @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(4238,plain,
! [SV1359: $i,SV895: $i,SV279: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV279 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV895 @ SV1359 @ SV279 ) @ SV1359 @ SV279 )
= ( c_Divides_Odiv__class_Omod @ SV895 @ SV1359 @ SV279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(4239,plain,
! [SV1603: $i,SV1360: $i,SV896: $i,SV280: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
| ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4240,plain,
! [SV1604: $i,SV1361: $i,SV899: $i,SV284: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV284 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4241,plain,
! [SV900: $i,SV285: $i] :
( ( ( class_Divides_Osemiring__div @ SV285 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV900 @ ( c_HOL_Ozero__class_Ozero @ SV285 ) @ SV285 )
= SV900 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(4242,plain,
! [SV901: $i,SV286: $i] :
( ( ( class_Divides_Osemiring__div @ SV286 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV901 @ SV901 @ SV286 )
= ( c_HOL_Ozero__class_Ozero @ SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3675]) ).
thf(4243,plain,
! [SV1362: $i,SV902: $i,SV287: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV287 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV902 @ SV1362 @ SV287 )
= ( c_HOL_Oplus__class_Oplus @ SV1362 @ SV902 @ SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(4244,plain,
! [SV1363: $i,SV904: $i,SV289: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV289 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV904 @ SV1363 @ SV289 )
= ( c_HOL_Oplus__class_Oplus @ SV1363 @ SV904 @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(4245,plain,
! [SV1364: $i,SV905: $i,SV290: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV290 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV905 @ SV1364 @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SV1364 @ SV905 @ SV290 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(4246,plain,
! [SV1365: $i,SV906: $i,SV291: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV291 ) )
= $true )
| ( ( ( c_lessequals @ SV906 @ SV1365 @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(4247,plain,
! [SV1366: $i,SV907: $i,SV292: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV292 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 )
| ~ ( c_lessequals @ SV1366 @ SV907 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(4248,plain,
! [SV1367: $i,SV908: $i,SV293: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV293 ) )
= $true )
| ( ( ( c_lessequals @ SV908 @ SV1367 @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(4249,plain,
! [SV1368: $i,SV909: $i,SV294: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV294 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
| ~ ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
| ~ ( c_lessequals @ SV1368 @ SV909 @ SV294 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(4250,plain,
! [SV295: $i] :
( ( ( ~ ( class_Power_Opower @ SV295 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV295 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV295 )
= ( c_HOL_Oone__class_Oone @ SV295 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(4251,plain,
! [SV910: $i,SV296: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV296 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(4252,plain,
! [SV911: $i,SV297: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV297 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(4253,plain,
! [SV912: $i,SV298: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV298 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(4254,plain,
! [SV913: $i,SV299: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV299 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
| ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(4255,plain,
! [SV1369: $i,SV914: $i,SV300: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV300 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV914 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV914 @ SV1369 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1369 @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(4256,plain,
! [SV1370: $i,SV915: $i,SV301: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV301 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV915 @ SV1370 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SV1370 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV915 @ SV1370 @ SV301 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(4257,plain,
! [SV916: $i,SV302: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV302 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV916 @ SV302 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV302 ) @ SV916 @ SV302 ) )
| ( SV916
= ( c_HOL_Ozero__class_Ozero @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(4258,plain,
! [SV1605: $i,SV1371: $i,SV917: $i,SV303: $i] :
( ( ~ ( class_Divides_Oring__div @ SV303 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ SV1371 @ SV303 ) @ SV1605 @ SV303 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ ( c_Divides_Odiv__class_Omod @ SV1371 @ SV1605 @ SV303 ) @ SV303 ) @ SV1605 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(4259,plain,
! [SV1606: $i,SV1372: $i,SV918: $i,SV304: $i] :
( ( ~ ( class_Divides_Oring__div @ SV304 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1372 @ SV304 ) @ SV1606 @ SV304 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV918 @ SV1606 @ SV304 ) @ SV1372 @ SV304 ) @ SV1606 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4260,plain,
! [SV1607: $i,SV1373: $i,SV919: $i,SV305: $i] :
( ( ~ ( class_Divides_Oring__div @ SV305 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV919 @ SV1373 @ SV305 ) @ SV1607 @ SV305 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV919 @ SV1607 @ SV305 ) @ ( c_Divides_Odiv__class_Omod @ SV1373 @ SV1607 @ SV305 ) @ SV305 ) @ SV1607 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4261,plain,
! [SV1608: $i,SV1374: $i,SV920: $i,SV306: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(4262,plain,
! [SV921: $i,SV307: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV307 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV921 @ SV921 @ SV307 )
= ( c_HOL_Ozero__class_Ozero @ SV307 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3695]) ).
thf(4263,plain,
! [SV922: $i,SV308: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV308 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV922 @ SV922 @ SV308 )
= ( c_HOL_Ozero__class_Ozero @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(4264,plain,
! [SV923: $i,SV309: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV309 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV923 @ ( c_HOL_Ozero__class_Ozero @ SV309 ) @ SV309 )
= SV923 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(4265,plain,
! [SV924: $i,SV310: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV310 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV924 @ SV924 @ SV310 )
= ( c_HOL_Ozero__class_Ozero @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(4266,plain,
! [SV925: $i,SV311: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV311 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV311 )
| ( ( c_HOL_Ominus__class_Ominus @ SV925 @ SV925 @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ SV311 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3699]) ).
thf(4267,plain,
! [SV1375: $i,SV926: $i,SV312: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV312 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV926 @ SV1375 @ SV312 ) @ SV1375 @ SV312 )
= SV926 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3700]) ).
thf(4268,plain,
! [SV1609: $i,SV1376: $i,SV927: $i,SV313: $i] :
( ( ! [SY3326: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV313 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV927 @ SV1376 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SV1609 @ SY3326 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV927 @ SV1609 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SV1376 @ SY3326 @ SV313 ) @ SV313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3701]) ).
thf(4269,plain,
! [SV1377: $i,SV928: $i,SV314: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV314 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV928 @ SV1377 @ SV314 ) @ SV1377 @ SV314 )
= SV928 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3702]) ).
thf(4270,plain,
! [SV1378: $i,SV929: $i,SV315: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV315 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV315 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV929 @ SV1378 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV929 @ SV315 ) @ SV1378 @ SV315 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3703]) ).
thf(4271,plain,
! [SV1610: $i,SV1379: $i,SV930: $i,SV316: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SV1379 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SV1610 @ SV1379 @ SV316 ) @ SV316 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SV1610 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4272,plain,
! [SV931: $i,SV317: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV317 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV317 )
| ( ( c_HOL_Ozero__class_Ozero @ SV317 )
= ( c_HOL_Oinverse__class_Odivide @ SV931 @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(4273,plain,
! [SV318: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV318 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= ( c_HOL_Ozero__class_Ozero @ SV318 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3706]) ).
thf(4274,plain,
! [SV1380: $i,SV932: $i,SV319: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV319 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV319 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV932 @ SV1380 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SV1380 @ SV932 @ SV319 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3707]) ).
thf(4275,plain,
! [SV933: $i,SV320: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV320 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ SV933 @ SV320 )
= ( c_HOL_Ozero__class_Ozero @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(4276,plain,
! [SV934: $i,SV321: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV321 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV321 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV934 @ ( c_HOL_Ozero__class_Ozero @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(4277,plain,
! [SV935: $i,SV322: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV322 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV322 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV322 ) @ SV322 )
= ( c_HOL_Ozero__class_Ozero @ SV322 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(4278,plain,
! [SV936: $i,SV323: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV323 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV323 ) @ SV936 @ SV323 )
= ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(4279,plain,
! [SV1611: $i,SV1381: $i,SV937: $i,SV324: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV324 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV1381 @ SV324 ) @ SV1611 @ SV324 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV937 @ SV1611 @ SV324 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1381 @ SV1611 @ SV324 ) @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(4280,plain,
! [SV1612: $i,SV1382: $i,SV938: $i,SV325: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV325 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV1382 @ SV325 ) @ SV1612 @ SV325 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV938 @ SV1612 @ SV325 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1382 @ SV1612 @ SV325 ) @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(4281,plain,
! [SV939: $i,SV326: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV326 ) @ ( c_Suc @ SV939 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV326 @ SV939 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3714]) ).
thf(4282,plain,
! [SV940: $i,SV327: $i] :
( ( ( c_lessequals @ SV327 @ SV940 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV327 ) @ ( c_Suc @ SV940 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3715]) ).
thf(4283,plain,
! [SV941: $i,SV329: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV329 ) @ SV941 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV329 @ SV941 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(4284,plain,
! [SV942: $i,SV330: $i] :
( ( ( c_lessequals @ SV330 @ SV942 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV330 @ ( c_Suc @ SV942 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(4285,plain,
! [SV943: $i,SV331: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV331 @ SV943 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV331 @ SV943 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(4286,plain,
! [SV944: $i,SV332: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV332 @ SV944 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV332 @ SV944 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(4287,plain,
! [SV1613: $i,SV1383: $i,SV949: $i,SV337: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1383 @ SV1613 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV949 @ SV1613 @ tc_nat )
| ~ ( c_lessequals @ SV337 @ SV1383 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(4288,plain,
! [SV950: $i,SV338: $i] :
( ( ( c_lessequals @ SV338 @ SV950 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV338 @ ( c_Suc @ SV950 ) @ tc_nat ) )
= $true )
| ( ( SV338
= ( c_Suc @ SV950 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3721]) ).
thf(4289,plain,
! [SV951: $i,SV339: $i] :
( ( ( SV339 = SV951 )
= $true )
| ( ( ~ ( c_lessequals @ SV339 @ SV951 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV339 @ SV951 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3722]) ).
thf(4290,plain,
! [SV952: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV340 @ SV952 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV340 @ SV952 @ tc_nat ) )
= $true )
| ( ( SV340 = SV952 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(4291,plain,
! [SV953: $i,SV341: $i] :
( ( ( SV341 = SV953 )
= $true )
| ( ( ~ ( c_lessequals @ SV341 @ SV953 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV341 @ SV953 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3724]) ).
thf(4292,plain,
! [SV1384: $i,SV954: $i,SV342: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV342 @ SV954 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV954 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV342 @ SV1384 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(4293,plain,
! [SV1385: $i,SV955: $i,SV343: $i] :
( ( ( c_lessequals @ SV343 @ SV955 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV343 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV955 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(4294,plain,
! [SV1386: $i,SV956: $i,SV344: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV956 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV1386 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV956 @ SV1386 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3727]) ).
thf(4295,plain,
! [SV1387: $i,SV957: $i,SV346: $i] :
( ( ( c_lessequals @ SV346 @ ( c_HOL_Oplus__class_Oplus @ SV957 @ SV1387 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV346 @ SV957 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(4296,plain,
! [SV1388: $i,SV958: $i,SV347: $i] :
( ( ( c_lessequals @ SV347 @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV1388 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV347 @ SV1388 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(4297,plain,
! [SV1389: $i,SV959: $i,SV348: $i] :
( ( ( c_lessequals @ SV348 @ SV959 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV348 @ SV1389 @ tc_nat ) @ SV959 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(4298,plain,
! [SV1390: $i,SV960: $i,SV349: $i] :
( ( ( c_lessequals @ SV349 @ SV960 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1390 @ SV349 @ tc_nat ) @ SV960 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3732]) ).
thf(4299,plain,
! [SV1391: $i,SV961: $i,SV350: $i] :
( ( ( c_lessequals @ SV350 @ ( c_HOL_Oplus__class_Oplus @ SV961 @ SV1391 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV350 @ SV961 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(4300,plain,
! [SV1392: $i,SV962: $i,SV351: $i] :
( ( ( c_lessequals @ SV351 @ ( c_HOL_Oplus__class_Oplus @ SV962 @ SV1392 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV351 @ SV1392 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3734]) ).
thf(4301,plain,
! [SV964: $i,SV354: $i] :
( ( ( c_lessequals @ SV354 @ SV964 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV964 ) @ SV354 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(4302,plain,
! [SV1393: $i,SV966: $i,SV357: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV357 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV966 @ SV1393 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV357 @ SV1393 @ tc_nat ) @ ( c_Suc @ SV966 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1393 @ SV966 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3737]) ).
thf(4303,plain,
! [SV1394: $i,SV967: $i,SV358: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV967 @ tc_nat ) ) @ SV1394 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV358 ) @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1394 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV967 @ SV358 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(4304,plain,
! [SV1395: $i,SV968: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV968 @ tc_nat ) @ SV1395 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV359 @ SV1395 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(4305,plain,
! [SV1396: $i,SV970: $i,SV361: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV970 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV1396 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV361 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV970 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(4306,plain,
! [SV1400: $i,SV974: $i,SV365: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SV974 @ SV1400 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV1400 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV974 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4307,plain,
! [SV372: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(4308,plain,
! [SV978: $i,SV373: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV373 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
| ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3747]) ).
thf(4309,plain,
! [SV979: $i,SV375: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV375 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(4310,plain,
! [SV1402: $i,SV980: $i,SV376: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV376 ) )
= $true )
| ( ( ( c_lessequals @ SV980 @ SV1402 @ SV376 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV980 @ SV1402 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3750]) ).
thf(4311,plain,
! [SV1403: $i,SV981: $i,SV377: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV377 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV981 @ SV1403 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
| ~ ( c_lessequals @ SV981 @ SV1403 @ SV377 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3751]) ).
thf(4312,plain,
! [SV1404: $i,SV982: $i,SV378: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV378 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SV982 @ SV1404 @ SV378 ) @ SV378 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SV982 @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3752]) ).
thf(4313,plain,
! [SV1405: $i,SV983: $i,SV379: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV379 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SV983 @ SV1405 @ SV379 ) @ SV379 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SV983 @ SV379 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3753]) ).
thf(4314,plain,
! [SV1614: $i,SV1406: $i,SV984: $i,SV380: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV380 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
| ~ ( c_lessequals @ SV984 @ SV1614 @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(4315,plain,
! [SV1407: $i,SV985: $i,SV381: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV381 ) )
= $true )
| ( ( ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
| ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SV1407 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3755]) ).
thf(4316,plain,
! [SV1408: $i,SV986: $i,SV382: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV382 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(4317,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV383 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3757]) ).
thf(4318,plain,
! [SV1410: $i,SV988: $i,SV384: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV384 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SV988 @ SV1410 @ SV384 ) @ SV384 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SV988 @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(4319,plain,
! [SV385: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV385 ) @ ( c_HOL_Ozero__class_Ozero @ SV385 ) @ SV385 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV385 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(4320,plain,
! [SV1411: $i,SV991: $i,SV388: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV388 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV991 @ SV1411 @ SV388 ) @ SV388 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV991 @ SV388 ) @ SV1411 @ SV388 ) )
| ( SV991
= ( c_HOL_Ozero__class_Ozero @ SV388 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(4321,plain,
! [SV995: $i,SV392: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV995 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV995 @ tc_nat )
= $true )
| ( ( SV392 = SV995 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(4322,plain,
! [SV393: $i,SV996: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV996 @ ( c_Suc @ SV393 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV996 @ SV393 @ tc_nat )
= $true )
| ( ( SV393 = SV996 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3767]) ).
thf(4323,plain,
! [SV997: $i,SV394: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV394 @ SV997 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV394 @ ( c_Suc @ SV997 ) @ tc_nat ) )
= $true )
| ( ( SV394 = SV997 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3768]) ).
thf(4324,plain,
! [SV998: $i,SV396: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV396 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV998 @ ( c_HOL_Ozero__class_Ozero @ SV396 ) @ SV396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(4325,plain,
! [SV999: $i,SV398: $i] :
( ( ( class_Divides_Osemiring__div @ SV398 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV999 @ ( c_HOL_Oone__class_Oone @ SV398 ) @ SV398 )
= ( c_HOL_Ozero__class_Ozero @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(4326,plain,
! [SV1000: $i,SV399: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ SV1000 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV399 @ ( c_HOL_Oplus__class_Oplus @ SV1000 @ SV399 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(4327,plain,
! [SV1001: $i,SV400: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ ( c_HOL_Oplus__class_Oplus @ SV1001 @ SV400 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV400 @ SV1001 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(4328,plain,
! [SV1002: $i,SV401: $i] :
( ( ( class_Orderings_Oorder @ SV401 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1002 @ SV1002 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(4329,plain,
! [SV1003: $i,SV404: $i] :
( ( ( class_Orderings_Olinorder @ SV404 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1003 @ SV1003 @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(4330,plain,
! [SV1004: $i,SV405: $i] :
( ( ( class_Orderings_Opreorder @ SV405 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1004 @ SV1004 @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(4331,plain,
! [SV1415: $i,SV1005: $i,SV406: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3776]) ).
thf(4332,plain,
! [SV1006: $i,SV407: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV407 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
| ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(4333,plain,
! [SV1007: $i,SV408: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV408 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(4334,plain,
! [SV1008: $i,SV409: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV409 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1008 @ SV409 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
| ~ ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(4335,plain,
! [SV1009: $i,SV410: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SV1009 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1009 @ SV410 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1009 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(4336,plain,
! [SV1615: $i,SV1416: $i,SV1010: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1615 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SV1615 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1416 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4337,plain,
! [SV1616: $i,SV1417: $i,SV1011: $i,SV412: $i] :
( ( ! [SY3327: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SY3327 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SY3327 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4338,plain,
! [SV1012: $i,SV413: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(4339,plain,
! [SV1418: $i,SV1013: $i,SV414: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV414 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1013 @ SV1418 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ SV1418 @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3784]) ).
thf(4340,plain,
! [SV1419: $i,SV1014: $i,SV415: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV415 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1419 @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1014 @ SV1419 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(4341,plain,
! [SV1420: $i,SV1015: $i,SV416: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV416 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1420 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1420 @ SV416 ) @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(4342,plain,
! [SV1421: $i,SV1016: $i,SV417: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV417 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1421 @ SV417 ) @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1016 @ SV1421 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(4343,plain,
! [SV1017: $i,SV419: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV419 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1017 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1017 @ SV419 ) @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(4344,plain,
! [SV1018: $i,SV420: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV420 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV420 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1018 @ SV420 ) @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1018 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3790]) ).
thf(4345,plain,
! [SV1617: $i,SV1422: $i,SV1019: $i,SV422: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV422 )
| ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1422 @ SV422 ) @ SV1617 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1617 @ SV422 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1617 @ SV1422 @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(4346,plain,
! [SV1020: $i,SV423: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV423 )
= $false )
| ( ( ( c_lessequals @ SV1020 @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1020 @ SV1020 @ SV423 ) @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3792]) ).
thf(4347,plain,
! [SV1021: $i,SV424: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV424 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1021 @ SV1021 @ SV424 ) @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
| ~ ( c_lessequals @ SV1021 @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(4348,plain,
! [SV1423: $i,SV1024: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV427 @ ( c_HOL_Ominus__class_Ominus @ SV1024 @ SV1423 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV427 @ SV1423 @ tc_nat ) @ SV1024 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(4349,plain,
! [SV1424: $i,SV1025: $i,SV428: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV428 @ SV1025 @ tc_nat ) @ SV1424 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV428 @ ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1025 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3797]) ).
thf(4350,plain,
! [SV429: $i,SV1026: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1026 @ SV429 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV429 @ SV1026 @ tc_nat )
= SV1026 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(4351,plain,
! [SV1027: $i,SV430: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV430 @ SV1027 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ SV430 @ SV1027 @ tc_nat )
= SV430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(4352,plain,
! [SV1425: $i,SV1029: $i,SV432: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV432 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3800]) ).
thf(4353,plain,
! [SV1426: $i,SV1030: $i,SV433: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV433 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(4354,plain,
! [SV1427: $i,SV1031: $i,SV434: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV434 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3802]) ).
thf(4355,plain,
! [SV1428: $i,SV1032: $i,SV435: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV435 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(4356,plain,
! [SV1429: $i,SV1033: $i,SV436: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1033 @ ( c_Power_Opower__class_Opower @ SV1033 @ SV1429 @ SV436 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1429 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3804]) ).
thf(4357,plain,
! [SV1430: $i,SV1034: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV1034 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1430 @ SV1034 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV437 @ SV1430 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3805]) ).
thf(4358,plain,
! [SV1431: $i,SV1035: $i,SV438: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV438 @ SV1035 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1431 @ SV438 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1431 @ SV1035 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(4359,plain,
! [SV1432: $i,SV1036: $i,SV439: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1036 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1432 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1036 @ SV1432 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(4360,plain,
! [SV1618: $i,SV1433: $i,SV1037: $i,SV440: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
| ( c_HOL_Oord__class_Oless @ SV1037 @ SV1433 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1433 @ SV440 ) @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4361,plain,
! [SV1619: $i,SV1434: $i,SV1038: $i,SV441: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1434 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1619 @ SV441 ) @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1619 @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(4362,plain,
! [SV1620: $i,SV1435: $i,SV1039: $i,SV442: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1435 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1620 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1435 @ SV1620 @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(4363,plain,
! [SV1621: $i,SV1436: $i,SV1040: $i,SV443: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
| ( c_HOL_Oord__class_Oless @ SV1040 @ SV1436 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SV1621 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SV1436 @ SV1621 @ SV443 ) @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(4364,plain,
! [SV1622: $i,SV1437: $i,SV1041: $i,SV444: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SV1437 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SV1622 @ SV1437 @ SV444 ) @ SV444 )
| ~ ( c_HOL_Oord__class_Oless @ SV1041 @ SV1622 @ SV444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(4365,plain,
! [SV1623: $i,SV1438: $i,SV1042: $i,SV445: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SV1438 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SV1623 @ SV1438 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1623 @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3813]) ).
thf(4366,plain,
! [SV1439: $i,SV1043: $i,SV446: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(4367,plain,
! [SV1044: $i,SV447: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV447 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(4368,plain,
! [SV1047: $i,SV450: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV450 @ ( c_Suc @ SV1047 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1047 @ SV450 @ tc_nat ) )
= $true )
| ( ( SV450 = SV1047 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3816]) ).
thf(4369,plain,
! [SV1049: $i,SV452: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV452 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1049 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV452 @ SV1049 @ tc_nat ) @ SV452 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(4370,plain,
! [SV1051: $i,SV454: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV454 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV454 @ ( c_Suc @ SV1051 ) @ tc_nat ) @ SV454 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3820]) ).
thf(4371,plain,
! [SV456: $i,SV1053: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1053 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV456 @ SV1053 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV456 @ SV1053 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(4372,plain,
! [SV1440: $i,SV1054: $i,SV457: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV457 @ SV1054 @ tc_nat ) @ SV1440 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1440 @ SV457 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV457 @ SV1440 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(4373,plain,
! [SV1441: $i,SV1055: $i,SV458: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV458 @ SV1055 @ tc_nat ) @ SV1441 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1441 @ SV1055 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1055 @ SV1441 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(4374,plain,
! [SV1442: $i,SV1056: $i,SV459: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV459 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1056 @ SV1442 @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SV1442 @ SV1056 @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4375,plain,
! [SV1443: $i,SV1057: $i,SV460: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV1057 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV460 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1443 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(4376,plain,
! [SV1444: $i,SV1058: $i,SV461: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SV1444 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1444 @ SV1058 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1444 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3826]) ).
thf(4377,plain,
! [SV1445: $i,SV1059: $i,SV462: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV462 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1059 @ SV1445 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1445 @ SV1059 @ SV462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4378,plain,
! [SV1446: $i,SV1060: $i,SV463: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV463 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1060 @ SV1446 @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SV1446 @ SV1060 @ SV463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3828]) ).
thf(4379,plain,
! [SV1447: $i,SV1061: $i,SV464: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV464 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1447 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SV1447 @ SV1061 @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3829]) ).
thf(4380,plain,
! [SV1448: $i,SV1062: $i,SV465: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV465 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
| ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3830]) ).
thf(4381,plain,
! [SV1449: $i,SV1063: $i,SV466: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV466 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
| ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(4382,plain,
! [SV1450: $i,SV1064: $i,SV467: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV467 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(4383,plain,
! [SV1451: $i,SV1065: $i,SV468: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV468 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
| ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(4384,plain,
! [SV1624: $i,SV1452: $i,SV1066: $i,SV469: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV469 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(4385,plain,
! [SV1625: $i,SV1453: $i,SV1067: $i,SV470: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV470 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4386,plain,
! [SV1454: $i,SV1068: $i,SV471: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV471 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(4387,plain,
! [SV1455: $i,SV1069: $i,SV472: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV472 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4388,plain,
! [SV1456: $i,SV1070: $i,SV473: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV473 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
| ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3838]) ).
thf(4389,plain,
! [SV1457: $i,SV1071: $i,SV474: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV474 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
| ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3839]) ).
thf(4390,plain,
! [SV1458: $i,SV1072: $i,SV475: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV475 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
| ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(4391,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV476 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
| ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3841]) ).
thf(4392,plain,
! [SV1074: $i,SV477: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV477 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1074 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV477 )
= ( c_HOL_Oone__class_Oone @ SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3842]) ).
thf(4393,plain,
! [SV1075: $i,SV478: $i] :
( ( ( class_Power_Opower @ SV478 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1075 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV478 )
= ( c_HOL_Oone__class_Oone @ SV478 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(4394,plain,
! [SV1076: $i,SV479: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV479 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Oone__class_Oone @ SV479 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV479 ) @ SV1076 @ SV479 ) @ SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4395,plain,
! [SV1077: $i,SV480: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV480 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1077 @ SV480 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV480 ) @ SV1077 @ SV480 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4396,plain,
! [SV1078: $i,SV481: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV481 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV481 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1078 @ SV481 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV481 ) @ SV1078 @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(4397,plain,
! [SV1079: $i,SV482: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV482 )
= $false )
| ( ( ( SV1079
= ( c_HOL_Ozero__class_Ozero @ SV482 ) )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1079 @ SV1079 @ SV482 )
= ( c_HOL_Oone__class_Oone @ SV482 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(4398,plain,
! [SV1080: $i,SV483: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV483 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1080 @ SV1080 @ SV483 )
= ( c_HOL_Oone__class_Oone @ SV483 ) )
| ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV483 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3848]) ).
thf(4399,plain,
! [SV1081: $i,SV484: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV484 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV484 )
| ( ( c_HOL_Oinverse__class_Odivide @ SV1081 @ SV1081 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
| ( SV1081
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(4400,plain,
! [SV1460: $i,SV1082: $i,SV485: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV485 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1082 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1460 @ SV485 ) @ SV485 )
| ~ ( c_lessequals @ SV1082 @ SV1460 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(4401,plain,
! [SV1461: $i,SV1083: $i,SV486: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV486 ) )
= $true )
| ( ( ( c_lessequals @ SV1083 @ SV1461 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1083 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1461 @ SV486 ) @ SV486 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3851]) ).
thf(4402,plain,
! [SV1462: $i,SV1084: $i,SV487: $i] :
( ( ( ~ ( class_SEQ_Obanach @ SV487 ) )
= $true )
| ( ( ~ ( class_RealVector_Oreal__normed__field @ SV487 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SV1084 @ SV1462 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SV1084 @ SV487 ) @ ( c_Transcendental_Oexp @ SV1462 @ SV487 ) @ SV487 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3852]) ).
thf(4403,plain,
! [SV1626: $i,SV1463: $i,SV1085: $i,SV488: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1085 @ SV1463 @ SV488 ) @ SV1626 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1085 @ SV1626 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SV1463 @ SV1626 @ SV488 ) @ SV488 ) )
| ( SV1463
= ( c_HOL_Ozero__class_Ozero @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4404,plain,
! [SV1627: $i,SV1464: $i,SV1086: $i,SV489: $i] :
( ( ! [SY3328: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
| ~ ( c_lessequals @ SV1464 @ SY3328 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SY3328 @ SV489 ) @ SV1627 @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4405,plain,
! [SV1628: $i,SV1465: $i,SV1087: $i,SV490: $i] :
( ( ! [SY3329: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SY3329 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SV1465 @ SY3329 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(4406,plain,
! [SV1629: $i,SV1466: $i,SV1088: $i,SV491: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1466 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1629 @ SV491 ) @ SV491 )
| ~ ( c_lessequals @ SV1466 @ SV1629 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(4407,plain,
! [SV1630: $i,SV1467: $i,SV1089: $i,SV492: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV492 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SV1630 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1630 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
| ~ ( c_lessequals @ SV1630 @ SV1467 @ tc_nat )
| ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4408,plain,
! [SV1468: $i,SV1090: $i,SV493: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1468 @ SV1090 @ tc_nat )
| ~ ( c_lessequals @ SV1468 @ SV493 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4409,plain,
! [SV1469: $i,SV1091: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV1469 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4410,plain,
! [SV1470: $i,SV1092: $i,SV495: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV495 @ ( c_HOL_Ominus__class_Ominus @ SV1092 @ SV1470 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV495 @ SV1092 @ tc_nat ) @ SV1470 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1470 @ SV1092 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4411,plain,
! [SV1471: $i,SV1093: $i,SV496: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV496 @ SV1093 @ tc_nat ) @ SV1471 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV496 @ SV1471 @ tc_nat ) @ SV1093 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1093 @ SV496 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4412,plain,
! [SV1094: $i,SV497: $i] :
( ( ( c_lessequals @ SV497 @ SV1094 @ tc_nat )
= $false )
| ( ( SV1094
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV1094 @ SV497 @ tc_nat ) @ SV497 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(4413,plain,
! [SV1095: $i,SV498: $i] :
( ( ( c_lessequals @ SV498 @ SV1095 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV498 @ ( c_HOL_Ominus__class_Ominus @ SV1095 @ SV498 @ tc_nat ) @ tc_nat )
= SV1095 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(4414,plain,
! [SV499: $i,SV1096: $i] :
( ( ( c_lessequals @ SV1096 @ SV499 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV499 @ SV1096 @ tc_nat ) @ SV1096 @ tc_nat )
= SV499 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(4415,plain,
! [SV1097: $i,SV500: $i] :
( ( ( c_lessequals @ SV500 @ ( c_HOL_Oplus__class_Oplus @ SV1097 @ SV500 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1097 @ SV500 @ tc_nat ) @ SV500 @ tc_nat )
= SV1097 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(4416,plain,
! [SV1472: $i,SV1098: $i,SV501: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV501 @ ( c_HOL_Ominus__class_Ominus @ SV1098 @ SV1472 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV1472 @ tc_nat ) @ SV1098 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1472 @ SV1098 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3866]) ).
thf(4417,plain,
! [SV1473: $i,SV1099: $i,SV502: $i] :
( ( ( c_lessequals @ SV502 @ ( c_HOL_Oplus__class_Oplus @ SV1099 @ SV1473 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV502 @ SV1473 @ tc_nat ) @ SV1099 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3867]) ).
thf(4418,plain,
! [SV1474: $i,SV1100: $i,SV503: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV503 @ SV1100 @ tc_nat ) @ SV1474 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV503 @ ( c_HOL_Oplus__class_Oplus @ SV1474 @ SV1100 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(4419,plain,
! [SV1475: $i,SV1101: $i,SV504: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1475 @ SV1101 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3869]) ).
thf(4420,plain,
! [SV1476: $i,SV1102: $i,SV505: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1102 @ SV1476 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3870]) ).
thf(4421,plain,
! [SV1103: $i,SV506: $i] :
( ( ( c_lessequals @ SV506 @ SV1103 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV506 @ SV1103 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3871]) ).
thf(4422,plain,
! [SV507: $i,SV1104: $i] :
( ( ( c_lessequals @ SV1104 @ SV507 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV507 @ SV1104 @ tc_nat ) @ SV1104 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV507 @ SV1104 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(4423,plain,
! [SV508: $i,SV1105: $i] :
( ( ( c_lessequals @ SV1105 @ SV508 @ tc_nat )
= $false )
| ( ( ( c_GCD_Ogcd__class_Ogcd @ ( c_HOL_Ominus__class_Ominus @ SV508 @ SV1105 @ tc_nat ) @ SV508 @ tc_nat )
= ( c_GCD_Ogcd__class_Ogcd @ SV1105 @ SV508 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4424,plain,
! [SV1477: $i,SV1106: $i,SV509: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV509 @ SV1106 @ tc_nat ) @ SV1477 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ominus__class_Ominus @ SV1106 @ SV1477 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1477 @ SV1106 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(4425,plain,
! [SV1478: $i,SV1107: $i,SV510: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV510 @ SV1107 @ tc_nat ) @ SV1478 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV510 @ SV1478 @ tc_nat ) @ SV1107 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1478 @ SV510 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(4426,plain,
! [SV511: $i,SV1108: $i] :
( ( ( c_lessequals @ SV1108 @ SV511 @ tc_nat )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV511 @ SV1108 @ tc_nat )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV511 @ SV1108 @ tc_nat ) @ SV1108 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(4427,plain,
! [SV512: $i,SV1109: $i] :
( ( ( c_lessequals @ SV1109 @ SV512 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV512 ) @ SV1109 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV512 @ SV1109 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3877]) ).
thf(4428,plain,
! [SV1479: $i,SV1110: $i,SV513: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SV1110 @ tc_nat ) @ SV1479 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SV1479 @ SV1110 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1110 @ SV1479 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4429,plain,
! [SV1480: $i,SV1111: $i,SV514: $i] :
( ( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SV1111 @ SV1480 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SV1480 @ tc_nat ) @ SV1111 @ tc_nat )
| ~ ( c_lessequals @ SV1480 @ SV1111 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4430,plain,
! [SV1481: $i,SV1112: $i,SV515: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV1112 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ SV1112 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1112 @ SV515 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV515 @ SV1481 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(4431,plain,
! [SV1482: $i,SV1113: $i,SV516: $i] :
( ( ( c_lessequals @ SV516 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1113 @ SV516 @ tc_nat ) @ SV1482 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1482 @ SV1113 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4432,plain,
! [SV1114: $i,SV517: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV517 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
| ~ ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3882]) ).
thf(4433,plain,
! [SV1115: $i,SV518: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV518 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
| ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3883]) ).
thf(4434,plain,
! [SV1116: $i,SV519: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV519 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(4435,plain,
! [SV1117: $i,SV520: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV520 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4436,plain,
! [SV1483: $i,SV1118: $i,SV521: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV521 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1483 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1118 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1483 @ SV521 ) @ SV521 ) )
| ~ ( c_lessequals @ SV1483 @ SV1118 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3886]) ).
thf(4437,plain,
! [SV1631: $i,SV1484: $i,SV1119: $i,SV522: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV522 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3887]) ).
thf(4438,plain,
! [SV1632: $i,SV1485: $i,SV1120: $i,SV523: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV523 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1485 @ SV1632 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(4439,plain,
! [SV1633: $i,SV1486: $i,SV1121: $i,SV524: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV524 )
| ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(4440,plain,
! [SV1634: $i,SV1487: $i,SV1122: $i,SV525: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV525 )
| ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3890]) ).
thf(4441,plain,
! [SV1635: $i,SV1488: $i,SV1123: $i,SV526: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV526 )
| ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SV1635 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1635 @ SV526 ) @ SV526 ) )
| ~ ( c_lessequals @ SV1635 @ SV1488 @ tc_nat )
| ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(4442,plain,
! [SV1489: $i,SV1125: $i,SV528: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV528 ) )
= $true )
| ( ( ( c_lessequals @ SV1125 @ SV1489 @ SV528 )
| ( c_lessequals @ SV1489 @ SV1125 @ SV528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3893]) ).
thf(4443,plain,
! [SV1636: $i,SV1490: $i,SV1126: $i,SV529: $i] :
( ( ~ ( class_Orderings_Oorder @ SV529 )
| ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
| ~ ( c_lessequals @ SV1126 @ SV1636 @ SV529 )
| ~ ( c_lessequals @ SV1636 @ SV1490 @ SV529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4444,plain,
! [SV1637: $i,SV1491: $i,SV1127: $i,SV530: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV530 )
| ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1637 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1127 @ SV1637 @ SV530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4445,plain,
! [SV1492: $i,SV1128: $i,SV532: $i] :
( ( ( c_lessequals @ SV532 @ SV1128 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1492 @ SV1128 @ tc_nat )
| ~ ( c_lessequals @ SV532 @ SV1492 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3896]) ).
thf(4446,plain,
! [SV1129: $i,SV534: $i] :
( ( ( class_Orderings_Oorder @ SV534 )
= $false )
| ( ( c_lessequals @ SV1129 @ SV1129 @ SV534 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3897]) ).
thf(4447,plain,
! [SV1130: $i,SV535: $i] :
( ( ( class_Orderings_Opreorder @ SV535 )
= $false )
| ( ( c_lessequals @ SV1130 @ SV1130 @ SV535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3898]) ).
thf(4448,plain,
! [SV1493: $i,SV1131: $i,SV536: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV536 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SV1131 @ SV1493 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SV1131 @ SV536 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(4449,plain,
! [SV1132: $i,SV537: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV537 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV537 ) @ SV1132 @ SV537 )
= ( c_HOL_Oone__class_Oone @ SV537 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(4450,plain,
! [SV1638: $i,SV1494: $i,SV1133: $i,SV538: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV538 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
| ~ ( c_lessequals @ SV1494 @ SV1638 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4451,plain,
! [SV1134: $i,SV539: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV539 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV1134 @ ( c_HOL_Oone__class_Oone @ SV539 ) @ SV539 )
= SV1134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(4452,plain,
! [SV540: $i,SV1135: $i] :
( ( ( c_lessequals @ SV1135 @ SV540 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV540 @ SV1135 @ tc_nat ) @ tc_nat )
= SV1135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(4453,plain,
! [SV1495: $i,SV1136: $i,SV541: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV541 ) )
= $true )
| ( ( ( SV1136 = SV1495 )
| ~ ( c_lessequals @ SV1136 @ SV1495 @ SV541 )
| ~ ( c_lessequals @ SV1495 @ SV1136 @ SV541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4454,plain,
! [SV542: $i,SV1137: $i] :
( ( ( ~ ( c_lessequals @ SV1137 @ SV542 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV542 @ SV1137 @ tc_nat ) )
= $true )
| ( ( SV542 = SV1137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4455,plain,
! [SV1496: $i,SV1138: $i,SV543: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV543 ) )
= $true )
| ( ( ( SV1138 = SV1496 )
| ~ ( c_lessequals @ SV1496 @ SV1138 @ SV543 )
| ~ ( c_lessequals @ SV1138 @ SV1496 @ SV543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(4456,plain,
! [SV1497: $i,SV1139: $i,SV544: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV544 ) )
= $true )
| ( ( ( SV1139 = SV1497 )
| ~ ( c_lessequals @ SV1497 @ SV1139 @ SV544 )
| ~ ( c_lessequals @ SV1139 @ SV1497 @ SV544 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3907]) ).
thf(4457,plain,
! [SV1639: $i,SV1498: $i,SV1140: $i,SV545: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV545 )
| ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SV1498 @ SV545 ) @ SV1639 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SV1639 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SV1498 @ SV1639 @ SV545 ) @ SV545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3908]) ).
thf(4458,plain,
! [SV1640: $i,SV1499: $i,SV1141: $i,SV546: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV546 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1141 @ SV1499 @ SV546 ) @ SV1640 @ SV546 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1141 @ SV1640 @ SV546 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1499 @ SV1640 @ SV546 ) @ SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(4459,plain,
! [SV1641: $i,SV1500: $i,SV1142: $i,SV547: $i] :
( ( ~ ( class_RealVector_Oreal__normed__field @ SV547 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1142 @ SV1500 @ SV547 ) @ SV1641 @ SV547 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1142 @ SV1641 @ SV547 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1500 @ SV1641 @ SV547 ) @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4460,plain,
! [SV1501: $i,SV1143: $i,SV548: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV548 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV548 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SV1143 @ SV1501 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SV1143 @ SV548 ) @ SV1501 @ SV548 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3911]) ).
thf(4461,plain,
! [SV1502: $i,SV1144: $i,SV549: $i] :
( ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1502 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ SV1502 @ SV549 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3912]) ).
thf(4462,plain,
! [SV1503: $i,SV1145: $i,SV550: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV550 @ SV1503 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV1503 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3913]) ).
thf(4463,plain,
! [SV1504: $i,SV1146: $i,SV551: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV551 @ SV1146 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ SV1146 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV551 @ SV1504 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3914]) ).
thf(4464,plain,
! [SV1505: $i,SV1147: $i,SV552: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1147 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1505 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1505 @ SV1147 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(4465,plain,
! [SV1507: $i,SV1150: $i,SV555: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1150 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1507 @ SV1150 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1507 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1150 @ SV1507 @ tc_nat )
| ~ ( c_lessequals @ SV1150 @ SV555 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3917]) ).
thf(4466,plain,
! [SV1151: $i,SV576: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV576 @ SV1151 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV576
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(4467,plain,
! [SV1642: $i,SV1508: $i,SV1152: $i,SV577: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1508 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1642 @ SV577 ) )
| ( SV1508 = SV1642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4468,plain,
! [SV1509: $i,SV1153: $i,SV578: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1153 @ SV1509 @ SV578 )
!= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV578 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4469,plain,
! [SV1510: $i,SV1154: $i,SV579: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV579 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1154 @ SV1510 @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
| ( SV1154 = SV1510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4470,plain,
! [SV1155: $i,SV580: $i] :
( ( ( ( c_Suc @ SV580 )
= ( c_Suc @ SV1155 ) )
= $false )
| ( ( SV580 = SV1155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4471,plain,
! [SV1156: $i,SV582: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV1156 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV582
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(4472,plain,
! [SV1157: $i,SV583: $i] :
( ( ( ( c_Suc @ ( c_Divides_Odiv__class_Omod @ SV583 @ SV1157 @ tc_nat ) )
= SV1157 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Suc @ SV583 ) @ SV1157 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3944]) ).
thf(4473,plain,
! [SV1158: $i,SV584: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV584 @ SV1158 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1158
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1158
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4474,plain,
! [SV1159: $i,SV586: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV586 @ SV1159 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1159
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4475,plain,
! [SV1160: $i,SV587: $i] :
( ( ( class_SEQ_Obanach @ SV587 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__field @ SV587 )
| ( ( c_Transcendental_Oexp @ SV1160 @ SV587 )
!= ( c_HOL_Ozero__class_Ozero @ SV587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(4476,plain,
! [SV1643: $i,SV1511: $i,SV1161: $i,SV588: $i] :
( ( ! [SY3330: $i,SY3331: $i] :
( ~ ( class_Divides_Osemiring__div @ SV588 )
| ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3330 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY3331 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3330 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3331 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3948]) ).
thf(4477,plain,
! [SV1644: $i,SV1512: $i,SV1162: $i,SV590: $i] :
( ( ! [SY3332: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SY3332 @ SV590 ) )
| ( c_lessequals @ SY3332 @ SV1644 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4478,plain,
! [SV1163: $i,SV591: $i] :
( ( ( SV591
= ( c_HOL_Oplus__class_Oplus @ SV591 @ SV1163 @ tc_nat ) )
= $false )
| ( ( SV1163
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(4479,plain,
! [SV1164: $i,SV592: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV592 @ SV1164 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1164
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3951]) ).
thf(4480,plain,
! [SV1513: $i,SV1165: $i,SV593: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV593 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
| ( SV1165 = SV1513 )
| ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4481,plain,
! [SV1166: $i,SV594: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV594 @ SV1166 @ tc_nat ) )
= $false )
| ( ( ( SV1166
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV1166
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4482,plain,
! [SV1645: $i,SV1514: $i,SV1167: $i,SV595: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SV1514 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SV1645 @ SV1514 @ SV595 ) )
| ( SV1167 = SV1645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4483,plain,
! [SV1646: $i,SV1515: $i,SV1168: $i,SV596: $i] :
( ( ! [SY3333: $i,SY3334: $i] :
( ~ ( class_Divides_Oring__div @ SV596 )
| ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SY3333 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY3334 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3333 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3334 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3955]) ).
thf(4484,plain,
! [SV1169: $i,SV597: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV597 @ SV1169 @ tc_nat )
= SV597 )
= $false )
| ( ( SV1169
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4485,plain,
! [SV1647: $i,SV1516: $i,SV1170: $i,SV598: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV598 )
| ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
| ( SV1170 = SV1647 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3957]) ).
thf(4486,plain,
! [SV1648: $i,SV1517: $i,SV1171: $i,SV599: $i] :
( ( ! [SY3335: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SY3335 @ SV599 ) )
| ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SY3335 @ SV1648 @ SV599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4487,plain,
! [SV1172: $i,SV600: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV600 @ SV1172 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV600
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3959]) ).
thf(4488,plain,
! [SV1649: $i,SV1518: $i,SV1173: $i,SV601: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1518 @ SV1649 @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV1173 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV601 @ SV1649 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3960]) ).
thf(4489,plain,
! [SV1174: $i,SV602: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV602 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
| ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4490,plain,
! [SV1650: $i,SV1519: $i,SV1175: $i,SV603: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV603 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SV1519 @ SV1650 @ SV603 ) )
| ( SV1519 = SV1650 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3962]) ).
thf(4491,plain,
! [SV1651: $i,SV1520: $i,SV1176: $i,SV604: $i] :
( ( ! [SY3336: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV604 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1651 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SY3336 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SV1651 @ SV604 )
= SY3336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3963]) ).
thf(4492,plain,
! [SV1177: $i,SV605: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV605 @ SV1177 @ tc_nat ) )
= $false )
| ( ( ( SV605
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV605
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4493,plain,
! [SV1521: $i,SV1178: $i,SV606: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV606 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1178 @ SV1521 @ SV606 )
!= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1521 @ SV1178 @ SV606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4494,plain,
! [SV1522: $i,SV1179: $i,SV607: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1179 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1522 @ tc_nat ) )
= $true )
| ( ( SV1179 = SV1522 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4495,plain,
! [SV1652: $i,SV1523: $i,SV1180: $i,SV608: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1523 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1652 @ SV608 ) )
| ( SV1523 = SV1652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3968]) ).
thf(4496,plain,
! [SV609: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV609 )
= ( c_HOL_Ozero__class_Ozero @ SV609 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV609 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3969]) ).
thf(4497,plain,
! [SV1653: $i,SV1524: $i,SV1181: $i,SV610: $i] :
( ( ! [SY3337: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SY3337 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SV1653 @ SY3337 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3970]) ).
thf(4498,plain,
! [SV1525: $i,SV1182: $i,SV611: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__ring @ SV611 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
| ( SV1182 = SV1525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(4499,plain,
! [SV1183: $i,SV612: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV612 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1183 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1183
= ( c_HOL_Ozero__class_Ozero @ SV612 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4500,plain,
! [SV1184: $i,SV613: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1184 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV613 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1184 = SV613 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4501,plain,
! [SV1654: $i,SV1526: $i,SV1185: $i,SV614: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV614 )
| ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SV1526 = SV1654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4502,plain,
! [SV615: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV615 )
= ( c_HOL_Oone__class_Oone @ SV615 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV615 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3976]) ).
thf(4503,plain,
! [SV1186: $i,SV616: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV616 @ SV1186 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( c_lessequals @ SV616 @ SV1186 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4504,plain,
! [SV1527: $i,SV1187: $i,SV617: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV617 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV617 )
| ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
| ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3978]) ).
thf(4505,plain,
! [SV1188: $i,SV618: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV618 @ SV1188 @ tc_nat ) )
= $false )
| ( ( ( SV1188
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV618
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4506,plain,
! [SV1189: $i,SV619: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV619 @ SV1189 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1189
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4507,plain,
! [SV1528: $i,SV1190: $i,SV620: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV620 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV620 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SV1190 = SV1528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3981]) ).
thf(4508,plain,
! [SV1191: $i,SV622: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV622 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1191 @ SV1191 @ SV622 )
!= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
| ( SV1191
= ( c_HOL_Ozero__class_Ozero @ SV622 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4509,plain,
! [SV1192: $i,SV623: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV623 @ SV1192 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false )
| ( ( ( SV1192
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3983]) ).
thf(4510,plain,
! [SV1193: $i,SV624: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV624 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4511,plain,
! [SV1529: $i,SV1194: $i,SV625: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV625 @ SV1194 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1529 @ SV1194 @ tc_nat ) )
= $true )
| ( ( SV625 = SV1529 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3985]) ).
thf(4512,plain,
! [SV1195: $i,SV627: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV627 @ SV1195 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV627
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3987]) ).
thf(4513,plain,
! [SV1655: $i,SV1530: $i,SV1196: $i,SV628: $i] :
( ( ! [SY3338: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SY3338 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SY3338 @ SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4514,plain,
! [SV1197: $i,SV629: $i] :
( ( ( ( c_Suc @ SV629 )
= ( c_Suc @ SV1197 ) )
= $false )
| ( ( SV629 = SV1197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4515,plain,
! [SV1531: $i,SV1198: $i,SV630: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV630 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1198 @ SV1531 @ SV630 )
!= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
| ( SV1198 = SV1531 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3991]) ).
thf(4516,plain,
! [SV1199: $i,SV631: $i] :
( ( ( ( c_GCD_Ogcd__class_Ogcd @ SV631 @ SV1199 @ tc_nat )
= SV631 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV631 @ SV1199 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4517,plain,
! [SV1532: $i,SV1200: $i,SV632: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
!= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3993]) ).
thf(4518,plain,
! [SV1201: $i,SV633: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV633 )
| ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3994]) ).
thf(4519,plain,
! [SV1656: $i,SV1533: $i,SV1202: $i,SV634: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV634 )
| ~ ( class_Int_Onumber__ring @ SV634 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
| ( SV1533 = SV1656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4520,plain,
! [SV1534: $i,SV1203: $i,SV635: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1203 @ SV1534 @ tc_nat )
| ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
| ( SV635 = SV1534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4521,plain,
! [SV1535: $i,SV1204: $i,SV636: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1204 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1535 @ tc_nat ) )
= $true )
| ( ( SV1204 = SV1535 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3997]) ).
thf(4522,plain,
! [SV1657: $i,SV1536: $i,SV1205: $i,SV637: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV637 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SV1536 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SV1657 @ SV1657 @ SV637 ) )
| ( SV1205 = SV1536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4523,plain,
! [SV1537: $i,SV1206: $i,SV638: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
!= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3999]) ).
thf(4524,plain,
! [SV1658: $i,SV1538: $i,SV1207: $i,SV639: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 )
| ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
| ( SV1207 = SV1658 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4525,plain,
! [SV1208: $i,SV640: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV640 @ SV1208 @ tc_nat ) )
= $false )
| ( ( ( SV640
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1208
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4526,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV641 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4002]) ).
thf(4527,plain,
! [SV1210: $i,SV643: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV643 @ SV1210 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1210
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4528,plain,
! [SV1540: $i,SV1211: $i,SV644: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV644 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SV1540 @ SV644 )
!= ( c_HOL_Oone__class_Oone @ SV644 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SV1211 = SV1540 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4004]) ).
thf(4529,plain,
! [SV1541: $i,SV1212: $i,SV645: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV645 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV645 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV645 ) )
| ( SV1212 = SV1541 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4005]) ).
thf(4530,plain,
! [SV1542: $i,SV1213: $i,SV646: $i,SV1: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV1 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV646 @ SV1213 @ SV1 ) @ SV1542 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV646 @ ( c_HOL_Oplus__class_Oplus @ SV1213 @ SV1542 @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4531,plain,
! [SV1543: $i,SV1214: $i,SV647: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV647 @ ( c_HOL_Oplus__class_Oplus @ SV1214 @ SV1543 @ SV2 ) @ SV2 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV647 @ SV1214 @ SV2 ) @ SV1543 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4532,plain,
! [SV1544: $i,SV1215: $i,SV648: $i,SV3: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV3 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV648 @ ( c_HOL_Oplus__class_Oplus @ SV1215 @ SV1544 @ SV3 ) @ SV3 )
= ( c_HOL_Oplus__class_Oplus @ SV1215 @ ( c_HOL_Oplus__class_Oplus @ SV648 @ SV1544 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4533,plain,
! [SV1545: $i,SV1218: $i,SV651: $i,SV6: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV6 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV1218 @ SV6 ) @ SV1545 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ SV651 @ ( c_HOL_Oplus__class_Oplus @ SV1218 @ SV1545 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4534,plain,
! [SV1546: $i,SV1219: $i,SV652: $i,SV7: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV652 @ ( c_HOL_Oplus__class_Oplus @ SV1219 @ SV1546 @ SV7 ) @ SV7 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV652 @ SV1219 @ SV7 ) @ SV1546 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4535,plain,
! [SV1547: $i,SV1220: $i,SV653: $i,SV8: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV8 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1220 @ SV8 ) @ SV1547 @ SV8 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1547 @ SV8 ) @ SV1220 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4011]) ).
thf(4536,plain,
! [SV1548: $i,SV1221: $i,SV654: $i,SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV654 @ ( c_HOL_Oplus__class_Oplus @ SV1221 @ SV1548 @ SV9 ) @ SV9 )
= ( c_HOL_Oplus__class_Oplus @ SV1221 @ ( c_HOL_Oplus__class_Oplus @ SV654 @ SV1548 @ SV9 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4537,plain,
! [SV1549: $i,SV1222: $i,SV655: $i,SV10: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV10 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV655 @ SV1222 @ SV10 ) @ SV1549 @ SV10 )
= ( c_HOL_Oplus__class_Oplus @ SV655 @ ( c_HOL_Oplus__class_Oplus @ SV1222 @ SV1549 @ SV10 ) @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4538,plain,
! [SV11: $i,SV656: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV656 @ SV11 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV656 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV11 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4539,plain,
! [SV1550: $i,SV1223: $i,SV657: $i,SV13: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV13 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ SV1223 @ SV13 ) @ SV1550 @ SV13 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ ( c_Divides_Odiv__class_Omod @ SV1223 @ SV1550 @ SV13 ) @ SV13 ) @ SV1550 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4540,plain,
! [SV1551: $i,SV1224: $i,SV658: $i,SV14: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV14 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV658 @ SV1224 @ SV14 ) @ SV1551 @ SV14 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV658 @ SV1551 @ SV14 ) @ SV1224 @ SV14 ) @ SV1551 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4541,plain,
! [SV1552: $i,SV1225: $i,SV659: $i,SV15: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4542,plain,
! [SV1226: $i,SV661: $i,SV17: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV17 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV661 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV661 @ SV1226 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4543,plain,
! [SV662: $i,SV21: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV21 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4544,plain,
! [SV1227: $i,SV663: $i,SV22: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV22 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4545,plain,
! [SV1228: $i,SV666: $i,SV25: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4546,plain,
! [SV1553: $i,SV1229: $i,SV667: $i,SV26: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4547,plain,
! [SV668: $i,SV27: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV27 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
| ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4024]) ).
thf(4548,plain,
! [SV669: $i,SV28: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV28 ) )
= $true )
| ( ( ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4025]) ).
thf(4549,plain,
! [SV670: $i,SV29: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV29 @ SV670 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV29 )
= SV670 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV29 ) @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4550,plain,
! [SV671: $i,SV30: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV30 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
| ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4551,plain,
! [SV672: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV672 @ SV31 ) @ SV31 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV672 @ SV31 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4552,plain,
! [SV673: $i,SV32: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV32 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4029]) ).
thf(4553,plain,
! [SV674: $i,SV33: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV33 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4030]) ).
thf(4554,plain,
! [SV34: $i,SV675: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV675 @ SV34 ) @ ( c_HOL_Ozero__class_Ozero @ SV34 ) @ SV34 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4031]) ).
thf(4555,plain,
! [SV1554: $i,SV1230: $i,SV676: $i,SV35: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV35 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV676 @ ( c_HOL_Oplus__class_Oplus @ SV1230 @ SV1554 @ SV35 ) @ SV35 )
= ( c_HOL_Oplus__class_Oplus @ SV1230 @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV1554 @ SV35 ) @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4032]) ).
thf(4556,plain,
! [SV1555: $i,SV1231: $i,SV677: $i,SV36: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV36 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4033]) ).
thf(4557,plain,
! [SV1556: $i,SV1232: $i,SV678: $i,SV37: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV37 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4034]) ).
thf(4558,plain,
! [SV38: $i,SV679: $i] :
( ( ( SV679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV679 @ SV38 ) @ SV38 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4559,plain,
! [SV1557: $i,SV1233: $i,SV680: $i,SV39: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV39 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV1233 @ SV39 ) @ SV1557 @ SV39 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV680 @ SV1557 @ SV39 ) @ ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1557 @ SV39 ) @ SV39 ) @ SV1557 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4036]) ).
thf(4560,plain,
! [SV41: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4561,plain,
! [SV681: $i,SV42: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV42 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV42 ) @ SV42 )
= SV681 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4562,plain,
! [SV684: $i,SV46: $i] :
( ( ( ~ ( class_Power_Opower @ SV46 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Suc @ SV684 ) @ SV46 )
= ( c_HOL_Ozero__class_Ozero @ SV46 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4563,plain,
! [SV1558: $i,SV1234: $i,SV688: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4564,plain,
! [SV1559: $i,SV1235: $i,SV689: $i,SV51: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
| ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4042]) ).
thf(4565,plain,
! [SV694: $i,SV1236: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ SV1236 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV56 @ ( c_HOL_Oplus__class_Oplus @ SV694 @ SV1236 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4566,plain,
! [SV1237: $i,SV695: $i,SV57: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV57 @ SV695 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV57 @ ( c_HOL_Oplus__class_Oplus @ SV695 @ SV1237 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4567,plain,
! [SV696: $i,SV1238: $i,SV58: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV58 @ SV1238 @ tc_nat ) @ SV696 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV58 @ SV696 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4568,plain,
! [SV697: $i,SV1239: $i,SV59: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV59 @ SV1239 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV59 @ ( c_HOL_Oplus__class_Oplus @ SV697 @ SV1239 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4569,plain,
! [SV1240: $i,SV698: $i,SV60: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV60 @ SV698 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV60 @ ( c_HOL_Oplus__class_Oplus @ SV698 @ SV1240 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4570,plain,
! [SV1560: $i,SV1241: $i,SV699: $i,SV61: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV61 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4052]) ).
thf(4571,plain,
! [SV1561: $i,SV1242: $i,SV700: $i,SV62: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV62 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4053]) ).
thf(4572,plain,
! [SV1562: $i,SV1243: $i,SV701: $i,SV63: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV63 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4054]) ).
thf(4573,plain,
! [SV1563: $i,SV1244: $i,SV702: $i,SV64: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV64 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4055]) ).
thf(4574,plain,
! [SV67: $i,SV705: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV705 @ SV705 @ SV67 ) @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV705 @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4575,plain,
! [SV68: $i,SV706: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV706 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV706 @ SV706 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4058]) ).
thf(4576,plain,
! [SV69: $i,SV707: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV707 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV707 @ SV707 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4577,plain,
! [SV70: $i,SV708: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV708 @ SV708 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV708 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4578,plain,
! [SV1245: $i,SV709: $i,SV72: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4579,plain,
! [SV1246: $i,SV710: $i,SV73: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4580,plain,
! [SV711: $i,SV74: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV74 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
| ~ ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4581,plain,
! [SV1247: $i,SV713: $i,SV76: $i] :
( ( ( class_Orderings_Olinorder @ SV76 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV713 @ SV1247 @ SV76 )
| ( c_HOL_Oord__class_Oless @ SV1247 @ SV713 @ SV76 )
| ( SV1247 = SV713 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4065]) ).
thf(4582,plain,
! [SV78: $i,SV715: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV715 @ SV78 @ tc_nat ) )
= $true )
| ( ( SV715 = SV78 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV78 @ SV715 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4067]) ).
thf(4583,plain,
! [SV79: $i,SV716: $i] :
( ( ( SV716 = SV79 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV716 @ SV79 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV79 @ SV716 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4584,plain,
! [SV717: $i,SV80: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV80 @ SV717 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV80 @ tc_nat ) )
= $true )
| ( ( SV80 = SV717 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4069]) ).
thf(4585,plain,
! [SV82: $i,SV719: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV719 @ SV82 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV82 @ SV719 @ tc_nat ) )
= $true )
| ( ( SV82 = SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4586,plain,
! [SV83: $i,SV720: $i] :
( ( ( SV720 = SV83 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV720 @ SV83 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV83 @ SV720 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4587,plain,
! [SV84: $i,SV721: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV721 @ SV84 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV84 @ SV721 @ tc_nat ) )
= $true )
| ( ( SV84 = SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4588,plain,
! [SV85: $i,SV722: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV85 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV85 @ SV722 @ tc_nat ) )
= $true )
| ( ( SV85 = SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4589,plain,
! [SV1248: $i,SV723: $i,SV86: $i] :
( ( ( class_Orderings_Olinorder @ SV86 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV723 @ SV1248 @ SV86 )
| ( SV1248 = SV723 )
| ( c_HOL_Oord__class_Oless @ SV1248 @ SV723 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4075]) ).
thf(4590,plain,
! [SV1249: $i,SV724: $i,SV87: $i] :
( ( ( class_Orderings_Olinorder @ SV87 )
= $false )
| ( ( ( SV724 = SV1249 )
| ( c_HOL_Oord__class_Oless @ SV724 @ SV1249 @ SV87 )
| ( c_HOL_Oord__class_Oless @ SV1249 @ SV724 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4591,plain,
! [SV1250: $i,SV725: $i,SV88: $i] :
( ( ( class_Orderings_Olinorder @ SV88 )
= $false )
| ( ( ( SV725 = SV1250 )
| ( c_HOL_Oord__class_Oless @ SV1250 @ SV725 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SV1250 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4592,plain,
! [SV1251: $i,SV726: $i,SV89: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV89 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV726 @ SV1251 @ SV89 )
| ( c_HOL_Oord__class_Oless @ SV1251 @ SV726 @ SV89 )
| ( SV1251 = SV726 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4593,plain,
! [SV727: $i,SV1252: $i,SV90: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ ( c_GCD_Ogcd__class_Ogcd @ SV1252 @ SV727 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV90 @ SV727 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4594,plain,
! [SV1253: $i,SV728: $i,SV91: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ ( c_GCD_Ogcd__class_Ogcd @ SV728 @ SV1253 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV91 @ SV728 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4080]) ).
thf(4595,plain,
! [SV1254: $i,SV729: $i,SV92: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ ( c_GCD_Ogcd__class_Ogcd @ SV729 @ SV1254 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV92 @ SV729 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4081]) ).
thf(4596,plain,
! [SV730: $i,SV1255: $i,SV93: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ ( c_GCD_Ogcd__class_Ogcd @ SV1255 @ SV730 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV93 @ SV730 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4082]) ).
thf(4597,plain,
! [SV731: $i,SV1256: $i,SV94: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV94 @ SV1256 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV94 @ SV731 @ tc_nat ) @ SV1256 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4598,plain,
! [SV95: $i,SV1257: $i,SV732: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV732 @ SV1257 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV95 @ SV732 @ tc_nat ) @ SV1257 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4084]) ).
thf(4599,plain,
! [SV1258: $i,SV733: $i,SV96: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ ( c_GCD_Ogcd__class_Ogcd @ SV733 @ SV1258 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV96 @ SV733 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4085]) ).
thf(4600,plain,
! [SV734: $i,SV1259: $i,SV97: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ ( c_GCD_Ogcd__class_Ogcd @ SV1259 @ SV734 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV97 @ SV734 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4086]) ).
thf(4601,plain,
! [SV98: $i,SV735: $i,SV1260: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1260 @ SV735 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV1260 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV735 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4087]) ).
thf(4602,plain,
! [SV99: $i,SV1261: $i,SV736: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4603,plain,
! [SV737: $i,SV100: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV100 @ SV737 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV737 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV100 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4604,plain,
! [SV1564: $i,SV1262: $i,SV739: $i,SV103: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4605,plain,
! [SV104: $i,SV740: $i,SV1263: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1263 @ SV740 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV1263 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SV740 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4092]) ).
thf(4606,plain,
! [SV742: $i,SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV108 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4094]) ).
thf(4607,plain,
! [SV743: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV109 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV109 )
| ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4095]) ).
thf(4608,plain,
! [SV744: $i,SV110: $i] :
( ( ( ~ ( class_Power_Opower @ SV110 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV744 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4096]) ).
thf(4609,plain,
! [SV1264: $i,SV745: $i,SV111: $i] :
( ( ( class_Divides_Osemiring__div @ SV111 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV745 @ SV1264 @ SV111 ) @ SV745 @ SV111 )
= ( c_Divides_Odiv__class_Omod @ SV1264 @ SV745 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4610,plain,
! [SV1265: $i,SV746: $i,SV112: $i] :
( ( ( class_Divides_Osemiring__div @ SV112 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV746 @ SV1265 @ SV112 ) @ SV1265 @ SV112 )
= ( c_Divides_Odiv__class_Omod @ SV746 @ SV1265 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4098]) ).
thf(4611,plain,
! [SV1565: $i,SV1266: $i,SV747: $i,SV113: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV113 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4099]) ).
thf(4612,plain,
! [SV114: $i,SV748: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
= $true )
| ( ( ( SV748
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV748 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4100]) ).
thf(4613,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV116 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
| ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4614,plain,
! [SV1268: $i,SV751: $i,SV117: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV117 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
| ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4615,plain,
! [SV1269: $i,SV752: $i,SV118: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV118 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
| ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4103]) ).
thf(4616,plain,
! [SV1270: $i,SV753: $i,SV119: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV119 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4104]) ).
thf(4617,plain,
! [SV1271: $i,SV754: $i,SV120: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV120 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4105]) ).
thf(4618,plain,
! [SV1272: $i,SV755: $i,SV121: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV121 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4619,plain,
! [SV1273: $i,SV756: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV122 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
| ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4620,plain,
! [SV762: $i,SV129: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV129 ) )
= $true )
| ( ( SV762
= ( c_HOL_Oplus__class_Oplus @ SV762 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4621,plain,
! [SV767: $i,SV1274: $i,SV137: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV1274 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV767 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SV767 @ SV1274 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4622,plain,
! [SV1275: $i,SV768: $i,SV138: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SV768 @ SV1275 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SV1275 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1275 @ SV138 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4119]) ).
thf(4623,plain,
! [SV1276: $i,SV769: $i,SV139: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SV769 @ SV1276 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SV769 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV769 @ SV139 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4120]) ).
thf(4624,plain,
! [SV770: $i,SV1277: $i,SV140: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV1277 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV770 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SV770 @ SV1277 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4625,plain,
! [SV771: $i,SV1278: $i,SV141: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV1278 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV771 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SV771 @ SV1278 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4122]) ).
thf(4626,plain,
! [SV778: $i,SV1279: $i,SV148: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV1279 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV778 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SV778 @ SV1279 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4123]) ).
thf(4627,plain,
! [SV779: $i,SV1280: $i,SV149: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV1280 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV779 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SV779 @ SV1280 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4628,plain,
! [SV780: $i,SV1281: $i,SV150: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV1281 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV780 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SV780 @ SV1281 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4125]) ).
thf(4629,plain,
! [SV1659: $i,SV1566: $i,SV1282: $i,SV781: $i,SV151: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SV1282 @ SV1659 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4126]) ).
thf(4630,plain,
! [SV1660: $i,SV1567: $i,SV1283: $i,SV782: $i,SV152: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(4631,plain,
! [SV1284: $i,SV786: $i,SV156: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4131]) ).
thf(4632,plain,
! [SV1285: $i,SV787: $i,SV157: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4132]) ).
thf(4633,plain,
! [SV1568: $i,SV1286: $i,SV788: $i,SV158: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV158 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
| ~ ( c_lessequals @ SV788 @ SV1568 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4133]) ).
thf(4634,plain,
! [SV1569: $i,SV1287: $i,SV789: $i,SV159: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV159 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 )
| ~ ( c_lessequals @ SV1569 @ SV1287 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4134]) ).
thf(4635,plain,
! [SV1661: $i,SV1570: $i,SV1288: $i,SV790: $i,SV160: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
| ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SV1661 @ SV1570 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4636,plain,
! [SV1571: $i,SV1289: $i,SV791: $i,SV161: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV161 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
| ~ ( c_lessequals @ SV1571 @ SV1289 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4637,plain,
! [SV1572: $i,SV1290: $i,SV792: $i,SV162: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV162 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 )
| ~ ( c_lessequals @ SV792 @ SV1572 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4137]) ).
thf(4638,plain,
! [SV1291: $i,SV793: $i,SV163: $i] :
( ( ( class_Orderings_Opreorder @ SV163 )
= $false )
| ( ( ( c_lessequals @ SV793 @ SV1291 @ SV163 )
| ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV1291 @ SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4639,plain,
! [SV1292: $i,SV794: $i,SV164: $i] :
( ( ( class_Orderings_Oorder @ SV164 )
= $false )
| ( ( ( c_lessequals @ SV794 @ SV1292 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV1292 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4139]) ).
thf(4640,plain,
! [SV1293: $i,SV795: $i,SV165: $i] :
( ( ( class_Orderings_Opreorder @ SV165 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1293 @ SV165 )
| ( c_lessequals @ SV1293 @ SV795 @ SV165 )
| ~ ( c_lessequals @ SV795 @ SV1293 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4140]) ).
thf(4641,plain,
! [SV1662: $i,SV1573: $i,SV1294: $i,SV796: $i,SV166: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
| ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SV1294 @ SV1662 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4642,plain,
! [SV1295: $i,SV797: $i,SV167: $i] :
( ( ( class_Orderings_Oorder @ SV167 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1295 @ SV167 )
| ( SV1295 = SV797 )
| ~ ( c_lessequals @ SV797 @ SV1295 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4643,plain,
! [SV1296: $i,SV798: $i,SV168: $i] :
( ( ( class_Orderings_Oorder @ SV168 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV798 @ SV1296 @ SV168 )
| ~ ( c_lessequals @ SV798 @ SV1296 @ SV168 )
| ( SV1296 = SV798 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4644,plain,
! [SV1297: $i,SV799: $i,SV169: $i] :
( ( ( class_Orderings_Olinorder @ SV169 )
= $false )
| ( ( ( SV799 = SV1297 )
| ( c_HOL_Oord__class_Oless @ SV799 @ SV1297 @ SV169 )
| ~ ( c_lessequals @ SV799 @ SV1297 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4645,plain,
! [SV1298: $i,SV800: $i,SV170: $i] :
( ( ( class_Orderings_Olinorder @ SV170 )
= $false )
| ( ( ( SV800 = SV1298 )
| ~ ( c_lessequals @ SV800 @ SV1298 @ SV170 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1298 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4646,plain,
! [SV1299: $i,SV801: $i,SV171: $i] :
( ( ( class_Orderings_Oorder @ SV171 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV801 @ SV1299 @ SV171 )
| ~ ( c_lessequals @ SV801 @ SV1299 @ SV171 )
| ( SV801 = SV1299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4146]) ).
thf(4647,plain,
! [SV1300: $i,SV802: $i,SV172: $i] :
( ( ( class_Orderings_Oorder @ SV172 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV802 @ SV1300 @ SV172 )
| ( SV802 = SV1300 )
| ~ ( c_lessequals @ SV802 @ SV1300 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4648,plain,
! [SV1301: $i,SV803: $i,SV173: $i] :
( ( ( class_Orderings_Oorder @ SV173 )
= $false )
| ( ( ( SV803 = SV1301 )
| ( c_HOL_Oord__class_Oless @ SV803 @ SV1301 @ SV173 )
| ~ ( c_lessequals @ SV803 @ SV1301 @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4649,plain,
! [SV1302: $i,SV804: $i,SV174: $i] :
( ( ( class_Orderings_Oorder @ SV174 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1302 @ SV174 )
| ( SV804 = SV1302 )
| ~ ( c_lessequals @ SV804 @ SV1302 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4650,plain,
! [SV1574: $i,SV1303: $i,SV805: $i,SV175: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SV1303 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1574 @ SV1303 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV805 @ SV1574 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4651,plain,
! [SV1575: $i,SV1304: $i,SV806: $i,SV176: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 ) )
= $true )
| ( ( ( c_lessequals @ SV806 @ SV1304 @ SV176 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1575 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SV1304 @ SV1575 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4652,plain,
! [SV1576: $i,SV1305: $i,SV807: $i,SV177: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1305 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1576 @ SV177 ) @ SV177 )
| ~ ( c_lessequals @ SV1305 @ SV1576 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4152]) ).
thf(4653,plain,
! [SV1577: $i,SV1306: $i,SV808: $i,SV178: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 ) )
= $true )
| ( ( ( c_lessequals @ SV808 @ SV1306 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV1306 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4654,plain,
! [SV1578: $i,SV1307: $i,SV809: $i,SV179: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SV1307 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SV1578 @ SV1307 @ SV179 ) @ SV179 )
| ~ ( c_lessequals @ SV809 @ SV1578 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4655,plain,
! [SV1579: $i,SV1308: $i,SV810: $i,SV180: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1308 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1579 @ SV180 ) @ SV180 )
| ~ ( c_lessequals @ SV1308 @ SV1579 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4656,plain,
! [SV1309: $i,SV811: $i,SV181: $i] :
( ( ( class_Orderings_Opreorder @ SV181 )
= $false )
| ( ( ~ ( c_lessequals @ SV811 @ SV1309 @ SV181 )
| ~ ( c_HOL_Oord__class_Oless @ SV1309 @ SV811 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4657,plain,
! [SV1310: $i,SV812: $i,SV182: $i] :
( ( ( class_Orderings_Olinorder @ SV182 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV812 @ SV1310 @ SV182 )
| ( c_lessequals @ SV1310 @ SV812 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4157]) ).
thf(4658,plain,
! [SV183: $i,SV813: $i] :
( ( ( ~ ( c_lessequals @ SV813 @ SV813 @ SV183 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV813 @ SV813 @ SV183 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4158]) ).
thf(4659,plain,
! [SV184: $i,SV814: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV814 @ SV814 @ SV184 )
= $true )
| ( ( c_lessequals @ SV814 @ SV814 @ SV184 )
= $true )
| ( ( class_Orderings_Olinorder @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4159]) ).
thf(4660,plain,
! [SV1311: $i,SV815: $i,SV185: $i] :
( ( ( class_Orderings_Olinorder @ SV185 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV815 @ SV1311 @ SV185 )
| ~ ( c_lessequals @ SV1311 @ SV815 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4661,plain,
! [SV1312: $i,SV816: $i,SV186: $i] :
( ( ( class_Orderings_Olinorder @ SV186 )
= $false )
| ( ( ( c_lessequals @ SV816 @ SV1312 @ SV186 )
| ( c_HOL_Oord__class_Oless @ SV1312 @ SV816 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4662,plain,
! [SV1313: $i,SV817: $i,SV187: $i] :
( ( ( class_Orderings_Olinorder @ SV187 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV817 @ SV1313 @ SV187 )
| ( c_lessequals @ SV1313 @ SV817 @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4162]) ).
thf(4663,plain,
! [SV1314: $i,SV818: $i,SV188: $i] :
( ( ( class_Orderings_Olinorder @ SV188 )
= $false )
| ( ( ~ ( c_lessequals @ SV818 @ SV1314 @ SV188 )
| ~ ( c_HOL_Oord__class_Oless @ SV1314 @ SV818 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4163]) ).
thf(4664,plain,
! [SV819: $i,SV189: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV189 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
| ~ ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4665,plain,
! [SV820: $i,SV190: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV190 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
| ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4165]) ).
thf(4666,plain,
! [SV1580: $i,SV1315: $i,SV821: $i,SV191: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 ) )
= $true )
| ( ( ( c_lessequals @ SV821 @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4667,plain,
! [SV192: $i,SV822: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV822 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV192 ) @ ( c_HOL_Ozero__class_Ozero @ SV192 ) @ SV192 )
= $false )
| ( ( class_Ring__and__Field_Oordered__idom @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4167]) ).
thf(4668,plain,
! [SV1581: $i,SV1316: $i,SV823: $i,SV193: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4168]) ).
thf(4669,plain,
! [SV1663: $i,SV1582: $i,SV1317: $i,SV824: $i,SV194: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV194 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4670,plain,
! [SV1318: $i,SV825: $i,SV195: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV195 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
| ~ ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
| ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4170]) ).
thf(4671,plain,
! [SV1319: $i,SV826: $i,SV196: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV196 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4672,plain,
! [SV1664: $i,SV1583: $i,SV1320: $i,SV827: $i,SV197: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV197 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4673,plain,
! [SV1321: $i,SV828: $i,SV198: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV198 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 )
| ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4173]) ).
thf(4674,plain,
! [SV1322: $i,SV829: $i,SV199: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV199 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4675,plain,
! [SV1665: $i,SV1584: $i,SV1323: $i,SV830: $i,SV200: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV200 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4676,plain,
! [SV1585: $i,SV1324: $i,SV831: $i,SV201: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV201 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
| ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4677,plain,
! [SV1586: $i,SV1325: $i,SV832: $i,SV202: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV202 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4177]) ).
thf(4678,plain,
! [SV1587: $i,SV1326: $i,SV833: $i,SV203: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV203 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4178]) ).
thf(4679,plain,
! [SV1588: $i,SV1327: $i,SV834: $i,SV204: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV204 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4179]) ).
thf(4680,plain,
! [SV206: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV206 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ SV206 ) @ SV206 )
= ( c_HOL_Oone__class_Oone @ SV206 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4180]) ).
thf(4681,plain,
! [SV1589: $i,SV1328: $i,SV836: $i,SV208: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV208 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4182]) ).
thf(4682,plain,
! [SV1590: $i,SV1329: $i,SV837: $i,SV209: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV209 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4183]) ).
thf(4683,plain,
! [SV1591: $i,SV1330: $i,SV838: $i,SV210: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV210 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4684,plain,
! [SV1592: $i,SV1331: $i,SV839: $i,SV211: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV211 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4185]) ).
thf(4685,plain,
! [SV1332: $i,SV840: $i,SV212: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV212 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV840 @ ( c_Suc @ SV1332 ) @ SV212 ) @ SV212 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SV840 @ SV212 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4186]) ).
thf(4686,plain,
! [SV1333: $i,SV841: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV213 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
| ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4687,plain,
! [SV218: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV218 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= ( c_HOL_Ozero__class_Ozero @ SV218 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4688,plain,
! [SV1334: $i,SV846: $i,SV221: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV221 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oplus__class_Oplus @ SV846 @ SV1334 @ tc_nat ) @ SV221 )
= ( c_HOL_Oplus__class_Oplus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV846 @ SV221 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1334 @ SV221 ) @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4689,plain,
! [SV1593: $i,SV1335: $i,SV847: $i,SV222: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV222 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ ( c_Divides_Odiv__class_Omod @ SV1335 @ SV1593 @ SV222 ) @ SV222 ) @ SV1593 @ SV222 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ SV1335 @ SV222 ) @ SV1593 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4194]) ).
thf(4690,plain,
! [SV1594: $i,SV1336: $i,SV848: $i,SV223: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV223 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV848 @ SV1336 @ SV223 ) @ SV1594 @ SV223 ) @ SV1336 @ SV223 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV848 @ SV1594 @ SV223 ) @ SV1336 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4195]) ).
thf(4691,plain,
! [SV851: $i,SV226: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV851 @ SV226 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ ( c_HOL_Oplus__class_Oplus @ SV851 @ SV851 @ SV226 ) @ SV226 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4198]) ).
thf(4692,plain,
! [SV852: $i,SV227: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV852 @ SV852 @ SV227 ) @ SV227 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV852 @ SV227 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4199]) ).
thf(4693,plain,
! [SV853: $i,SV228: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV228 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
| ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4200]) ).
thf(4694,plain,
! [SV1595: $i,SV1337: $i,SV855: $i,SV231: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV231 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4202]) ).
thf(4695,plain,
! [SV1596: $i,SV1338: $i,SV856: $i,SV232: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV232 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4696,plain,
! [SV1597: $i,SV1339: $i,SV857: $i,SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV233 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4697,plain,
! [SV1598: $i,SV1340: $i,SV858: $i,SV234: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV234 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4205]) ).
thf(4698,plain,
! [SV238: $i,SV861: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV861 @ ( c_Suc @ SV238 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV238 @ SV861 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4699,plain,
! [SV1341: $i,SV863: $i,SV240: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV240 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4207]) ).
thf(4700,plain,
! [SV1342: $i,SV864: $i,SV241: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV241 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4208]) ).
thf(4701,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4209]) ).
thf(4702,plain,
! [SV1344: $i,SV866: $i,SV243: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4210]) ).
thf(4703,plain,
! [SV867: $i,SV244: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV244 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4704,plain,
! [SV1599: $i,SV1345: $i,SV868: $i,SV245: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4212]) ).
thf(4705,plain,
! [SV1666: $i,SV1600: $i,SV1346: $i,SV869: $i,SV246: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 )
| ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1346 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV1666 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1600 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1346 @ SV1666 @ SV246 ) @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4706,plain,
! [SV1601: $i,SV1347: $i,SV870: $i,SV247: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV247 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4214]) ).
thf(4707,plain,
! [SV1602: $i,SV1348: $i,SV871: $i,SV248: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV248 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4215]) ).
thf(4708,plain,
! [SV1349: $i,SV872: $i,SV249: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4216]) ).
thf(4709,plain,
! [SV1350: $i,SV873: $i,SV250: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4217]) ).
thf(4710,plain,
! [SV1351: $i,SV874: $i,SV251: $i] :
( ( ( class_Divides_Osemiring__div @ SV251 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV874 @ SV1351 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1351 @ SV874 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4711,plain,
! [SV252: $i,SV875: $i] :
( ( ( SV875
= ( c_HOL_Ozero__class_Ozero @ SV252 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV875 @ SV252 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4712,plain,
! [SV253: $i,SV876: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV876 @ SV253 ) @ SV253 )
= SV876 )
= $true )
| ( ( SV876
= ( c_HOL_Ozero__class_Ozero @ SV253 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4713,plain,
! [SV1352: $i,SV879: $i,SV257: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4714,plain,
! [SV881: $i,SV259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV881 @ SV259 )
= $true )
| ( ( ( SV881
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV881 @ SV259 ) @ SV259 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4715,plain,
! [SV1353: $i,SV882: $i,SV262: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV262 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4716,plain,
! [SV1354: $i,SV883: $i,SV263: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV263 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4717,plain,
! [SV1355: $i,SV884: $i,SV264: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV264 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4227]) ).
thf(4718,plain,
! [SV1356: $i,SV885: $i,SV265: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV265 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4719,plain,
! [SV1357: $i,SV886: $i,SV266: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV266 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4720,plain,
! [SV1358: $i,SV887: $i,SV267: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4230]) ).
thf(4721,plain,
! [SV269: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV269 )
= $false )
| ( ( ( c_Transcendental_Oexp @ ( c_HOL_Ozero__class_Ozero @ SV269 ) @ SV269 )
= ( c_HOL_Oone__class_Oone @ SV269 ) )
= $true )
| ( ( class_SEQ_Obanach @ SV269 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4722,plain,
! [SV891: $i,SV273: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV273 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4234]) ).
thf(4723,plain,
! [SV892: $i,SV274: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV274 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4724,plain,
! [SV893: $i,SV275: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ SV893 @ SV275 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ ( c_HOL_Oplus__class_Oplus @ SV893 @ SV893 @ SV275 ) @ SV275 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV275 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4236]) ).
thf(4725,plain,
! [SV894: $i,SV276: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ ( c_HOL_Oplus__class_Oplus @ SV894 @ SV894 @ SV276 ) @ SV276 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV894 @ SV276 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV276 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4237]) ).
thf(4726,plain,
! [SV1359: $i,SV895: $i,SV279: $i] :
( ( ( class_Divides_Osemiring__div @ SV279 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV895 @ SV1359 @ SV279 ) @ SV1359 @ SV279 )
= ( c_Divides_Odiv__class_Omod @ SV895 @ SV1359 @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4727,plain,
! [SV1603: $i,SV1360: $i,SV896: $i,SV280: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
| ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4239]) ).
thf(4728,plain,
! [SV1604: $i,SV1361: $i,SV899: $i,SV284: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV284 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4240]) ).
thf(4729,plain,
! [SV1362: $i,SV902: $i,SV287: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV287 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV902 @ SV1362 @ SV287 )
= ( c_HOL_Oplus__class_Oplus @ SV1362 @ SV902 @ SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4243]) ).
thf(4730,plain,
! [SV1363: $i,SV904: $i,SV289: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV289 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV904 @ SV1363 @ SV289 )
= ( c_HOL_Oplus__class_Oplus @ SV1363 @ SV904 @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4731,plain,
! [SV1364: $i,SV905: $i,SV290: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV290 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV905 @ SV1364 @ SV290 )
= ( c_HOL_Oplus__class_Oplus @ SV1364 @ SV905 @ SV290 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4732,plain,
! [SV1365: $i,SV906: $i,SV291: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV291 )
= $false )
| ( ( ( c_lessequals @ SV906 @ SV1365 @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4733,plain,
! [SV1366: $i,SV907: $i,SV292: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV292 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 )
| ~ ( c_lessequals @ SV1366 @ SV907 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4734,plain,
! [SV1367: $i,SV908: $i,SV293: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV293 )
= $false )
| ( ( ( c_lessequals @ SV908 @ SV1367 @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4735,plain,
! [SV1368: $i,SV909: $i,SV294: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV294 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
| ~ ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
| ~ ( c_lessequals @ SV1368 @ SV909 @ SV294 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4249]) ).
thf(4736,plain,
! [SV295: $i] :
( ( ( class_Power_Opower @ SV295 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV295 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV295 )
= ( c_HOL_Oone__class_Oone @ SV295 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4250]) ).
thf(4737,plain,
! [SV910: $i,SV296: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV296 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4738,plain,
! [SV911: $i,SV297: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV297 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4739,plain,
! [SV912: $i,SV298: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV298 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4253]) ).
thf(4740,plain,
! [SV913: $i,SV299: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV299 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4254]) ).
thf(4741,plain,
! [SV1369: $i,SV914: $i,SV300: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV300 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV914 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV914 @ SV1369 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1369 @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4742,plain,
! [SV1370: $i,SV915: $i,SV301: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV301 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV915 @ SV1370 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SV1370 @ SV301 )
| ~ ( c_HOL_Oord__class_Oless @ SV915 @ SV1370 @ SV301 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4256]) ).
thf(4743,plain,
! [SV302: $i,SV916: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV916 @ SV302 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV302 ) @ SV916 @ SV302 ) )
= $true )
| ( ( SV916
= ( c_HOL_Ozero__class_Ozero @ SV302 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4257]) ).
thf(4744,plain,
! [SV1605: $i,SV1371: $i,SV917: $i,SV303: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV303 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ SV1371 @ SV303 ) @ SV1605 @ SV303 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ ( c_Divides_Odiv__class_Omod @ SV1371 @ SV1605 @ SV303 ) @ SV303 ) @ SV1605 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4258]) ).
thf(4745,plain,
! [SV1606: $i,SV1372: $i,SV918: $i,SV304: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV304 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1372 @ SV304 ) @ SV1606 @ SV304 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV918 @ SV1606 @ SV304 ) @ SV1372 @ SV304 ) @ SV1606 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4259]) ).
thf(4746,plain,
! [SV1607: $i,SV1373: $i,SV919: $i,SV305: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV305 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV919 @ SV1373 @ SV305 ) @ SV1607 @ SV305 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV919 @ SV1607 @ SV305 ) @ ( c_Divides_Odiv__class_Omod @ SV1373 @ SV1607 @ SV305 ) @ SV305 ) @ SV1607 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4747,plain,
! [SV1608: $i,SV1374: $i,SV920: $i,SV306: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4748,plain,
! [SV925: $i,SV311: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV311 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV925 @ SV925 @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ SV311 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4749,plain,
! [SV1375: $i,SV926: $i,SV312: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV312 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV926 @ SV1375 @ SV312 ) @ SV1375 @ SV312 )
= SV926 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4267]) ).
thf(4750,plain,
! [SV1667: $i,SV1609: $i,SV1376: $i,SV927: $i,SV313: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV313 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV927 @ SV1376 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SV1609 @ SV1667 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV927 @ SV1609 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SV1376 @ SV1667 @ SV313 ) @ SV313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4751,plain,
! [SV1377: $i,SV928: $i,SV314: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV314 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV928 @ SV1377 @ SV314 ) @ SV1377 @ SV314 )
= SV928 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4269]) ).
thf(4752,plain,
! [SV1378: $i,SV929: $i,SV315: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV315 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV315 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV929 @ SV1378 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV929 @ SV315 ) @ SV1378 @ SV315 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4753,plain,
! [SV1610: $i,SV1379: $i,SV930: $i,SV316: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SV1379 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SV1610 @ SV1379 @ SV316 ) @ SV316 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SV1610 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4271]) ).
thf(4754,plain,
! [SV931: $i,SV317: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV317 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV317 )
= ( c_HOL_Oinverse__class_Odivide @ SV931 @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4272]) ).
thf(4755,plain,
! [SV318: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV318 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV318 )
= ( c_HOL_Ozero__class_Ozero @ SV318 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4273]) ).
thf(4756,plain,
! [SV1380: $i,SV932: $i,SV319: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV319 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV319 )
| ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV932 @ SV1380 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SV1380 @ SV932 @ SV319 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4274]) ).
thf(4757,plain,
! [SV934: $i,SV321: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV321 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV934 @ ( c_HOL_Ozero__class_Ozero @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4276]) ).
thf(4758,plain,
! [SV935: $i,SV322: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV322 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV322 ) @ SV322 )
= ( c_HOL_Ozero__class_Ozero @ SV322 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV322 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4277]) ).
thf(4759,plain,
! [SV1611: $i,SV1381: $i,SV937: $i,SV324: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV324 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV1381 @ SV324 ) @ SV1611 @ SV324 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV937 @ SV1611 @ SV324 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1381 @ SV1611 @ SV324 ) @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4760,plain,
! [SV1612: $i,SV1382: $i,SV938: $i,SV325: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV325 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV1382 @ SV325 ) @ SV1612 @ SV325 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV938 @ SV1612 @ SV325 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1382 @ SV1612 @ SV325 ) @ SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4280]) ).
thf(4761,plain,
! [SV1613: $i,SV1383: $i,SV949: $i,SV337: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1383 @ SV1613 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV949 @ SV1613 @ tc_nat )
| ~ ( c_lessequals @ SV337 @ SV1383 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4287]) ).
thf(4762,plain,
! [SV950: $i,SV338: $i] :
( ( ( c_lessequals @ SV338 @ ( c_Suc @ SV950 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV338 @ SV950 @ tc_nat )
= $true )
| ( ( SV338
= ( c_Suc @ SV950 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4288]) ).
thf(4763,plain,
! [SV951: $i,SV339: $i] :
( ( ( c_lessequals @ SV339 @ SV951 @ tc_nat )
= $false )
| ( ( SV339 = SV951 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV339 @ SV951 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4289]) ).
thf(4764,plain,
! [SV952: $i,SV340: $i] :
( ( ( c_lessequals @ SV340 @ SV952 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV340 @ SV952 @ tc_nat )
= $true )
| ( ( SV340 = SV952 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4290]) ).
thf(4765,plain,
! [SV953: $i,SV341: $i] :
( ( ( c_lessequals @ SV341 @ SV953 @ tc_nat )
= $false )
| ( ( SV341 = SV953 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV341 @ SV953 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4766,plain,
! [SV954: $i,SV1384: $i,SV342: $i] :
( ( ( c_lessequals @ SV342 @ SV1384 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV342 @ SV954 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1384 @ SV954 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4767,plain,
! [SV955: $i,SV343: $i,SV1385: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV343 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1385 @ SV955 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV343 @ SV955 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4293]) ).
thf(4768,plain,
! [SV344: $i,SV1386: $i,SV956: $i] :
( ( ( c_lessequals @ SV956 @ SV1386 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV956 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV344 @ SV1386 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4294]) ).
thf(4769,plain,
! [SV1387: $i,SV957: $i,SV346: $i] :
( ( ( c_lessequals @ SV346 @ SV957 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV346 @ ( c_HOL_Oplus__class_Oplus @ SV957 @ SV1387 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4295]) ).
thf(4770,plain,
! [SV958: $i,SV1388: $i,SV347: $i] :
( ( ( c_lessequals @ SV347 @ SV1388 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV347 @ ( c_HOL_Oplus__class_Oplus @ SV958 @ SV1388 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4296]) ).
thf(4771,plain,
! [SV959: $i,SV1389: $i,SV348: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV348 @ SV1389 @ tc_nat ) @ SV959 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV348 @ SV959 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4772,plain,
! [SV960: $i,SV349: $i,SV1390: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1390 @ SV349 @ tc_nat ) @ SV960 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV349 @ SV960 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4773,plain,
! [SV1391: $i,SV961: $i,SV350: $i] :
( ( ( c_lessequals @ SV350 @ SV961 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV350 @ ( c_HOL_Oplus__class_Oplus @ SV961 @ SV1391 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4299]) ).
thf(4774,plain,
! [SV962: $i,SV1392: $i,SV351: $i] :
( ( ( c_lessequals @ SV351 @ SV1392 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV351 @ ( c_HOL_Oplus__class_Oplus @ SV962 @ SV1392 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4775,plain,
! [SV354: $i,SV964: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV964 ) @ SV354 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV354 @ SV964 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4776,plain,
! [SV357: $i,SV966: $i,SV1393: $i] :
( ( ( c_lessequals @ SV1393 @ SV966 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV357 @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV966 @ SV1393 @ tc_nat ) ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV357 @ SV1393 @ tc_nat ) @ ( c_Suc @ SV966 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4777,plain,
! [SV1394: $i,SV358: $i,SV967: $i] :
( ( ( c_lessequals @ SV967 @ SV358 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV358 @ SV967 @ tc_nat ) ) @ SV1394 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV358 ) @ ( c_HOL_Oplus__class_Oplus @ SV967 @ SV1394 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4303]) ).
thf(4778,plain,
! [SV968: $i,SV1395: $i,SV359: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV359 @ SV1395 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV359 @ SV968 @ tc_nat ) @ SV1395 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4779,plain,
! [SV970: $i,SV361: $i,SV1396: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV361 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV970 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV970 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV1396 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4305]) ).
thf(4780,plain,
! [SV974: $i,SV1400: $i,SV365: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV1400 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV974 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SV974 @ SV1400 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4306]) ).
thf(4781,plain,
! [SV978: $i,SV373: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV373 ) )
= $true )
| ( ( ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4308]) ).
thf(4782,plain,
! [SV979: $i,SV375: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV375 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4783,plain,
! [SV1402: $i,SV980: $i,SV376: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV376 )
= $false )
| ( ( ( c_lessequals @ SV980 @ SV1402 @ SV376 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV980 @ SV1402 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4310]) ).
thf(4784,plain,
! [SV1403: $i,SV981: $i,SV377: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV377 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV981 @ SV1403 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
| ~ ( c_lessequals @ SV981 @ SV1403 @ SV377 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4311]) ).
thf(4785,plain,
! [SV1404: $i,SV982: $i,SV378: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV378 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SV982 @ SV1404 @ SV378 ) @ SV378 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SV982 @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4312]) ).
thf(4786,plain,
! [SV1405: $i,SV983: $i,SV379: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV379 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SV983 @ SV1405 @ SV379 ) @ SV379 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SV983 @ SV379 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4787,plain,
! [SV1614: $i,SV1406: $i,SV984: $i,SV380: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV380 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
| ~ ( c_lessequals @ SV984 @ SV1614 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(4788,plain,
! [SV1407: $i,SV985: $i,SV381: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV381 )
= $false )
| ( ( ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
| ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SV1407 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4315]) ).
thf(4789,plain,
! [SV1408: $i,SV986: $i,SV382: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4790,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4791,plain,
! [SV1410: $i,SV988: $i,SV384: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV384 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SV988 @ SV1410 @ SV384 ) @ SV384 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SV988 @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4792,plain,
! [SV1411: $i,SV991: $i,SV388: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV388 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV991 @ SV1411 @ SV388 ) @ SV388 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV991 @ SV388 ) @ SV1411 @ SV388 ) )
| ( SV991
= ( c_HOL_Ozero__class_Ozero @ SV388 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4793,plain,
! [SV995: $i,SV392: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV392 @ ( c_Suc @ SV995 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV392 @ SV995 @ tc_nat )
= $true )
| ( ( SV392 = SV995 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4794,plain,
! [SV393: $i,SV996: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV996 @ ( c_Suc @ SV393 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV996 @ SV393 @ tc_nat )
= $true )
| ( ( SV393 = SV996 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4795,plain,
! [SV997: $i,SV394: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV394 @ ( c_Suc @ SV997 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV394 @ SV997 @ tc_nat )
= $true )
| ( ( SV394 = SV997 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4796,plain,
! [SV401: $i,SV1002: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1002 @ SV1002 @ SV401 )
= $false )
| ( ( class_Orderings_Oorder @ SV401 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4328]) ).
thf(4797,plain,
! [SV404: $i,SV1003: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1003 @ SV1003 @ SV404 )
= $false )
| ( ( class_Orderings_Olinorder @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4329]) ).
thf(4798,plain,
! [SV405: $i,SV1004: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1004 @ SV1004 @ SV405 )
= $false )
| ( ( class_Orderings_Opreorder @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4330]) ).
thf(4799,plain,
! [SV1415: $i,SV1005: $i,SV406: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4800,plain,
! [SV1006: $i,SV407: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV407 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4332]) ).
thf(4801,plain,
! [SV1007: $i,SV408: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV408 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4333]) ).
thf(4802,plain,
! [SV409: $i,SV1008: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1008 @ SV409 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV409 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4334]) ).
thf(4803,plain,
! [SV410: $i,SV1009: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1009 @ SV410 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1009 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SV1009 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4335]) ).
thf(4804,plain,
! [SV1615: $i,SV1416: $i,SV1010: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1615 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SV1615 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1416 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4336]) ).
thf(4805,plain,
! [SV1668: $i,SV1616: $i,SV1417: $i,SV1011: $i,SV412: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(4806,plain,
! [SV1012: $i,SV413: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV413 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4338]) ).
thf(4807,plain,
! [SV1418: $i,SV1013: $i,SV414: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1013 @ SV1418 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
| ~ ( c_HOL_Oord__class_Oless @ SV1013 @ SV1418 @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4339]) ).
thf(4808,plain,
! [SV1419: $i,SV1014: $i,SV415: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1419 @ SV415 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1014 @ SV1419 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(4809,plain,
! [SV1420: $i,SV1015: $i,SV416: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV416 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1420 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1420 @ SV416 ) @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4341]) ).
thf(4810,plain,
! [SV1421: $i,SV1016: $i,SV417: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV417 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1421 @ SV417 ) @ SV417 )
| ~ ( c_HOL_Oord__class_Oless @ SV1016 @ SV1421 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4811,plain,
! [SV419: $i,SV1017: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1017 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1017 @ SV419 ) @ SV419 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4343]) ).
thf(4812,plain,
! [SV1018: $i,SV420: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV420 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1018 @ SV420 ) @ SV420 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1018 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4344]) ).
thf(4813,plain,
! [SV1617: $i,SV1422: $i,SV1019: $i,SV422: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV422 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1422 @ SV422 ) @ SV1617 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1617 @ SV422 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1617 @ SV1422 @ SV422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4814,plain,
! [SV423: $i,SV1020: $i] :
( ( ( c_lessequals @ SV1020 @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1020 @ SV1020 @ SV423 ) @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4815,plain,
! [SV424: $i,SV1021: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1021 @ SV1021 @ SV424 ) @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
= $true )
| ( ( ~ ( c_lessequals @ SV1021 @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4347]) ).
thf(4816,plain,
! [SV1024: $i,SV1423: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV427 @ SV1423 @ tc_nat ) @ SV1024 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV427 @ ( c_HOL_Ominus__class_Ominus @ SV1024 @ SV1423 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4348]) ).
thf(4817,plain,
! [SV1025: $i,SV1424: $i,SV428: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV428 @ ( c_HOL_Ominus__class_Ominus @ SV1424 @ SV1025 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV428 @ SV1025 @ tc_nat ) @ SV1424 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4349]) ).
thf(4818,plain,
! [SV1425: $i,SV1029: $i,SV432: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV432 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4352]) ).
thf(4819,plain,
! [SV1426: $i,SV1030: $i,SV433: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV433 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4820,plain,
! [SV1427: $i,SV1031: $i,SV434: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4821,plain,
! [SV1428: $i,SV1032: $i,SV435: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4355]) ).
thf(4822,plain,
! [SV1429: $i,SV1033: $i,SV436: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1033 @ ( c_Power_Opower__class_Opower @ SV1033 @ SV1429 @ SV436 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1429 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4823,plain,
! [SV1034: $i,SV1430: $i,SV437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV437 @ SV1430 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV437 @ SV1034 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1430 @ SV1034 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4357]) ).
thf(4824,plain,
! [SV1035: $i,SV438: $i,SV1431: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1431 @ SV438 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1431 @ SV1035 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV438 @ SV1035 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4358]) ).
thf(4825,plain,
! [SV439: $i,SV1432: $i,SV1036: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1036 @ SV1432 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1036 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV439 @ SV1432 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4826,plain,
! [SV1618: $i,SV1433: $i,SV1037: $i,SV440: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1037 @ SV1433 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1433 @ SV440 ) @ SV440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4360]) ).
thf(4827,plain,
! [SV1619: $i,SV1434: $i,SV1038: $i,SV441: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1434 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1619 @ SV441 ) @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1619 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4361]) ).
thf(4828,plain,
! [SV1620: $i,SV1435: $i,SV1039: $i,SV442: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1435 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1620 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1435 @ SV1620 @ SV442 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4362]) ).
thf(4829,plain,
! [SV1621: $i,SV1436: $i,SV1040: $i,SV443: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1040 @ SV1436 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SV1621 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SV1436 @ SV1621 @ SV443 ) @ SV443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4830,plain,
! [SV1622: $i,SV1437: $i,SV1041: $i,SV444: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SV1437 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SV1622 @ SV1437 @ SV444 ) @ SV444 )
| ~ ( c_HOL_Oord__class_Oless @ SV1041 @ SV1622 @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4831,plain,
! [SV1623: $i,SV1438: $i,SV1042: $i,SV445: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SV1438 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SV1623 @ SV1438 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1623 @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(4832,plain,
! [SV1439: $i,SV1043: $i,SV446: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4366]) ).
thf(4833,plain,
! [SV1044: $i,SV447: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV447 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(4834,plain,
! [SV1047: $i,SV450: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV450 @ ( c_Suc @ SV1047 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1047 @ SV450 @ tc_nat ) )
= $true )
| ( ( SV450 = SV1047 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4835,plain,
! [SV1049: $i,SV452: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV452 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1049 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV452 @ SV1049 @ tc_nat ) @ SV452 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4369]) ).
thf(4836,plain,
! [SV456: $i,SV1053: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1053 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV456 @ SV1053 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV456 @ SV1053 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4371]) ).
thf(4837,plain,
! [SV1054: $i,SV457: $i,SV1440: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1440 @ SV457 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV457 @ SV1440 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV457 @ SV1054 @ tc_nat ) @ SV1440 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4372]) ).
thf(4838,plain,
! [SV458: $i,SV1055: $i,SV1441: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1441 @ SV1055 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1055 @ SV1441 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV458 @ SV1055 @ tc_nat ) @ SV1441 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(4839,plain,
! [SV1442: $i,SV1056: $i,SV459: $i] :
( ( ( class_Orderings_Opreorder @ SV459 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1056 @ SV1442 @ SV459 )
| ~ ( c_HOL_Oord__class_Oless @ SV1442 @ SV1056 @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4374]) ).
thf(4840,plain,
! [SV460: $i,SV1057: $i,SV1443: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV1057 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV460 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1443 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4375]) ).
thf(4841,plain,
! [SV461: $i,SV1444: $i,SV1058: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SV1444 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1444 @ SV1058 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1444 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4376]) ).
thf(4842,plain,
! [SV1445: $i,SV1059: $i,SV462: $i] :
( ( ( class_Orderings_Opreorder @ SV462 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1059 @ SV1445 @ SV462 )
| ~ ( c_HOL_Oord__class_Oless @ SV1445 @ SV1059 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(4843,plain,
! [SV1446: $i,SV1060: $i,SV463: $i] :
( ( ( class_Orderings_Olinorder @ SV463 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1060 @ SV1446 @ SV463 )
| ~ ( c_HOL_Oord__class_Oless @ SV1446 @ SV1060 @ SV463 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4844,plain,
! [SV1447: $i,SV1061: $i,SV464: $i] :
( ( ( class_Orderings_Oorder @ SV464 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1447 @ SV464 )
| ~ ( c_HOL_Oord__class_Oless @ SV1447 @ SV1061 @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4379]) ).
thf(4845,plain,
! [SV1448: $i,SV1062: $i,SV465: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV465 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
| ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4846,plain,
! [SV1449: $i,SV1063: $i,SV466: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV466 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
| ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4847,plain,
! [SV1450: $i,SV1064: $i,SV467: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV467 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4382]) ).
thf(4848,plain,
! [SV1451: $i,SV1065: $i,SV468: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV468 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
| ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4849,plain,
! [SV1624: $i,SV1452: $i,SV1066: $i,SV469: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV469 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4384]) ).
thf(4850,plain,
! [SV1625: $i,SV1453: $i,SV1067: $i,SV470: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV470 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(4851,plain,
! [SV1454: $i,SV1068: $i,SV471: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4386]) ).
thf(4852,plain,
! [SV1455: $i,SV1069: $i,SV472: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4387]) ).
thf(4853,plain,
! [SV1456: $i,SV1070: $i,SV473: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV473 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
| ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4854,plain,
! [SV1457: $i,SV1071: $i,SV474: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV474 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
| ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4855,plain,
! [SV1458: $i,SV1072: $i,SV475: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV475 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
| ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4390]) ).
thf(4856,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV476 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
| ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(4857,plain,
! [SV1078: $i,SV481: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV481 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1078 @ SV481 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV481 ) @ SV1078 @ SV481 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV481 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4396]) ).
thf(4858,plain,
! [SV482: $i,SV1079: $i] :
( ( ( SV1079
= ( c_HOL_Ozero__class_Ozero @ SV482 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV1079 @ SV1079 @ SV482 )
= ( c_HOL_Oone__class_Oone @ SV482 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV482 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4397]) ).
thf(4859,plain,
! [SV483: $i,SV1080: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1080 @ SV1080 @ SV483 )
= ( c_HOL_Oone__class_Oone @ SV483 ) )
= $true )
| ( ( SV1080
= ( c_HOL_Ozero__class_Ozero @ SV483 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4398]) ).
thf(4860,plain,
! [SV1081: $i,SV484: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV484 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1081 @ SV1081 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
| ( SV1081
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4399]) ).
thf(4861,plain,
! [SV1460: $i,SV1082: $i,SV485: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV485 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1082 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1460 @ SV485 ) @ SV485 )
| ~ ( c_lessequals @ SV1082 @ SV1460 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4400]) ).
thf(4862,plain,
! [SV1461: $i,SV1083: $i,SV486: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV486 )
= $false )
| ( ( ( c_lessequals @ SV1083 @ SV1461 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1083 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1461 @ SV486 ) @ SV486 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4401]) ).
thf(4863,plain,
! [SV1462: $i,SV1084: $i,SV487: $i] :
( ( ( class_SEQ_Obanach @ SV487 )
= $false )
| ( ( ~ ( class_RealVector_Oreal__normed__field @ SV487 )
| ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SV1084 @ SV1462 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SV1084 @ SV487 ) @ ( c_Transcendental_Oexp @ SV1462 @ SV487 ) @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(4864,plain,
! [SV1626: $i,SV1463: $i,SV1085: $i,SV488: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV488 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1085 @ SV1463 @ SV488 ) @ SV1626 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1085 @ SV1626 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SV1463 @ SV1626 @ SV488 ) @ SV488 ) )
| ( SV1463
= ( c_HOL_Ozero__class_Ozero @ SV488 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4403]) ).
thf(4865,plain,
! [SV1669: $i,SV1627: $i,SV1464: $i,SV1086: $i,SV489: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
| ~ ( c_lessequals @ SV1464 @ SV1669 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4404]) ).
thf(4866,plain,
! [SV1670: $i,SV1628: $i,SV1465: $i,SV1087: $i,SV490: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
| ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SV1465 @ SV1670 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4405]) ).
thf(4867,plain,
! [SV1629: $i,SV1466: $i,SV1088: $i,SV491: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1466 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1629 @ SV491 ) @ SV491 )
| ~ ( c_lessequals @ SV1466 @ SV1629 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4868,plain,
! [SV1630: $i,SV1467: $i,SV1089: $i,SV492: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV492 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SV1630 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1630 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
| ~ ( c_lessequals @ SV1630 @ SV1467 @ tc_nat )
| ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4407]) ).
thf(4869,plain,
! [SV1090: $i,SV1468: $i,SV493: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1468 @ SV1090 @ tc_nat )
| ~ ( c_lessequals @ SV1468 @ SV493 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4408]) ).
thf(4870,plain,
! [SV1091: $i,SV1469: $i,SV494: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1091 @ SV1469 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4409]) ).
thf(4871,plain,
! [SV495: $i,SV1092: $i,SV1470: $i] :
( ( ( c_lessequals @ SV1470 @ SV1092 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV495 @ ( c_HOL_Ominus__class_Ominus @ SV1092 @ SV1470 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV495 @ SV1092 @ tc_nat ) @ SV1470 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4872,plain,
! [SV1471: $i,SV496: $i,SV1093: $i] :
( ( ( c_lessequals @ SV1093 @ SV496 @ tc_nat )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV496 @ SV1093 @ tc_nat ) @ SV1471 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV496 @ SV1471 @ tc_nat ) @ SV1093 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4873,plain,
! [SV501: $i,SV1098: $i,SV1472: $i] :
( ( ( c_lessequals @ SV1472 @ SV1098 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV501 @ ( c_HOL_Ominus__class_Ominus @ SV1098 @ SV1472 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV501 @ SV1472 @ tc_nat ) @ SV1098 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4416]) ).
thf(4874,plain,
! [SV1099: $i,SV1473: $i,SV502: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV502 @ SV1473 @ tc_nat ) @ SV1099 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV502 @ ( c_HOL_Oplus__class_Oplus @ SV1099 @ SV1473 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4417]) ).
thf(4875,plain,
! [SV1100: $i,SV1474: $i,SV503: $i] :
( ( ( c_lessequals @ SV503 @ ( c_HOL_Oplus__class_Oplus @ SV1474 @ SV1100 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV503 @ SV1100 @ tc_nat ) @ SV1474 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4418]) ).
thf(4876,plain,
! [SV504: $i,SV1101: $i,SV1475: $i] :
( ( ( ~ ( c_lessequals @ SV1475 @ SV1101 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(4877,plain,
! [SV505: $i,SV1476: $i,SV1102: $i] :
( ( ( ~ ( c_lessequals @ SV1102 @ SV1476 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4878,plain,
! [SV509: $i,SV1106: $i,SV1477: $i] :
( ( ( c_lessequals @ SV1477 @ SV1106 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV509 @ SV1106 @ tc_nat ) @ SV1477 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV509 @ ( c_HOL_Ominus__class_Ominus @ SV1106 @ SV1477 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4424]) ).
thf(4879,plain,
! [SV1107: $i,SV510: $i,SV1478: $i] :
( ( ( c_lessequals @ SV1478 @ SV510 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV510 @ SV1107 @ tc_nat ) @ SV1478 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV510 @ SV1478 @ tc_nat ) @ SV1107 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4425]) ).
thf(4880,plain,
! [SV1110: $i,SV1479: $i,SV513: $i] :
( ( ( ~ ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SV1479 @ SV1110 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1110 @ SV1479 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SV1110 @ tc_nat ) @ SV1479 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4428]) ).
thf(4881,plain,
! [SV1111: $i,SV1480: $i,SV514: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SV1480 @ tc_nat ) @ SV1111 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1480 @ SV1111 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SV1111 @ SV1480 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4429]) ).
thf(4882,plain,
! [SV1481: $i,SV515: $i,SV1112: $i] :
( ( ( ~ ( c_lessequals @ SV1112 @ SV515 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV515 @ SV1481 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV1112 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ SV1112 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(4883,plain,
! [SV516: $i,SV1113: $i,SV1482: $i] :
( ( ( c_lessequals @ SV1482 @ SV1113 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV516 @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV1113 @ SV516 @ tc_nat ) @ SV1482 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4431]) ).
thf(4884,plain,
! [SV1114: $i,SV517: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV517 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
| ~ ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4432]) ).
thf(4885,plain,
! [SV1115: $i,SV518: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV518 ) )
= $true )
| ( ( ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4886,plain,
! [SV1116: $i,SV519: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV519 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4434]) ).
thf(4887,plain,
! [SV1117: $i,SV520: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV520 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4888,plain,
! [SV1483: $i,SV1118: $i,SV521: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV521 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1483 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1118 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1483 @ SV521 ) @ SV521 ) )
| ~ ( c_lessequals @ SV1483 @ SV1118 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4436]) ).
thf(4889,plain,
! [SV1631: $i,SV1484: $i,SV1119: $i,SV522: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV522 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(4890,plain,
! [SV1632: $i,SV1485: $i,SV1120: $i,SV523: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV523 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1485 @ SV1632 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4438]) ).
thf(4891,plain,
! [SV1633: $i,SV1486: $i,SV1121: $i,SV524: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV524 ) )
= $true )
| ( ( ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4439]) ).
thf(4892,plain,
! [SV1634: $i,SV1487: $i,SV1122: $i,SV525: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV525 ) )
= $true )
| ( ( ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(4893,plain,
! [SV1635: $i,SV1488: $i,SV1123: $i,SV526: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV526 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SV1635 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1635 @ SV526 ) @ SV526 ) )
| ~ ( c_lessequals @ SV1635 @ SV1488 @ tc_nat )
| ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4441]) ).
thf(4894,plain,
! [SV1489: $i,SV1125: $i,SV528: $i] :
( ( ( class_Orderings_Olinorder @ SV528 )
= $false )
| ( ( ( c_lessequals @ SV1125 @ SV1489 @ SV528 )
| ( c_lessequals @ SV1489 @ SV1125 @ SV528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4442]) ).
thf(4895,plain,
! [SV1636: $i,SV1490: $i,SV1126: $i,SV529: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV529 ) )
= $true )
| ( ( ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
| ~ ( c_lessequals @ SV1126 @ SV1636 @ SV529 )
| ~ ( c_lessequals @ SV1636 @ SV1490 @ SV529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(4896,plain,
! [SV1637: $i,SV1491: $i,SV1127: $i,SV530: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV530 ) )
= $true )
| ( ( ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1637 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1127 @ SV1637 @ SV530 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(4897,plain,
! [SV532: $i,SV1128: $i,SV1492: $i] :
( ( ( ~ ( c_lessequals @ SV1492 @ SV1128 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV532 @ SV1492 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV532 @ SV1128 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(4898,plain,
! [SV1493: $i,SV1131: $i,SV536: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV536 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SV1131 @ SV1493 @ SV536 ) @ SV536 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SV1131 @ SV536 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(4899,plain,
! [SV1638: $i,SV1494: $i,SV1133: $i,SV538: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV538 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
| ~ ( c_lessequals @ SV1494 @ SV1638 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4450]) ).
thf(4900,plain,
! [SV1495: $i,SV1136: $i,SV541: $i] :
( ( ( class_Orderings_Oorder @ SV541 )
= $false )
| ( ( ( SV1136 = SV1495 )
| ~ ( c_lessequals @ SV1136 @ SV1495 @ SV541 )
| ~ ( c_lessequals @ SV1495 @ SV1136 @ SV541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4453]) ).
thf(4901,plain,
! [SV542: $i,SV1137: $i] :
( ( ( c_lessequals @ SV1137 @ SV542 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV542 @ SV1137 @ tc_nat ) )
= $true )
| ( ( SV542 = SV1137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4454]) ).
thf(4902,plain,
! [SV1496: $i,SV1138: $i,SV543: $i] :
( ( ( class_Orderings_Oorder @ SV543 )
= $false )
| ( ( ( SV1138 = SV1496 )
| ~ ( c_lessequals @ SV1496 @ SV1138 @ SV543 )
| ~ ( c_lessequals @ SV1138 @ SV1496 @ SV543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4455]) ).
thf(4903,plain,
! [SV1497: $i,SV1139: $i,SV544: $i] :
( ( ( class_Orderings_Oorder @ SV544 )
= $false )
| ( ( ( SV1139 = SV1497 )
| ~ ( c_lessequals @ SV1497 @ SV1139 @ SV544 )
| ~ ( c_lessequals @ SV1139 @ SV1497 @ SV544 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(4904,plain,
! [SV1639: $i,SV1498: $i,SV1140: $i,SV545: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV545 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SV1498 @ SV545 ) @ SV1639 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SV1639 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SV1498 @ SV1639 @ SV545 ) @ SV545 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4457]) ).
thf(4905,plain,
! [SV1640: $i,SV1499: $i,SV1141: $i,SV546: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV546 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1141 @ SV1499 @ SV546 ) @ SV1640 @ SV546 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1141 @ SV1640 @ SV546 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1499 @ SV1640 @ SV546 ) @ SV546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4458]) ).
thf(4906,plain,
! [SV1641: $i,SV1500: $i,SV1142: $i,SV547: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV547 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1142 @ SV1500 @ SV547 ) @ SV1641 @ SV547 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1142 @ SV1641 @ SV547 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1500 @ SV1641 @ SV547 ) @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4459]) ).
thf(4907,plain,
! [SV1501: $i,SV1143: $i,SV548: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV548 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV548 )
| ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SV1143 @ SV1501 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SV1143 @ SV548 ) @ SV1501 @ SV548 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4460]) ).
thf(4908,plain,
! [SV1144: $i,SV1502: $i,SV549: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1502 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ SV1502 @ SV549 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(4909,plain,
! [SV1145: $i,SV1503: $i,SV550: $i] :
( ( ( ~ ( c_lessequals @ SV550 @ SV1503 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1145 @ SV1503 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4462]) ).
thf(4910,plain,
! [SV1146: $i,SV1504: $i,SV551: $i] :
( ( ( c_lessequals @ SV551 @ SV1504 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV551 @ SV1146 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ SV1146 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4463]) ).
thf(4911,plain,
! [SV552: $i,SV1147: $i,SV1505: $i] :
( ( ( c_lessequals @ SV1505 @ SV1147 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1147 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV552 @ SV1505 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(4912,plain,
! [SV555: $i,SV1507: $i,SV1150: $i] :
( ( ( ~ ( c_lessequals @ SV1150 @ SV1507 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1150 @ SV555 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1150 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1507 @ SV1150 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1507 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(4913,plain,
! [SV1642: $i,SV1508: $i,SV1152: $i,SV577: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1508 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1642 @ SV577 ) )
| ( SV1508 = SV1642 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4914,plain,
! [SV1509: $i,SV1153: $i,SV578: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1153 @ SV1509 @ SV578 )
!= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
| ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV578 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4915,plain,
! [SV1510: $i,SV1154: $i,SV579: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV579 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1154 @ SV1510 @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
| ( SV1154 = SV1510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4916,plain,
! [SV1156: $i,SV582: $i] :
( ( ( SV582
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV582
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV582 @ SV1156 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(4917,plain,
! [SV584: $i,SV1158: $i] :
( ( ( SV1158
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1158
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV584 @ SV1158 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(4918,plain,
! [SV1160: $i,SV587: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV587 ) )
= $true )
| ( ( ( c_Transcendental_Oexp @ SV1160 @ SV587 )
!= ( c_HOL_Ozero__class_Ozero @ SV587 ) )
= $true )
| ( ( class_SEQ_Obanach @ SV587 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(4919,plain,
! [SV1671: $i,SV1643: $i,SV1511: $i,SV1161: $i,SV588: $i] :
( ( ! [SY3339: $i] :
( ~ ( class_Divides_Osemiring__div @ SV588 )
| ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SY3339 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SY3339 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4476]) ).
thf(4920,plain,
! [SV1672: $i,SV1644: $i,SV1512: $i,SV1162: $i,SV590: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
| ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4477]) ).
thf(4921,plain,
! [SV1513: $i,SV1165: $i,SV593: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV593 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
| ( SV1165 = SV1513 )
| ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4480]) ).
thf(4922,plain,
! [SV594: $i,SV1166: $i] :
( ( ( SV1166
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV1166
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV594 @ SV1166 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4481]) ).
thf(4923,plain,
! [SV1645: $i,SV1514: $i,SV1167: $i,SV595: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SV1514 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SV1645 @ SV1514 @ SV595 ) )
| ( SV1167 = SV1645 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(4924,plain,
! [SV1673: $i,SV1646: $i,SV1515: $i,SV1168: $i,SV596: $i] :
( ( ! [SY3340: $i] :
( ~ ( class_Divides_Oring__div @ SV596 )
| ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SY3340 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SY3340 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4483]) ).
thf(4925,plain,
! [SV1647: $i,SV1516: $i,SV1170: $i,SV598: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV598 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
| ( SV1170 = SV1647 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4485]) ).
thf(4926,plain,
! [SV1674: $i,SV1648: $i,SV1517: $i,SV1171: $i,SV599: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
| ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SV1674 @ SV1648 @ SV599 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4486]) ).
thf(4927,plain,
! [SV1649: $i,SV1518: $i,SV1173: $i,SV601: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
!= ( c_HOL_Oplus__class_Oplus @ SV1518 @ SV1649 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV1173 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV601 @ SV1649 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4488]) ).
thf(4928,plain,
! [SV1174: $i,SV602: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV602 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
| ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV602 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4489]) ).
thf(4929,plain,
! [SV1650: $i,SV1519: $i,SV1175: $i,SV603: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV603 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SV1519 @ SV1650 @ SV603 ) )
| ( SV1519 = SV1650 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4490]) ).
thf(4930,plain,
! [SV1675: $i,SV1651: $i,SV1520: $i,SV1176: $i,SV604: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV604 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1651 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1675 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SV1651 @ SV604 )
= SV1675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4491]) ).
thf(4931,plain,
! [SV1177: $i,SV605: $i] :
( ( ( SV605
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV605
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV605 @ SV1177 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4492]) ).
thf(4932,plain,
! [SV1521: $i,SV1178: $i,SV606: $i] :
( ( ( class_Divides_Osemiring__div @ SV606 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1178 @ SV1521 @ SV606 )
!= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1521 @ SV1178 @ SV606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4493]) ).
thf(4933,plain,
! [SV1522: $i,SV1179: $i,SV607: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1179 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV607 @ SV1522 @ tc_nat ) )
= $false )
| ( ( SV1179 = SV1522 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4494]) ).
thf(4934,plain,
! [SV1652: $i,SV1523: $i,SV1180: $i,SV608: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1523 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1652 @ SV608 ) )
| ( SV1523 = SV1652 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4495]) ).
thf(4935,plain,
! [SV1676: $i,SV1653: $i,SV1524: $i,SV1181: $i,SV610: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4497]) ).
thf(4936,plain,
! [SV1525: $i,SV1182: $i,SV611: $i] :
( ( ( class_Ring__and__Field_Odivision__ring @ SV611 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
| ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
| ( SV1182 = SV1525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4937,plain,
! [SV612: $i,SV1183: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1183 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
= $true )
| ( ( SV1183
= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV612 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(4938,plain,
! [SV613: $i,SV1184: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV613 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1184 = SV613 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1184 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4500]) ).
thf(4939,plain,
! [SV1654: $i,SV1526: $i,SV1185: $i,SV614: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV614 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SV1526 = SV1654 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(4940,plain,
! [SV1527: $i,SV1187: $i,SV617: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV617 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV617 )
| ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
| ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4504]) ).
thf(4941,plain,
! [SV618: $i,SV1188: $i] :
( ( ( SV1188
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV618
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV618 @ SV1188 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4942,plain,
! [SV1189: $i,SV619: $i] :
( ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1189
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV619 @ SV1189 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4506]) ).
thf(4943,plain,
! [SV1528: $i,SV1190: $i,SV620: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV620 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV620 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SV1190 = SV1528 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(4944,plain,
! [SV622: $i,SV1191: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1191 @ SV1191 @ SV622 )
!= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
= $true )
| ( ( SV1191
= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV622 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4508]) ).
thf(4945,plain,
! [SV623: $i,SV1192: $i] :
( ( ( SV1192
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( SV623
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV623 @ SV1192 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4946,plain,
! [SV1193: $i,SV624: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV624 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(4947,plain,
! [SV1529: $i,SV1194: $i,SV625: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV625 @ SV1194 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1529 @ SV1194 @ tc_nat ) )
= $false )
| ( ( SV625 = SV1529 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(4948,plain,
! [SV1677: $i,SV1655: $i,SV1530: $i,SV1196: $i,SV628: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4513]) ).
thf(4949,plain,
! [SV1531: $i,SV1198: $i,SV630: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV630 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1198 @ SV1531 @ SV630 )
!= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
| ( SV1198 = SV1531 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4515]) ).
thf(4950,plain,
! [SV1532: $i,SV1200: $i,SV632: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
!= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(4951,plain,
! [SV1201: $i,SV633: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV633 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV633 )
| ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4952,plain,
! [SV1656: $i,SV1533: $i,SV1202: $i,SV634: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV634 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV634 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
| ( SV1533 = SV1656 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(4953,plain,
! [SV1534: $i,SV1203: $i,SV635: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1203 @ SV1534 @ tc_nat )
| ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
| ( SV635 = SV1534 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(4954,plain,
! [SV1535: $i,SV1204: $i,SV636: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1204 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV636 @ SV1535 @ tc_nat ) )
= $false )
| ( ( SV1204 = SV1535 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(4955,plain,
! [SV1657: $i,SV1536: $i,SV1205: $i,SV637: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV637 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SV1536 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SV1657 @ SV1657 @ SV637 ) )
| ( SV1205 = SV1536 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4522]) ).
thf(4956,plain,
! [SV1537: $i,SV1206: $i,SV638: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
!= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4957,plain,
! [SV1658: $i,SV1538: $i,SV1207: $i,SV639: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV639 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
| ( SV1207 = SV1658 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4958,plain,
! [SV1208: $i,SV640: $i] :
( ( ( SV640
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1208
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Oplus__class_Oplus @ SV640 @ SV1208 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4959,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(4960,plain,
! [SV1540: $i,SV1211: $i,SV644: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV644 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SV1540 @ SV644 )
!= ( c_HOL_Oone__class_Oone @ SV644 ) )
| ( SV1540
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SV1211 = SV1540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4528]) ).
thf(4961,plain,
! [SV1541: $i,SV1212: $i,SV645: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV645 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV645 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV645 ) )
| ( SV1212 = SV1541 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4529]) ).
thf(4962,plain,
! [SV1542: $i,SV1213: $i,SV646: $i,SV1: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV1 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV646 @ SV1213 @ SV1 ) @ SV1542 @ SV1 )
= ( c_HOL_Oplus__class_Oplus @ SV646 @ ( c_HOL_Oplus__class_Oplus @ SV1213 @ SV1542 @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4530]) ).
thf(4963,plain,
! [SV1543: $i,SV1214: $i,SV647: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV2 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV647 @ ( c_HOL_Oplus__class_Oplus @ SV1214 @ SV1543 @ SV2 ) @ SV2 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV647 @ SV1214 @ SV2 ) @ SV1543 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4531]) ).
thf(4964,plain,
! [SV1544: $i,SV1215: $i,SV648: $i,SV3: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV3 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV648 @ ( c_HOL_Oplus__class_Oplus @ SV1215 @ SV1544 @ SV3 ) @ SV3 )
= ( c_HOL_Oplus__class_Oplus @ SV1215 @ ( c_HOL_Oplus__class_Oplus @ SV648 @ SV1544 @ SV3 ) @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(4965,plain,
! [SV1545: $i,SV1218: $i,SV651: $i,SV6: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV6 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV651 @ SV1218 @ SV6 ) @ SV1545 @ SV6 )
= ( c_HOL_Oplus__class_Oplus @ SV651 @ ( c_HOL_Oplus__class_Oplus @ SV1218 @ SV1545 @ SV6 ) @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4533]) ).
thf(4966,plain,
! [SV1546: $i,SV1219: $i,SV652: $i,SV7: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV7 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV652 @ ( c_HOL_Oplus__class_Oplus @ SV1219 @ SV1546 @ SV7 ) @ SV7 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV652 @ SV1219 @ SV7 ) @ SV1546 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4534]) ).
thf(4967,plain,
! [SV1547: $i,SV1220: $i,SV653: $i,SV8: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV8 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1220 @ SV8 ) @ SV1547 @ SV8 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV653 @ SV1547 @ SV8 ) @ SV1220 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4968,plain,
! [SV1548: $i,SV1221: $i,SV654: $i,SV9: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV9 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV654 @ ( c_HOL_Oplus__class_Oplus @ SV1221 @ SV1548 @ SV9 ) @ SV9 )
= ( c_HOL_Oplus__class_Oplus @ SV1221 @ ( c_HOL_Oplus__class_Oplus @ SV654 @ SV1548 @ SV9 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4536]) ).
thf(4969,plain,
! [SV1549: $i,SV1222: $i,SV655: $i,SV10: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV10 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV655 @ SV1222 @ SV10 ) @ SV1549 @ SV10 )
= ( c_HOL_Oplus__class_Oplus @ SV655 @ ( c_HOL_Oplus__class_Oplus @ SV1222 @ SV1549 @ SV10 ) @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4537]) ).
thf(4970,plain,
! [SV1550: $i,SV1223: $i,SV657: $i,SV13: $i] :
( ( ( class_Divides_Osemiring__div @ SV13 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ SV1223 @ SV13 ) @ SV1550 @ SV13 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV657 @ ( c_Divides_Odiv__class_Omod @ SV1223 @ SV1550 @ SV13 ) @ SV13 ) @ SV1550 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4971,plain,
! [SV1551: $i,SV1224: $i,SV658: $i,SV14: $i] :
( ( ( class_Divides_Osemiring__div @ SV14 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV658 @ SV1224 @ SV14 ) @ SV1551 @ SV14 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV658 @ SV1551 @ SV14 ) @ SV1224 @ SV14 ) @ SV1551 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4972,plain,
! [SV1552: $i,SV1225: $i,SV659: $i,SV15: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4541]) ).
thf(4973,plain,
! [SV1226: $i,SV17: $i,SV661: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV661 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV661 @ SV1226 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4542]) ).
thf(4974,plain,
! [SV662: $i,SV21: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4543]) ).
thf(4975,plain,
! [SV1227: $i,SV663: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4976,plain,
! [SV25: $i,SV1228: $i,SV666: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4545]) ).
thf(4977,plain,
! [SV1553: $i,SV1229: $i,SV667: $i,SV26: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4978,plain,
! [SV668: $i,SV27: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
| ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(4979,plain,
! [SV669: $i,SV28: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
= $false )
| ( ( ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4548]) ).
thf(4980,plain,
! [SV671: $i,SV30: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
| ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4550]) ).
thf(4981,plain,
! [SV672: $i,SV31: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ SV672 @ SV31 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV31 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV672 @ SV31 ) @ SV31 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4551]) ).
thf(4982,plain,
! [SV673: $i,SV32: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4552]) ).
thf(4983,plain,
! [SV674: $i,SV33: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4553]) ).
thf(4984,plain,
! [SV1554: $i,SV1230: $i,SV676: $i,SV35: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV35 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV676 @ ( c_HOL_Oplus__class_Oplus @ SV1230 @ SV1554 @ SV35 ) @ SV35 )
= ( c_HOL_Oplus__class_Oplus @ SV1230 @ ( c_HOL_Oplus__class_Oplus @ SV676 @ SV1554 @ SV35 ) @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4555]) ).
thf(4985,plain,
! [SV1555: $i,SV1231: $i,SV677: $i,SV36: $i] :
( ( ( class_Orderings_Opreorder @ SV36 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4556]) ).
thf(4986,plain,
! [SV1556: $i,SV1232: $i,SV678: $i,SV37: $i] :
( ( ( class_Orderings_Oorder @ SV37 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4987,plain,
! [SV679: $i,SV38: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV679 @ SV38 ) @ SV38 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 )
= $true )
| ( ( SV679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4558]) ).
thf(4988,plain,
! [SV1557: $i,SV1233: $i,SV680: $i,SV39: $i] :
( ( ( class_Divides_Osemiring__div @ SV39 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV680 @ SV1233 @ SV39 ) @ SV1557 @ SV39 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV680 @ SV1557 @ SV39 ) @ ( c_Divides_Odiv__class_Omod @ SV1233 @ SV1557 @ SV39 ) @ SV39 ) @ SV1557 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4559]) ).
thf(4989,plain,
! [SV41: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(4990,plain,
! [SV681: $i,SV42: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV42 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ SV681 @ SV42 ) @ SV42 )
= SV681 )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4991,plain,
! [SV684: $i,SV46: $i] :
( ( ( class_Power_Opower @ SV46 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV46 ) @ ( c_Suc @ SV684 ) @ SV46 )
= ( c_HOL_Ozero__class_Ozero @ SV46 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4992,plain,
! [SV1558: $i,SV1234: $i,SV688: $i,SV50: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
| ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4563]) ).
thf(4993,plain,
! [SV1559: $i,SV1235: $i,SV689: $i,SV51: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
| ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4564]) ).
thf(4994,plain,
! [SV1560: $i,SV1241: $i,SV699: $i,SV61: $i] :
( ( ( class_Divides_Osemiring__div @ SV61 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(4995,plain,
! [SV1561: $i,SV1242: $i,SV700: $i,SV62: $i] :
( ( ( class_Divides_Osemiring__div @ SV62 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4996,plain,
! [SV1562: $i,SV1243: $i,SV701: $i,SV63: $i] :
( ( ( class_Divides_Osemiring__div @ SV63 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4997,plain,
! [SV1563: $i,SV1244: $i,SV702: $i,SV64: $i] :
( ( ( class_Divides_Osemiring__div @ SV64 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4998,plain,
! [SV67: $i,SV705: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV705 @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV705 @ SV705 @ SV67 ) @ ( c_HOL_Ozero__class_Ozero @ SV67 ) @ SV67 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4999,plain,
! [SV68: $i,SV706: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV706 @ SV706 @ SV68 ) @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV706 @ ( c_HOL_Ozero__class_Ozero @ SV68 ) @ SV68 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(5000,plain,
! [SV69: $i,SV707: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV707 @ SV707 @ SV69 ) @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV707 @ ( c_HOL_Ozero__class_Ozero @ SV69 ) @ SV69 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(5001,plain,
! [SV70: $i,SV708: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV708 @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV708 @ SV708 @ SV70 ) @ ( c_HOL_Ozero__class_Ozero @ SV70 ) @ SV70 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4577]) ).
thf(5002,plain,
! [SV72: $i,SV1245: $i,SV709: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $true )
| ( ( ~ ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4578]) ).
thf(5003,plain,
! [SV73: $i,SV1246: $i,SV710: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
| ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(5004,plain,
! [SV711: $i,SV74: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
| ~ ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(5005,plain,
! [SV76: $i,SV1247: $i,SV713: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV713 @ SV1247 @ SV76 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1247 @ SV713 @ SV76 )
| ( SV1247 = SV713 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(5006,plain,
! [SV78: $i,SV715: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV715 @ SV78 @ tc_nat )
= $false )
| ( ( SV715 = SV78 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV78 @ SV715 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(5007,plain,
! [SV79: $i,SV716: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV716 @ SV79 @ tc_nat )
= $false )
| ( ( SV716 = SV79 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV79 @ SV716 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4583]) ).
thf(5008,plain,
! [SV80: $i,SV717: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV717 @ SV80 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV80 @ SV717 @ tc_nat )
= $false )
| ( ( SV80 = SV717 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(5009,plain,
! [SV719: $i,SV82: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV82 @ SV719 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV719 @ SV82 @ tc_nat )
= $false )
| ( ( SV82 = SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(5010,plain,
! [SV83: $i,SV720: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV720 @ SV83 @ tc_nat )
= $false )
| ( ( SV720 = SV83 )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV83 @ SV720 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(5011,plain,
! [SV721: $i,SV84: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV84 @ SV721 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV721 @ SV84 @ tc_nat )
= $false )
| ( ( SV84 = SV721 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4587]) ).
thf(5012,plain,
! [SV722: $i,SV85: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV85 @ SV722 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV722 @ SV85 @ tc_nat )
= $false )
| ( ( SV85 = SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(5013,plain,
! [SV86: $i,SV1248: $i,SV723: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV723 @ SV1248 @ SV86 )
= $true )
| ( ( ( SV1248 = SV723 )
| ( c_HOL_Oord__class_Oless @ SV1248 @ SV723 @ SV86 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4589]) ).
thf(5014,plain,
! [SV87: $i,SV1249: $i,SV724: $i] :
( ( ( SV724 = SV1249 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV724 @ SV1249 @ SV87 )
| ( c_HOL_Oord__class_Oless @ SV1249 @ SV724 @ SV87 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4590]) ).
thf(5015,plain,
! [SV88: $i,SV1250: $i,SV725: $i] :
( ( ( SV725 = SV1250 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1250 @ SV725 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SV1250 @ SV88 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4591]) ).
thf(5016,plain,
! [SV89: $i,SV1251: $i,SV726: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV726 @ SV1251 @ SV89 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1251 @ SV726 @ SV89 )
| ( SV1251 = SV726 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4592]) ).
thf(5017,plain,
! [SV98: $i,SV735: $i,SV1260: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1260 @ SV735 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV1260 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV735 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(5018,plain,
! [SV99: $i,SV736: $i,SV1261: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(5019,plain,
! [SV100: $i,SV737: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV737 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV100 @ SV737 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV100 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4603]) ).
thf(5020,plain,
! [SV1564: $i,SV1262: $i,SV739: $i,SV103: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4604]) ).
thf(5021,plain,
! [SV104: $i,SV740: $i,SV1263: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV740 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV104 @ SV1263 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SV740 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4605]) ).
thf(5022,plain,
! [SV742: $i,SV108: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4606]) ).
thf(5023,plain,
! [SV743: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV109 )
| ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4607]) ).
thf(5024,plain,
! [SV744: $i,SV110: $i] :
( ( ( class_Power_Opower @ SV110 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV744 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
| ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(5025,plain,
! [SV1565: $i,SV1266: $i,SV747: $i,SV113: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4611]) ).
thf(5026,plain,
! [SV114: $i,SV748: $i] :
( ( ( SV748
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV748 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4612]) ).
thf(5027,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV116 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4613]) ).
thf(5028,plain,
! [SV1268: $i,SV751: $i,SV117: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV117 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(5029,plain,
! [SV1269: $i,SV752: $i,SV118: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV118 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4615]) ).
thf(5030,plain,
! [SV1270: $i,SV753: $i,SV119: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV119 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4616]) ).
thf(5031,plain,
! [SV1271: $i,SV754: $i,SV120: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV120 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(5032,plain,
! [SV1272: $i,SV755: $i,SV121: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV121 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4618]) ).
thf(5033,plain,
! [SV1273: $i,SV756: $i,SV122: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV122 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4619]) ).
thf(5034,plain,
! [SV762: $i,SV129: $i] :
( ( ( class_Int_Onumber__ring @ SV129 )
= $false )
| ( ( SV762
= ( c_HOL_Oplus__class_Oplus @ SV762 @ ( c_HOL_Ozero__class_Ozero @ SV129 ) @ SV129 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(5035,plain,
! [SV767: $i,SV1274: $i,SV137: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV1274 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV767 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SV767 @ SV1274 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(5036,plain,
! [SV768: $i,SV1275: $i,SV138: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SV1275 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1275 @ SV138 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SV768 @ SV1275 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(5037,plain,
! [SV1276: $i,SV769: $i,SV139: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SV769 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV769 @ SV139 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SV769 @ SV1276 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(5038,plain,
! [SV770: $i,SV1277: $i,SV140: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV1277 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV770 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SV770 @ SV1277 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(5039,plain,
! [SV771: $i,SV1278: $i,SV141: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV1278 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV771 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SV771 @ SV1278 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4625]) ).
thf(5040,plain,
! [SV778: $i,SV1279: $i,SV148: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV1279 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV778 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SV778 @ SV1279 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(5041,plain,
! [SV779: $i,SV1280: $i,SV149: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV1280 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV779 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SV779 @ SV1280 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(5042,plain,
! [SV780: $i,SV1281: $i,SV150: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV1281 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV780 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SV780 @ SV1281 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(5043,plain,
! [SV1659: $i,SV1566: $i,SV1282: $i,SV781: $i,SV151: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SV1282 @ SV1659 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4629]) ).
thf(5044,plain,
! [SV1660: $i,SV1567: $i,SV1283: $i,SV782: $i,SV152: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4630]) ).
thf(5045,plain,
! [SV786: $i,SV1284: $i,SV156: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(5046,plain,
! [SV787: $i,SV157: $i,SV1285: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(5047,plain,
! [SV1568: $i,SV1286: $i,SV788: $i,SV158: $i] :
( ( ( class_Orderings_Oorder @ SV158 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
| ~ ( c_lessequals @ SV788 @ SV1568 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(5048,plain,
! [SV1569: $i,SV1287: $i,SV789: $i,SV159: $i] :
( ( ( class_Orderings_Oorder @ SV159 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
| ~ ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 )
| ~ ( c_lessequals @ SV1569 @ SV1287 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(5049,plain,
! [SV1661: $i,SV1570: $i,SV1288: $i,SV790: $i,SV160: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV160 ) )
= $true )
| ( ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SV1661 @ SV1570 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(5050,plain,
! [SV1571: $i,SV1289: $i,SV791: $i,SV161: $i] :
( ( ( class_Orderings_Opreorder @ SV161 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
| ~ ( c_lessequals @ SV1571 @ SV1289 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4636]) ).
thf(5051,plain,
! [SV1572: $i,SV1290: $i,SV792: $i,SV162: $i] :
( ( ( class_Orderings_Opreorder @ SV162 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
| ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 )
| ~ ( c_lessequals @ SV792 @ SV1572 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(5052,plain,
! [SV163: $i,SV1291: $i,SV793: $i] :
( ( ( c_lessequals @ SV793 @ SV1291 @ SV163 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV793 @ SV1291 @ SV163 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(5053,plain,
! [SV164: $i,SV1292: $i,SV794: $i] :
( ( ( c_lessequals @ SV794 @ SV1292 @ SV164 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV794 @ SV1292 @ SV164 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4639]) ).
thf(5054,plain,
! [SV165: $i,SV1293: $i,SV795: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1293 @ SV165 )
= $true )
| ( ( ( c_lessequals @ SV1293 @ SV795 @ SV165 )
| ~ ( c_lessequals @ SV795 @ SV1293 @ SV165 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(5055,plain,
! [SV1662: $i,SV1573: $i,SV1294: $i,SV796: $i,SV166: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SV1294 @ SV1662 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(5056,plain,
! [SV167: $i,SV1295: $i,SV797: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1295 @ SV167 )
= $true )
| ( ( ( SV1295 = SV797 )
| ~ ( c_lessequals @ SV797 @ SV1295 @ SV167 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(5057,plain,
! [SV168: $i,SV1296: $i,SV798: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV798 @ SV1296 @ SV168 )
= $true )
| ( ( ~ ( c_lessequals @ SV798 @ SV1296 @ SV168 )
| ( SV1296 = SV798 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(5058,plain,
! [SV169: $i,SV1297: $i,SV799: $i] :
( ( ( SV799 = SV1297 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1297 @ SV169 )
| ~ ( c_lessequals @ SV799 @ SV1297 @ SV169 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4644]) ).
thf(5059,plain,
! [SV170: $i,SV1298: $i,SV800: $i] :
( ( ( SV800 = SV1298 )
= $true )
| ( ( ~ ( c_lessequals @ SV800 @ SV1298 @ SV170 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1298 @ SV170 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4645]) ).
thf(5060,plain,
! [SV171: $i,SV1299: $i,SV801: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV801 @ SV1299 @ SV171 )
= $true )
| ( ( ~ ( c_lessequals @ SV801 @ SV1299 @ SV171 )
| ( SV801 = SV1299 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4646]) ).
thf(5061,plain,
! [SV172: $i,SV1300: $i,SV802: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV802 @ SV1300 @ SV172 )
= $true )
| ( ( ( SV802 = SV1300 )
| ~ ( c_lessequals @ SV802 @ SV1300 @ SV172 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(5062,plain,
! [SV173: $i,SV1301: $i,SV803: $i] :
( ( ( SV803 = SV1301 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV803 @ SV1301 @ SV173 )
| ~ ( c_lessequals @ SV803 @ SV1301 @ SV173 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(5063,plain,
! [SV174: $i,SV1302: $i,SV804: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1302 @ SV174 )
= $true )
| ( ( ( SV804 = SV1302 )
| ~ ( c_lessequals @ SV804 @ SV1302 @ SV174 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(5064,plain,
! [SV1574: $i,SV1303: $i,SV805: $i,SV175: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SV1303 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1574 @ SV1303 @ SV175 ) @ SV175 )
| ~ ( c_lessequals @ SV805 @ SV1574 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4650]) ).
thf(5065,plain,
! [SV1575: $i,SV1304: $i,SV806: $i,SV176: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
= $false )
| ( ( ( c_lessequals @ SV806 @ SV1304 @ SV176 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1575 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SV1304 @ SV1575 @ SV176 ) @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(5066,plain,
! [SV1576: $i,SV1305: $i,SV807: $i,SV177: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1305 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1576 @ SV177 ) @ SV177 )
| ~ ( c_lessequals @ SV1305 @ SV1576 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4652]) ).
thf(5067,plain,
! [SV1577: $i,SV1306: $i,SV808: $i,SV178: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
= $false )
| ( ( ( c_lessequals @ SV808 @ SV1306 @ SV178 )
| ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV1306 @ SV178 ) @ SV178 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(5068,plain,
! [SV1578: $i,SV1307: $i,SV809: $i,SV179: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SV1307 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SV1578 @ SV1307 @ SV179 ) @ SV179 )
| ~ ( c_lessequals @ SV809 @ SV1578 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(5069,plain,
! [SV1579: $i,SV1308: $i,SV810: $i,SV180: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1308 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1579 @ SV180 ) @ SV180 )
| ~ ( c_lessequals @ SV1308 @ SV1579 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(5070,plain,
! [SV181: $i,SV1309: $i,SV811: $i] :
( ( ( ~ ( c_lessequals @ SV811 @ SV1309 @ SV181 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1309 @ SV811 @ SV181 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(5071,plain,
! [SV182: $i,SV1310: $i,SV812: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV812 @ SV1310 @ SV182 )
= $true )
| ( ( c_lessequals @ SV1310 @ SV812 @ SV182 )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(5072,plain,
! [SV183: $i,SV813: $i] :
( ( ( c_lessequals @ SV813 @ SV813 @ SV183 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV813 @ SV813 @ SV183 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4658]) ).
thf(5073,plain,
! [SV185: $i,SV1311: $i,SV815: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV815 @ SV1311 @ SV185 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1311 @ SV815 @ SV185 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(5074,plain,
! [SV186: $i,SV1312: $i,SV816: $i] :
( ( ( c_lessequals @ SV816 @ SV1312 @ SV186 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1312 @ SV816 @ SV186 )
= $true )
| ( ( class_Orderings_Olinorder @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(5075,plain,
! [SV187: $i,SV1313: $i,SV817: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV817 @ SV1313 @ SV187 )
= $true )
| ( ( c_lessequals @ SV1313 @ SV817 @ SV187 )
= $true )
| ( ( class_Orderings_Olinorder @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4662]) ).
thf(5076,plain,
! [SV188: $i,SV1314: $i,SV818: $i] :
( ( ( ~ ( c_lessequals @ SV818 @ SV1314 @ SV188 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1314 @ SV818 @ SV188 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(5077,plain,
! [SV819: $i,SV189: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
| ~ ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4664]) ).
thf(5078,plain,
! [SV820: $i,SV190: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
| ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4665]) ).
thf(5079,plain,
! [SV1580: $i,SV1315: $i,SV821: $i,SV191: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false )
| ( ( ( c_lessequals @ SV821 @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4666]) ).
thf(5080,plain,
! [SV1581: $i,SV1316: $i,SV823: $i,SV193: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(5081,plain,
! [SV1663: $i,SV1582: $i,SV1317: $i,SV824: $i,SV194: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV194 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4669]) ).
thf(5082,plain,
! [SV1318: $i,SV825: $i,SV195: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
| ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(5083,plain,
! [SV1319: $i,SV826: $i,SV196: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(5084,plain,
! [SV1664: $i,SV1583: $i,SV1320: $i,SV827: $i,SV197: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV197 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4672]) ).
thf(5085,plain,
! [SV198: $i,SV1321: $i,SV828: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 )
| ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4673]) ).
thf(5086,plain,
! [SV199: $i,SV1322: $i,SV829: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(5087,plain,
! [SV1665: $i,SV1584: $i,SV1323: $i,SV830: $i,SV200: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV200 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(5088,plain,
! [SV1585: $i,SV1324: $i,SV831: $i,SV201: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
| ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4676]) ).
thf(5089,plain,
! [SV1586: $i,SV1325: $i,SV832: $i,SV202: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
| ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4677]) ).
thf(5090,plain,
! [SV1587: $i,SV1326: $i,SV833: $i,SV203: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(5091,plain,
! [SV1588: $i,SV1327: $i,SV834: $i,SV204: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(5092,plain,
! [SV1589: $i,SV1328: $i,SV836: $i,SV208: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV208 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
| ~ ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(5093,plain,
! [SV1590: $i,SV1329: $i,SV837: $i,SV209: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV209 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(5094,plain,
! [SV1591: $i,SV1330: $i,SV838: $i,SV210: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV210 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4683]) ).
thf(5095,plain,
! [SV1592: $i,SV1331: $i,SV839: $i,SV211: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV211 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(5096,plain,
! [SV1332: $i,SV840: $i,SV212: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV840 @ ( c_Suc @ SV1332 ) @ SV212 ) @ SV212 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SV840 @ SV212 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4685]) ).
thf(5097,plain,
! [SV1333: $i,SV841: $i,SV213: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV213 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4686]) ).
thf(5098,plain,
! [SV1593: $i,SV1335: $i,SV847: $i,SV222: $i] :
( ( ( class_Divides_Osemiring__div @ SV222 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ ( c_Divides_Odiv__class_Omod @ SV1335 @ SV1593 @ SV222 ) @ SV222 ) @ SV1593 @ SV222 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV847 @ SV1335 @ SV222 ) @ SV1593 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(5099,plain,
! [SV1594: $i,SV1336: $i,SV848: $i,SV223: $i] :
( ( ( class_Divides_Osemiring__div @ SV223 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ ( c_Divides_Odiv__class_Omod @ SV848 @ SV1336 @ SV223 ) @ SV1594 @ SV223 ) @ SV1336 @ SV223 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV848 @ SV1594 @ SV223 ) @ SV1336 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4690]) ).
thf(5100,plain,
! [SV851: $i,SV226: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ ( c_HOL_Oplus__class_Oplus @ SV851 @ SV851 @ SV226 ) @ SV226 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV226 ) @ SV851 @ SV226 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(5101,plain,
! [SV852: $i,SV227: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ SV852 @ SV227 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV227 ) @ ( c_HOL_Oplus__class_Oplus @ SV852 @ SV852 @ SV227 ) @ SV227 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(5102,plain,
! [SV853: $i,SV228: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
| ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(5103,plain,
! [SV1595: $i,SV1337: $i,SV855: $i,SV231: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(5104,plain,
! [SV1596: $i,SV1338: $i,SV856: $i,SV232: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(5105,plain,
! [SV1597: $i,SV1339: $i,SV857: $i,SV233: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(5106,plain,
! [SV1598: $i,SV1340: $i,SV858: $i,SV234: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(5107,plain,
! [SV1341: $i,SV863: $i,SV240: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(5108,plain,
! [SV1342: $i,SV864: $i,SV241: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4700]) ).
thf(5109,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV242 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(5110,plain,
! [SV1344: $i,SV866: $i,SV243: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV243 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5111,plain,
! [SV867: $i,SV244: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(5112,plain,
! [SV1599: $i,SV1345: $i,SV868: $i,SV245: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4704]) ).
thf(5113,plain,
! [SV1666: $i,SV1600: $i,SV1346: $i,SV869: $i,SV246: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1346 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV1666 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1600 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1346 @ SV1666 @ SV246 ) @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4705]) ).
thf(5114,plain,
! [SV1601: $i,SV1347: $i,SV870: $i,SV247: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV247 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(5115,plain,
! [SV1602: $i,SV1348: $i,SV871: $i,SV248: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV248 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(5116,plain,
! [SV1349: $i,SV872: $i,SV249: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4708]) ).
thf(5117,plain,
! [SV1350: $i,SV873: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4709]) ).
thf(5118,plain,
! [SV251: $i,SV1351: $i,SV874: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV874 @ SV1351 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1351 @ SV874 @ SV251 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4710]) ).
thf(5119,plain,
! [SV875: $i,SV252: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV875 @ SV252 )
= $false )
| ( ( SV875
= ( c_HOL_Ozero__class_Ozero @ SV252 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(5120,plain,
! [SV879: $i,SV1352: $i,SV257: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
| ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4713]) ).
thf(5121,plain,
! [SV259: $i,SV881: $i] :
( ( ( SV881
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV881 @ SV259 ) @ SV259 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV881 @ SV259 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4714]) ).
thf(5122,plain,
! [SV262: $i,SV1353: $i,SV882: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(5123,plain,
! [SV263: $i,SV1354: $i,SV883: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(5124,plain,
! [SV1355: $i,SV264: $i,SV884: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(5125,plain,
! [SV265: $i,SV1356: $i,SV885: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(5126,plain,
! [SV1357: $i,SV266: $i,SV886: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
| ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(5127,plain,
! [SV1358: $i,SV887: $i,SV267: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4720]) ).
thf(5128,plain,
! [SV891: $i,SV273: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(5129,plain,
! [SV892: $i,SV274: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4723]) ).
thf(5130,plain,
! [SV893: $i,SV275: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ ( c_HOL_Oplus__class_Oplus @ SV893 @ SV893 @ SV275 ) @ SV275 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV275 ) @ SV893 @ SV275 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV275 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4724]) ).
thf(5131,plain,
! [SV894: $i,SV276: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ SV894 @ SV276 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV276 ) @ ( c_HOL_Oplus__class_Oplus @ SV894 @ SV894 @ SV276 ) @ SV276 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV276 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(5132,plain,
! [SV1603: $i,SV1360: $i,SV896: $i,SV280: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
| ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(5133,plain,
! [SV1604: $i,SV1361: $i,SV899: $i,SV284: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(5134,plain,
! [SV291: $i,SV1365: $i,SV906: $i] :
( ( ( c_lessequals @ SV906 @ SV1365 @ SV291 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(5135,plain,
! [SV1366: $i,SV292: $i,SV907: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 )
| ~ ( c_lessequals @ SV1366 @ SV907 @ SV292 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4733]) ).
thf(5136,plain,
! [SV293: $i,SV1367: $i,SV908: $i] :
( ( ( c_lessequals @ SV908 @ SV1367 @ SV293 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4734]) ).
thf(5137,plain,
! [SV1368: $i,SV294: $i,SV909: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
| ~ ( c_lessequals @ SV1368 @ SV909 @ SV294 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4735]) ).
thf(5138,plain,
! [SV910: $i,SV296: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4737]) ).
thf(5139,plain,
! [SV911: $i,SV297: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4738]) ).
thf(5140,plain,
! [SV912: $i,SV298: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
| ~ ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4739]) ).
thf(5141,plain,
! [SV913: $i,SV299: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4740]) ).
thf(5142,plain,
! [SV300: $i,SV1369: $i,SV914: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV914 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV914 @ SV1369 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1369 @ SV300 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4741]) ).
thf(5143,plain,
! [SV301: $i,SV1370: $i,SV915: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV915 @ SV1370 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SV1370 @ SV301 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV915 @ SV1370 @ SV301 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV301 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(5144,plain,
! [SV1605: $i,SV1371: $i,SV917: $i,SV303: $i] :
( ( ( class_Divides_Oring__div @ SV303 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ SV1371 @ SV303 ) @ SV1605 @ SV303 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV917 @ ( c_Divides_Odiv__class_Omod @ SV1371 @ SV1605 @ SV303 ) @ SV303 ) @ SV1605 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4744]) ).
thf(5145,plain,
! [SV1606: $i,SV1372: $i,SV918: $i,SV304: $i] :
( ( ( class_Divides_Oring__div @ SV304 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV918 @ SV1372 @ SV304 ) @ SV1606 @ SV304 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV918 @ SV1606 @ SV304 ) @ SV1372 @ SV304 ) @ SV1606 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4745]) ).
thf(5146,plain,
! [SV1607: $i,SV1373: $i,SV919: $i,SV305: $i] :
( ( ( class_Divides_Oring__div @ SV305 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV919 @ SV1373 @ SV305 ) @ SV1607 @ SV305 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ ( c_Divides_Odiv__class_Omod @ SV919 @ SV1607 @ SV305 ) @ ( c_Divides_Odiv__class_Omod @ SV1373 @ SV1607 @ SV305 ) @ SV305 ) @ SV1607 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4746]) ).
thf(5147,plain,
! [SV1608: $i,SV1374: $i,SV920: $i,SV306: $i] :
( ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4747]) ).
thf(5148,plain,
! [SV925: $i,SV311: $i] :
( ( ( class_Int_Onumber__ring @ SV311 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV925 @ SV925 @ SV311 )
= ( c_HOL_Ozero__class_Ozero @ SV311 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4748]) ).
thf(5149,plain,
! [SV1667: $i,SV1609: $i,SV1376: $i,SV927: $i,SV313: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV313 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV927 @ SV1376 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SV1609 @ SV1667 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV927 @ SV1609 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SV1376 @ SV1667 @ SV313 ) @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(5150,plain,
! [SV1378: $i,SV929: $i,SV315: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV315 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV929 @ SV1378 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV929 @ SV315 ) @ SV1378 @ SV315 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(5151,plain,
! [SV1610: $i,SV1379: $i,SV930: $i,SV316: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SV1379 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SV1610 @ SV1379 @ SV316 ) @ SV316 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SV1610 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4753]) ).
thf(5152,plain,
! [SV931: $i,SV317: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV317 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV317 )
= ( c_HOL_Oinverse__class_Odivide @ SV931 @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV317 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4754]) ).
thf(5153,plain,
! [SV1380: $i,SV932: $i,SV319: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV319 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV932 @ SV1380 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SV1380 @ SV932 @ SV319 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(5154,plain,
! [SV934: $i,SV321: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV321 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV934 @ ( c_HOL_Ozero__class_Ozero @ SV321 ) @ SV321 )
= ( c_HOL_Ozero__class_Ozero @ SV321 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4757]) ).
thf(5155,plain,
! [SV935: $i,SV322: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV322 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV935 @ ( c_HOL_Ozero__class_Ozero @ SV322 ) @ SV322 )
= ( c_HOL_Ozero__class_Ozero @ SV322 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4758]) ).
thf(5156,plain,
! [SV1611: $i,SV1381: $i,SV937: $i,SV324: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV324 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV937 @ SV1381 @ SV324 ) @ SV1611 @ SV324 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV937 @ SV1611 @ SV324 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1381 @ SV1611 @ SV324 ) @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(5157,plain,
! [SV1612: $i,SV1382: $i,SV938: $i,SV325: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV325 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV938 @ SV1382 @ SV325 ) @ SV1612 @ SV325 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ SV938 @ SV1612 @ SV325 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1382 @ SV1612 @ SV325 ) @ SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(5158,plain,
! [SV1383: $i,SV337: $i,SV1613: $i,SV949: $i] :
( ( ( ~ ( c_lessequals @ SV949 @ SV1613 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV337 @ SV1383 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1383 @ SV1613 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5159,plain,
! [SV970: $i,SV361: $i,SV1396: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1396 @ SV361 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1396 @ SV970 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV970 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV1396 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4779]) ).
thf(5160,plain,
! [SV974: $i,SV1400: $i,SV365: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV1400 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV974 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SV974 @ SV1400 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4780]) ).
thf(5161,plain,
! [SV978: $i,SV373: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
= $false )
| ( ( ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(5162,plain,
! [SV979: $i,SV375: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(5163,plain,
! [SV376: $i,SV1402: $i,SV980: $i] :
( ( ( c_lessequals @ SV980 @ SV1402 @ SV376 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV980 @ SV1402 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(5164,plain,
! [SV377: $i,SV1403: $i,SV981: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV981 @ SV1403 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
= $true )
| ( ( ~ ( c_lessequals @ SV981 @ SV1403 @ SV377 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(5165,plain,
! [SV1404: $i,SV982: $i,SV378: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SV982 @ SV1404 @ SV378 ) @ SV378 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SV982 @ SV378 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4785]) ).
thf(5166,plain,
! [SV1405: $i,SV983: $i,SV379: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SV983 @ SV1405 @ SV379 ) @ SV379 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SV983 @ SV379 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV379 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(5167,plain,
! [SV1614: $i,SV1406: $i,SV984: $i,SV380: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV380 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
| ~ ( c_lessequals @ SV984 @ SV1614 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4787]) ).
thf(5168,plain,
! [SV1407: $i,SV381: $i,SV985: $i] :
( ( ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
= $true )
| ( ( ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SV1407 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4788]) ).
thf(5169,plain,
! [SV1408: $i,SV986: $i,SV382: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV382 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(5170,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV383 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4790]) ).
thf(5171,plain,
! [SV1410: $i,SV988: $i,SV384: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SV988 @ SV1410 @ SV384 ) @ SV384 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SV988 @ SV384 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV384 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(5172,plain,
! [SV388: $i,SV1411: $i,SV991: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV991 @ SV1411 @ SV388 ) @ SV388 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV991 @ SV388 ) @ SV1411 @ SV388 ) )
= $true )
| ( ( SV991
= ( c_HOL_Ozero__class_Ozero @ SV388 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(5173,plain,
! [SV1415: $i,SV1005: $i,SV406: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(5174,plain,
! [SV1006: $i,SV407: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(5175,plain,
! [SV1007: $i,SV408: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
| ~ ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4801]) ).
thf(5176,plain,
! [SV409: $i,SV1008: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1008 @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1008 @ SV409 ) @ ( c_HOL_Ozero__class_Ozero @ SV409 ) @ SV409 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV409 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4802]) ).
thf(5177,plain,
! [SV410: $i,SV1009: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV410 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1009 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SV1009 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(5178,plain,
! [SV1416: $i,SV411: $i,SV1615: $i,SV1010: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1010 @ SV1615 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1416 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1615 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4804]) ).
thf(5179,plain,
! [SV1668: $i,SV1616: $i,SV1417: $i,SV1011: $i,SV412: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4805]) ).
thf(5180,plain,
! [SV1012: $i,SV413: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(5181,plain,
! [SV414: $i,SV1418: $i,SV1013: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1013 @ SV1418 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1013 @ SV1418 @ SV414 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4807]) ).
thf(5182,plain,
! [SV415: $i,SV1419: $i,SV1014: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1419 @ SV415 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1014 @ SV1419 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4808]) ).
thf(5183,plain,
! [SV416: $i,SV1420: $i,SV1015: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1420 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1420 @ SV416 ) @ SV416 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4809]) ).
thf(5184,plain,
! [SV1421: $i,SV417: $i,SV1016: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1421 @ SV417 ) @ SV417 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1016 @ SV1421 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV417 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5185,plain,
! [SV1017: $i,SV419: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1017 @ SV419 ) @ SV419 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1017 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4811]) ).
thf(5186,plain,
! [SV420: $i,SV1018: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1018 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV420 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1018 @ SV420 ) @ SV420 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(5187,plain,
! [SV1617: $i,SV1422: $i,SV1019: $i,SV422: $i] :
( ( ( class_Divides_Osemiring__div @ SV422 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1422 @ SV422 ) @ SV1617 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1617 @ SV422 ) )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1617 @ SV1422 @ SV422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(5188,plain,
! [SV423: $i,SV1020: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1020 @ SV1020 @ SV423 ) @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
= $false )
| ( ( c_lessequals @ SV1020 @ ( c_HOL_Ozero__class_Ozero @ SV423 ) @ SV423 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4814]) ).
thf(5189,plain,
! [SV424: $i,SV1021: $i] :
( ( ( c_lessequals @ SV1021 @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1021 @ SV1021 @ SV424 ) @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV424 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4815]) ).
thf(5190,plain,
! [SV432: $i,SV1425: $i,SV1029: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 )
| ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4818]) ).
thf(5191,plain,
! [SV433: $i,SV1426: $i,SV1030: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4819]) ).
thf(5192,plain,
! [SV1427: $i,SV1031: $i,SV434: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV434 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(5193,plain,
! [SV1428: $i,SV1032: $i,SV435: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV435 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4821]) ).
thf(5194,plain,
! [SV436: $i,SV1429: $i,SV1033: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1033 @ ( c_Power_Opower__class_Opower @ SV1033 @ SV1429 @ SV436 ) @ SV436 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1429 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4822]) ).
thf(5195,plain,
! [SV1618: $i,SV1433: $i,SV1037: $i,SV440: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1037 @ SV1433 @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1433 @ SV440 ) @ SV440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4826]) ).
thf(5196,plain,
! [SV1619: $i,SV1434: $i,SV1038: $i,SV441: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1434 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1619 @ SV441 ) @ SV441 )
| ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1619 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4827]) ).
thf(5197,plain,
! [SV1620: $i,SV1435: $i,SV1039: $i,SV442: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1435 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1620 @ SV442 ) @ SV442 )
| ~ ( c_HOL_Oord__class_Oless @ SV1435 @ SV1620 @ SV442 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4828]) ).
thf(5198,plain,
! [SV1621: $i,SV1436: $i,SV1040: $i,SV443: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1040 @ SV1436 @ SV443 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SV1621 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SV1436 @ SV1621 @ SV443 ) @ SV443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(5199,plain,
! [SV1622: $i,SV1437: $i,SV1041: $i,SV444: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SV1437 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SV1622 @ SV1437 @ SV444 ) @ SV444 )
| ~ ( c_HOL_Oord__class_Oless @ SV1041 @ SV1622 @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(5200,plain,
! [SV1623: $i,SV1438: $i,SV1042: $i,SV445: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SV1438 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SV1623 @ SV1438 @ SV445 ) @ SV445 )
| ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1623 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4831]) ).
thf(5201,plain,
! [SV446: $i,SV1439: $i,SV1043: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $true )
| ( ( ~ ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
| ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(5202,plain,
! [SV1044: $i,SV447: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4833]) ).
thf(5203,plain,
! [SV450: $i,SV1047: $i] :
( ( ( c_lessequals @ SV1047 @ SV450 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV450 @ ( c_Suc @ SV1047 ) @ tc_nat )
= $false )
| ( ( SV450 = SV1047 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(5204,plain,
! [SV452: $i,SV1049: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1049 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV452 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV452 @ SV1049 @ tc_nat ) @ SV452 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4835]) ).
thf(5205,plain,
! [SV1053: $i,SV456: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV456 @ SV1053 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1053 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV456 @ SV1053 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(5206,plain,
! [SV1054: $i,SV1440: $i,SV457: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV457 @ SV1440 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1440 @ SV457 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV457 @ SV1054 @ tc_nat ) @ SV1440 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(5207,plain,
! [SV458: $i,SV1441: $i,SV1055: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1055 @ SV1441 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1441 @ SV1055 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_GCD_Ogcd__class_Ogcd @ SV458 @ SV1055 @ tc_nat ) @ SV1441 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(5208,plain,
! [SV459: $i,SV1442: $i,SV1056: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1056 @ SV1442 @ SV459 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1442 @ SV1056 @ SV459 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(5209,plain,
! [SV460: $i,SV1057: $i,SV1443: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV1057 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV460 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1443 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4840]) ).
thf(5210,plain,
! [SV461: $i,SV1058: $i,SV1444: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1444 @ SV1058 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1444 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SV1444 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(5211,plain,
! [SV462: $i,SV1445: $i,SV1059: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1059 @ SV1445 @ SV462 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1445 @ SV1059 @ SV462 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(5212,plain,
! [SV463: $i,SV1446: $i,SV1060: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1060 @ SV1446 @ SV463 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1446 @ SV1060 @ SV463 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5213,plain,
! [SV464: $i,SV1447: $i,SV1061: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1447 @ SV464 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1447 @ SV1061 @ SV464 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV464 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(5214,plain,
! [SV1448: $i,SV1062: $i,SV465: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV465 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
| ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4845]) ).
thf(5215,plain,
! [SV1449: $i,SV1063: $i,SV466: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV466 ) )
= $true )
| ( ( ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(5216,plain,
! [SV1450: $i,SV1064: $i,SV467: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV467 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4847]) ).
thf(5217,plain,
! [SV1451: $i,SV1065: $i,SV468: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV468 ) )
= $true )
| ( ( ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4848]) ).
thf(5218,plain,
! [SV1624: $i,SV1452: $i,SV1066: $i,SV469: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(5219,plain,
! [SV1625: $i,SV1453: $i,SV1067: $i,SV470: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
| ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(5220,plain,
! [SV1454: $i,SV1068: $i,SV471: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV471 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4851]) ).
thf(5221,plain,
! [SV1455: $i,SV1069: $i,SV472: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV472 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4852]) ).
thf(5222,plain,
! [SV1456: $i,SV1070: $i,SV473: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV473 ) )
= $true )
| ( ( ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(5223,plain,
! [SV1457: $i,SV1071: $i,SV474: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV474 ) )
= $true )
| ( ( ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4854]) ).
thf(5224,plain,
! [SV1458: $i,SV1072: $i,SV475: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV475 ) )
= $true )
| ( ( ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(5225,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV476 ) )
= $true )
| ( ( ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4856]) ).
thf(5226,plain,
! [SV1078: $i,SV481: $i] :
( ( ( class_Int_Onumber__ring @ SV481 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1078 @ SV481 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV481 ) @ SV1078 @ SV481 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(5227,plain,
! [SV1081: $i,SV484: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV484 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1081 @ SV1081 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
| ( SV1081
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(5228,plain,
! [SV1460: $i,SV485: $i,SV1082: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1082 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1460 @ SV485 ) @ SV485 )
= $true )
| ( ( ~ ( c_lessequals @ SV1082 @ SV1460 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(5229,plain,
! [SV486: $i,SV1461: $i,SV1083: $i] :
( ( ( c_lessequals @ SV1083 @ SV1461 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1083 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1461 @ SV486 ) @ SV486 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV486 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4862]) ).
thf(5230,plain,
! [SV1462: $i,SV1084: $i,SV487: $i] :
( ( ( ~ ( class_RealVector_Oreal__normed__field @ SV487 ) )
= $true )
| ( ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SV1084 @ SV1462 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SV1084 @ SV487 ) @ ( c_Transcendental_Oexp @ SV1462 @ SV487 ) @ SV487 ) )
= $true )
| ( ( class_SEQ_Obanach @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4863]) ).
thf(5231,plain,
! [SV1626: $i,SV1463: $i,SV1085: $i,SV488: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV488 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1085 @ SV1463 @ SV488 ) @ SV1626 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1085 @ SV1626 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SV1463 @ SV1626 @ SV488 ) @ SV488 ) )
| ( SV1463
= ( c_HOL_Ozero__class_Ozero @ SV488 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(5232,plain,
! [SV1669: $i,SV1627: $i,SV1464: $i,SV1086: $i,SV489: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
| ~ ( c_lessequals @ SV1464 @ SV1669 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4865]) ).
thf(5233,plain,
! [SV1670: $i,SV1628: $i,SV1465: $i,SV1087: $i,SV490: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SV1465 @ SV1670 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5234,plain,
! [SV1629: $i,SV1466: $i,SV1088: $i,SV491: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1466 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1629 @ SV491 ) @ SV491 )
| ~ ( c_lessequals @ SV1466 @ SV1629 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4867]) ).
thf(5235,plain,
! [SV1630: $i,SV1467: $i,SV1089: $i,SV492: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV492 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SV1630 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1630 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
| ~ ( c_lessequals @ SV1630 @ SV1467 @ tc_nat )
| ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4868]) ).
thf(5236,plain,
! [SV1090: $i,SV1468: $i,SV493: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1468 @ SV1090 @ tc_nat )
| ~ ( c_lessequals @ SV1468 @ SV493 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4869]) ).
thf(5237,plain,
! [SV1091: $i,SV1469: $i,SV494: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1091 @ SV1469 @ tc_nat )
| ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4870]) ).
thf(5238,plain,
! [SV504: $i,SV1101: $i,SV1475: $i] :
( ( ( c_lessequals @ SV1475 @ SV1101 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4876]) ).
thf(5239,plain,
! [SV505: $i,SV1476: $i,SV1102: $i] :
( ( ( c_lessequals @ SV1102 @ SV1476 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4877]) ).
thf(5240,plain,
! [SV1110: $i,SV1479: $i,SV513: $i] :
( ( ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SV1479 @ SV1110 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1110 @ SV1479 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SV1110 @ tc_nat ) @ SV1479 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4880]) ).
thf(5241,plain,
! [SV1111: $i,SV1480: $i,SV514: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SV1480 @ tc_nat ) @ SV1111 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1480 @ SV1111 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SV1111 @ SV1480 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4881]) ).
thf(5242,plain,
! [SV1481: $i,SV515: $i,SV1112: $i] :
( ( ( c_lessequals @ SV1112 @ SV515 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV515 @ SV1481 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV1112 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ SV1112 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4882]) ).
thf(5243,plain,
! [SV1114: $i,SV517: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
| ~ ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4884]) ).
thf(5244,plain,
! [SV1115: $i,SV518: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
= $false )
| ( ( ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(5245,plain,
! [SV1116: $i,SV519: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5246,plain,
! [SV1117: $i,SV520: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(5247,plain,
! [SV521: $i,SV1483: $i,SV1118: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1483 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1118 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1483 @ SV521 ) @ SV521 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1483 @ SV1118 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV521 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4888]) ).
thf(5248,plain,
! [SV1631: $i,SV1484: $i,SV1119: $i,SV522: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(5249,plain,
! [SV1632: $i,SV1485: $i,SV1120: $i,SV523: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV523 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
| ~ ( c_lessequals @ SV1485 @ SV1632 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4890]) ).
thf(5250,plain,
! [SV1633: $i,SV1486: $i,SV1121: $i,SV524: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV524 )
= $false )
| ( ( ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4891]) ).
thf(5251,plain,
! [SV1634: $i,SV1487: $i,SV1122: $i,SV525: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV525 )
= $false )
| ( ( ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4892]) ).
thf(5252,plain,
! [SV1635: $i,SV1488: $i,SV1123: $i,SV526: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV526 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SV1635 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1635 @ SV526 ) @ SV526 ) )
| ~ ( c_lessequals @ SV1635 @ SV1488 @ tc_nat )
| ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4893]) ).
thf(5253,plain,
! [SV528: $i,SV1489: $i,SV1125: $i] :
( ( ( c_lessequals @ SV1125 @ SV1489 @ SV528 )
= $true )
| ( ( c_lessequals @ SV1489 @ SV1125 @ SV528 )
= $true )
| ( ( class_Orderings_Olinorder @ SV528 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4894]) ).
thf(5254,plain,
! [SV1636: $i,SV1490: $i,SV1126: $i,SV529: $i] :
( ( ( class_Orderings_Oorder @ SV529 )
= $false )
| ( ( ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
| ~ ( c_lessequals @ SV1126 @ SV1636 @ SV529 )
| ~ ( c_lessequals @ SV1636 @ SV1490 @ SV529 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4895]) ).
thf(5255,plain,
! [SV1637: $i,SV1491: $i,SV1127: $i,SV530: $i] :
( ( ( class_Orderings_Opreorder @ SV530 )
= $false )
| ( ( ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1637 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1127 @ SV1637 @ SV530 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4896]) ).
thf(5256,plain,
! [SV532: $i,SV1128: $i,SV1492: $i] :
( ( ( c_lessequals @ SV1492 @ SV1128 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV532 @ SV1492 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV532 @ SV1128 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4897]) ).
thf(5257,plain,
! [SV1493: $i,SV1131: $i,SV536: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SV1131 @ SV1493 @ SV536 ) @ SV536 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SV1131 @ SV536 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV536 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4898]) ).
thf(5258,plain,
! [SV1638: $i,SV1494: $i,SV1133: $i,SV538: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV538 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
| ~ ( c_lessequals @ SV1494 @ SV1638 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(5259,plain,
! [SV541: $i,SV1495: $i,SV1136: $i] :
( ( ( SV1136 = SV1495 )
= $true )
| ( ( ~ ( c_lessequals @ SV1136 @ SV1495 @ SV541 )
| ~ ( c_lessequals @ SV1495 @ SV1136 @ SV541 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4900]) ).
thf(5260,plain,
! [SV1137: $i,SV542: $i] :
( ( ( c_lessequals @ SV542 @ SV1137 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1137 @ SV542 @ tc_nat )
= $false )
| ( ( SV542 = SV1137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4901]) ).
thf(5261,plain,
! [SV543: $i,SV1496: $i,SV1138: $i] :
( ( ( SV1138 = SV1496 )
= $true )
| ( ( ~ ( c_lessequals @ SV1496 @ SV1138 @ SV543 )
| ~ ( c_lessequals @ SV1138 @ SV1496 @ SV543 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4902]) ).
thf(5262,plain,
! [SV544: $i,SV1497: $i,SV1139: $i] :
( ( ( SV1139 = SV1497 )
= $true )
| ( ( ~ ( c_lessequals @ SV1497 @ SV1139 @ SV544 )
| ~ ( c_lessequals @ SV1139 @ SV1497 @ SV544 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV544 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5263,plain,
! [SV1639: $i,SV1498: $i,SV1140: $i,SV545: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV545 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SV1498 @ SV545 ) @ SV1639 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SV1639 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SV1498 @ SV1639 @ SV545 ) @ SV545 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4904]) ).
thf(5264,plain,
! [SV1640: $i,SV1499: $i,SV1141: $i,SV546: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV546 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1141 @ SV1499 @ SV546 ) @ SV1640 @ SV546 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1141 @ SV1640 @ SV546 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1499 @ SV1640 @ SV546 ) @ SV546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4905]) ).
thf(5265,plain,
! [SV1641: $i,SV1500: $i,SV1142: $i,SV547: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV547 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ SV1142 @ SV1500 @ SV547 ) @ SV1641 @ SV547 )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ SV1142 @ SV1641 @ SV547 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1500 @ SV1641 @ SV547 ) @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(5266,plain,
! [SV1501: $i,SV1143: $i,SV548: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV548 ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SV1143 @ SV1501 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SV1143 @ SV548 ) @ SV1501 @ SV548 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV548 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4907]) ).
thf(5267,plain,
! [SV1144: $i,SV1502: $i,SV549: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1502 @ SV1144 @ tc_nat )
| ~ ( c_lessequals @ SV1502 @ SV549 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4908]) ).
thf(5268,plain,
! [SV1145: $i,SV1503: $i,SV550: $i] :
( ( ( c_lessequals @ SV550 @ SV1503 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1145 @ SV1503 @ tc_nat )
| ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4909]) ).
thf(5269,plain,
! [SV555: $i,SV1507: $i,SV1150: $i] :
( ( ( c_lessequals @ SV1150 @ SV1507 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1150 @ SV555 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1150 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1507 @ SV1150 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1507 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5270,plain,
! [SV1642: $i,SV1508: $i,SV1152: $i,SV577: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1508 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1642 @ SV577 ) )
| ( SV1508 = SV1642 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5271,plain,
! [SV578: $i,SV1509: $i,SV1153: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1153 @ SV1509 @ SV578 )
!= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= $true )
| ( ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5272,plain,
! [SV579: $i,SV1510: $i,SV1154: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1154 @ SV1510 @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
= $true )
| ( ( SV1154 = SV1510 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV579 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(5273,plain,
! [SV1160: $i,SV587: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV587 )
= $false )
| ( ( ( c_Transcendental_Oexp @ SV1160 @ SV587 )
!= ( c_HOL_Ozero__class_Ozero @ SV587 ) )
= $true )
| ( ( class_SEQ_Obanach @ SV587 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4918]) ).
thf(5274,plain,
! [SV1678: $i,SV1671: $i,SV1643: $i,SV1511: $i,SV1161: $i,SV588: $i] :
( ( ~ ( class_Divides_Osemiring__div @ SV588 )
| ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4919]) ).
thf(5275,plain,
! [SV1672: $i,SV1644: $i,SV1512: $i,SV1162: $i,SV590: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV590 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
| ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5276,plain,
! [SV1513: $i,SV593: $i,SV1165: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
= $true )
| ( ( ( SV1165 = SV1513 )
| ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5277,plain,
! [SV1645: $i,SV1514: $i,SV1167: $i,SV595: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SV1514 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SV1645 @ SV1514 @ SV595 ) )
| ( SV1167 = SV1645 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4923]) ).
thf(5278,plain,
! [SV1679: $i,SV1673: $i,SV1646: $i,SV1515: $i,SV1168: $i,SV596: $i] :
( ( ~ ( class_Divides_Oring__div @ SV596 )
| ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4924]) ).
thf(5279,plain,
! [SV1647: $i,SV1516: $i,SV1170: $i,SV598: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
| ( SV1170 = SV1647 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(5280,plain,
! [SV1674: $i,SV1648: $i,SV1517: $i,SV1171: $i,SV599: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV599 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
| ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SV1674 @ SV1648 @ SV599 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4926]) ).
thf(5281,plain,
! [SV1649: $i,SV1518: $i,SV1173: $i,SV601: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1518 @ SV1649 @ tc_nat ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV1173 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV601 @ SV1649 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(5282,plain,
! [SV1174: $i,SV602: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
| ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV602 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4928]) ).
thf(5283,plain,
! [SV1650: $i,SV1519: $i,SV1175: $i,SV603: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV603 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SV1519 @ SV1650 @ SV603 ) )
| ( SV1519 = SV1650 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4929]) ).
thf(5284,plain,
! [SV1675: $i,SV1651: $i,SV1520: $i,SV1176: $i,SV604: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV604 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1651 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1675 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SV1651 @ SV604 )
= SV1675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4930]) ).
thf(5285,plain,
! [SV606: $i,SV1521: $i,SV1178: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1178 @ SV1521 @ SV606 )
!= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1521 @ SV1178 @ SV606 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV606 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(5286,plain,
! [SV1652: $i,SV1523: $i,SV1180: $i,SV608: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1523 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1652 @ SV608 ) )
| ( SV1523 = SV1652 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5287,plain,
! [SV1676: $i,SV1653: $i,SV1524: $i,SV1181: $i,SV610: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV610 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5288,plain,
! [SV1525: $i,SV1182: $i,SV611: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV611 ) )
= $true )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
| ( SV1182 = SV1525 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV611 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4936]) ).
thf(5289,plain,
! [SV612: $i,SV1183: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1183 @ SV612 )
= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
= $false )
| ( ( SV1183
= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV612 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4937]) ).
thf(5290,plain,
! [SV613: $i,SV1184: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1184 @ SV613 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1184 = SV613 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV613 @ SV1184 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(5291,plain,
! [SV1654: $i,SV1526: $i,SV1185: $i,SV614: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV614 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SV1526 = SV1654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4939]) ).
thf(5292,plain,
! [SV1527: $i,SV1187: $i,SV617: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV617 ) )
= $true )
| ( ( ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
| ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV617 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4940]) ).
thf(5293,plain,
! [SV1528: $i,SV1190: $i,SV620: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV620 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SV1190 = SV1528 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4943]) ).
thf(5294,plain,
! [SV622: $i,SV1191: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1191 @ SV1191 @ SV622 )
= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
= $false )
| ( ( SV1191
= ( c_HOL_Ozero__class_Ozero @ SV622 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV622 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5295,plain,
! [SV1193: $i,SV624: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5296,plain,
! [SV1677: $i,SV1655: $i,SV1530: $i,SV1196: $i,SV628: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV628 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4948]) ).
thf(5297,plain,
! [SV630: $i,SV1531: $i,SV1198: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1198 @ SV1531 @ SV630 )
!= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
= $true )
| ( ( SV1198 = SV1531 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV630 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4949]) ).
thf(5298,plain,
! [SV632: $i,SV1532: $i,SV1200: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
!= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4950]) ).
thf(5299,plain,
! [SV1201: $i,SV633: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV633 )
| ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4951]) ).
thf(5300,plain,
! [SV1656: $i,SV1533: $i,SV1202: $i,SV634: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV634 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV634 )
| ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
| ( SV1533 = SV1656 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(5301,plain,
! [SV635: $i,SV1534: $i,SV1203: $i] :
( ( ( ~ ( c_lessequals @ SV1203 @ SV1534 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
| ( SV635 = SV1534 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4953]) ).
thf(5302,plain,
! [SV1657: $i,SV1536: $i,SV1205: $i,SV637: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV637 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SV1536 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SV1657 @ SV1657 @ SV637 ) )
| ( SV1205 = SV1536 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4955]) ).
thf(5303,plain,
! [SV638: $i,SV1537: $i,SV1206: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
!= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(5304,plain,
! [SV1658: $i,SV1538: $i,SV1207: $i,SV639: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
| ( SV1207 = SV1658 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4957]) ).
thf(5305,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV641 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4959]) ).
thf(5306,plain,
! [SV644: $i,SV1540: $i,SV1211: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SV1540 @ SV644 )
!= ( c_HOL_Oone__class_Oone @ SV644 ) )
= $true )
| ( ( ( SV1540
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SV1211 = SV1540 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV644 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(5307,plain,
! [SV1541: $i,SV645: $i,SV1212: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV645 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV645 ) )
= $true )
| ( ( SV1212 = SV1541 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV645 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4961]) ).
thf(5308,plain,
! [SV1552: $i,SV1225: $i,SV659: $i,SV15: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV15 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4972]) ).
thf(5309,plain,
! [SV17: $i,SV1226: $i,SV661: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV661 @ SV1226 @ SV17 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV661 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4973]) ).
thf(5310,plain,
! [SV662: $i,SV21: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(5311,plain,
! [SV663: $i,SV22: $i,SV1227: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4975]) ).
thf(5312,plain,
! [SV666: $i,SV25: $i,SV1228: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4976]) ).
thf(5313,plain,
! [SV1553: $i,SV26: $i,SV1229: $i,SV667: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(5314,plain,
! [SV27: $i,SV668: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
= $true )
| ( ( ~ ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(5315,plain,
! [SV28: $i,SV669: $i] :
( ( ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(5316,plain,
! [SV671: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
= $true )
| ( ( ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4980]) ).
thf(5317,plain,
! [SV673: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(5318,plain,
! [SV674: $i,SV33: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4983]) ).
thf(5319,plain,
! [SV1555: $i,SV36: $i,SV1231: $i,SV677: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 )
| ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5320,plain,
! [SV1556: $i,SV37: $i,SV1232: $i,SV678: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 )
| ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5321,plain,
! [SV679: $i,SV38: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV679 @ SV38 ) @ SV38 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ ( c_HOL_Ozero__class_Ozero @ SV38 ) @ SV38 )
= $true )
| ( ( SV679
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4987]) ).
thf(5322,plain,
! [SV41: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= ( c_HOL_Ozero__class_Ozero @ SV41 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ ( c_HOL_Ozero__class_Ozero @ SV41 ) @ SV41 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5323,plain,
! [SV1558: $i,SV1234: $i,SV688: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV50 ) )
= $true )
| ( ( ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4992]) ).
thf(5324,plain,
! [SV1559: $i,SV1235: $i,SV689: $i,SV51: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV51 ) )
= $true )
| ( ( ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4993]) ).
thf(5325,plain,
! [SV61: $i,SV1560: $i,SV1241: $i,SV699: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4994]) ).
thf(5326,plain,
! [SV1561: $i,SV62: $i,SV1242: $i,SV700: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4995]) ).
thf(5327,plain,
! [SV63: $i,SV1562: $i,SV1243: $i,SV701: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4996]) ).
thf(5328,plain,
! [SV1563: $i,SV64: $i,SV1244: $i,SV702: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4997]) ).
thf(5329,plain,
! [SV709: $i,SV72: $i,SV1245: $i] :
( ( ( ~ ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5002]) ).
thf(5330,plain,
! [SV710: $i,SV73: $i,SV1246: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5003]) ).
thf(5331,plain,
! [SV74: $i,SV711: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
= $true )
| ( ( ~ ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5332,plain,
! [SV76: $i,SV713: $i,SV1247: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1247 @ SV713 @ SV76 )
= $true )
| ( ( SV1247 = SV713 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV713 @ SV1247 @ SV76 )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5005]) ).
thf(5333,plain,
! [SV86: $i,SV723: $i,SV1248: $i] :
( ( ( SV1248 = SV723 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1248 @ SV723 @ SV86 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV723 @ SV1248 @ SV86 )
= $true )
| ( ( class_Orderings_Olinorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5013]) ).
thf(5334,plain,
! [SV87: $i,SV1249: $i,SV724: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV724 @ SV1249 @ SV87 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1249 @ SV724 @ SV87 )
= $true )
| ( ( SV724 = SV1249 )
= $true )
| ( ( class_Orderings_Olinorder @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5014]) ).
thf(5335,plain,
! [SV88: $i,SV725: $i,SV1250: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1250 @ SV725 @ SV88 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV725 @ SV1250 @ SV88 )
= $true )
| ( ( SV725 = SV1250 )
= $true )
| ( ( class_Orderings_Olinorder @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5336,plain,
! [SV89: $i,SV726: $i,SV1251: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1251 @ SV726 @ SV89 )
= $true )
| ( ( SV1251 = SV726 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV726 @ SV1251 @ SV89 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5016]) ).
thf(5337,plain,
! [SV735: $i,SV1260: $i,SV98: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV1260 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1260 @ SV735 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV98 @ SV735 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5017]) ).
thf(5338,plain,
! [SV99: $i,SV736: $i,SV1261: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5018]) ).
thf(5339,plain,
! [SV1564: $i,SV103: $i,SV1262: $i,SV739: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5020]) ).
thf(5340,plain,
! [SV740: $i,SV1263: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV104 @ SV1263 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1263 @ SV740 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV104 ) @ SV740 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5021]) ).
thf(5341,plain,
! [SV742: $i,SV108: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5022]) ).
thf(5342,plain,
! [SV743: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV109 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5023]) ).
thf(5343,plain,
! [SV744: $i,SV110: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV744 @ SV110 )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= $true )
| ( ( SV744
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV110 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5024]) ).
thf(5344,plain,
! [SV113: $i,SV1565: $i,SV1266: $i,SV747: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5345,plain,
! [SV114: $i,SV748: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV748 @ SV114 ) @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
= $false )
| ( ( SV748
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV114 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5346,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5027]) ).
thf(5347,plain,
! [SV1268: $i,SV751: $i,SV117: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5028]) ).
thf(5348,plain,
! [SV1269: $i,SV752: $i,SV118: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5349,plain,
! [SV1270: $i,SV753: $i,SV119: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
| ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5350,plain,
! [SV1271: $i,SV754: $i,SV120: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5351,plain,
! [SV1272: $i,SV755: $i,SV121: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5352,plain,
! [SV1273: $i,SV756: $i,SV122: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5033]) ).
thf(5353,plain,
! [SV1274: $i,SV767: $i,SV137: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV767 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ SV1274 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV137 @ ( c_GCD_Ogcd__class_Ogcd @ SV767 @ SV1274 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5354,plain,
! [SV768: $i,SV138: $i,SV1275: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1275 @ SV138 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ SV1275 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV138 @ ( c_GCD_Ogcd__class_Ogcd @ SV768 @ SV1275 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5355,plain,
! [SV1276: $i,SV139: $i,SV769: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV769 @ SV139 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ SV769 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV139 @ ( c_GCD_Ogcd__class_Ogcd @ SV769 @ SV1276 @ tc_nat ) @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5356,plain,
! [SV1277: $i,SV770: $i,SV140: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV770 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ SV1277 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV140 @ ( c_GCD_Ogcd__class_Ogcd @ SV770 @ SV1277 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5357,plain,
! [SV1278: $i,SV771: $i,SV141: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV771 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ SV1278 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV141 @ ( c_GCD_Ogcd__class_Ogcd @ SV771 @ SV1278 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5039]) ).
thf(5358,plain,
! [SV1279: $i,SV778: $i,SV148: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV778 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ SV1279 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV148 @ ( c_GCD_Ogcd__class_Ogcd @ SV778 @ SV1279 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5359,plain,
! [SV1280: $i,SV779: $i,SV149: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV779 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ SV1280 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV149 @ ( c_GCD_Ogcd__class_Ogcd @ SV779 @ SV1280 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5041]) ).
thf(5360,plain,
! [SV1281: $i,SV780: $i,SV150: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV780 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ SV1281 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV150 @ ( c_GCD_Ogcd__class_Ogcd @ SV780 @ SV1281 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5042]) ).
thf(5361,plain,
! [SV1659: $i,SV1566: $i,SV1282: $i,SV781: $i,SV151: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
| ~ ( c_lessequals @ SV1282 @ SV1659 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5362,plain,
! [SV1660: $i,SV1567: $i,SV1283: $i,SV782: $i,SV152: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
| ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5363,plain,
! [SV786: $i,SV156: $i,SV1284: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5364,plain,
! [SV787: $i,SV157: $i,SV1285: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5046]) ).
thf(5365,plain,
! [SV1568: $i,SV158: $i,SV1286: $i,SV788: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
= $true )
| ( ( ~ ( c_lessequals @ SV788 @ SV1568 @ SV158 )
| ~ ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5366,plain,
! [SV1569: $i,SV159: $i,SV1287: $i,SV789: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 )
| ~ ( c_lessequals @ SV1569 @ SV1287 @ SV159 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5048]) ).
thf(5367,plain,
! [SV1661: $i,SV1570: $i,SV1288: $i,SV790: $i,SV160: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
= $false )
| ( ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
| ~ ( c_lessequals @ SV1661 @ SV1570 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5368,plain,
! [SV1571: $i,SV161: $i,SV1289: $i,SV791: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
= $true )
| ( ( ~ ( c_lessequals @ SV1571 @ SV1289 @ SV161 )
| ~ ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5050]) ).
thf(5369,plain,
! [SV1572: $i,SV162: $i,SV1290: $i,SV792: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 )
| ~ ( c_lessequals @ SV792 @ SV1572 @ SV162 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5051]) ).
thf(5370,plain,
! [SV163: $i,SV1291: $i,SV793: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV793 @ SV1291 @ SV163 )
= $false )
| ( ( c_lessequals @ SV793 @ SV1291 @ SV163 )
= $true )
| ( ( class_Orderings_Opreorder @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5052]) ).
thf(5371,plain,
! [SV164: $i,SV1292: $i,SV794: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV794 @ SV1292 @ SV164 )
= $false )
| ( ( c_lessequals @ SV794 @ SV1292 @ SV164 )
= $true )
| ( ( class_Orderings_Oorder @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5053]) ).
thf(5372,plain,
! [SV165: $i,SV795: $i,SV1293: $i] :
( ( ( c_lessequals @ SV1293 @ SV795 @ SV165 )
= $true )
| ( ( ~ ( c_lessequals @ SV795 @ SV1293 @ SV165 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1293 @ SV165 )
= $true )
| ( ( class_Orderings_Opreorder @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5054]) ).
thf(5373,plain,
! [SV1662: $i,SV1573: $i,SV1294: $i,SV796: $i,SV166: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
| ~ ( c_lessequals @ SV1294 @ SV1662 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5055]) ).
thf(5374,plain,
! [SV167: $i,SV797: $i,SV1295: $i] :
( ( ( SV1295 = SV797 )
= $true )
| ( ( ~ ( c_lessequals @ SV797 @ SV1295 @ SV167 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1295 @ SV167 )
= $true )
| ( ( class_Orderings_Oorder @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(5375,plain,
! [SV168: $i,SV1296: $i,SV798: $i] :
( ( ( ~ ( c_lessequals @ SV798 @ SV1296 @ SV168 ) )
= $true )
| ( ( SV1296 = SV798 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV798 @ SV1296 @ SV168 )
= $true )
| ( ( class_Orderings_Oorder @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5057]) ).
thf(5376,plain,
! [SV169: $i,SV1297: $i,SV799: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1297 @ SV169 )
= $true )
| ( ( ~ ( c_lessequals @ SV799 @ SV1297 @ SV169 ) )
= $true )
| ( ( SV799 = SV1297 )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5377,plain,
! [SV170: $i,SV1298: $i,SV800: $i] :
( ( ( ~ ( c_lessequals @ SV800 @ SV1298 @ SV170 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV800 @ SV1298 @ SV170 )
= $true )
| ( ( SV800 = SV1298 )
= $true )
| ( ( class_Orderings_Olinorder @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5059]) ).
thf(5378,plain,
! [SV171: $i,SV1299: $i,SV801: $i] :
( ( ( ~ ( c_lessequals @ SV801 @ SV1299 @ SV171 ) )
= $true )
| ( ( SV801 = SV1299 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV801 @ SV1299 @ SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5060]) ).
thf(5379,plain,
! [SV172: $i,SV1300: $i,SV802: $i] :
( ( ( SV802 = SV1300 )
= $true )
| ( ( ~ ( c_lessequals @ SV802 @ SV1300 @ SV172 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV802 @ SV1300 @ SV172 )
= $true )
| ( ( class_Orderings_Oorder @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5061]) ).
thf(5380,plain,
! [SV173: $i,SV1301: $i,SV803: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV803 @ SV1301 @ SV173 )
= $true )
| ( ( ~ ( c_lessequals @ SV803 @ SV1301 @ SV173 ) )
= $true )
| ( ( SV803 = SV1301 )
= $true )
| ( ( class_Orderings_Oorder @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5062]) ).
thf(5381,plain,
! [SV174: $i,SV1302: $i,SV804: $i] :
( ( ( SV804 = SV1302 )
= $true )
| ( ( ~ ( c_lessequals @ SV804 @ SV1302 @ SV174 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1302 @ SV174 )
= $true )
| ( ( class_Orderings_Oorder @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5063]) ).
thf(5382,plain,
! [SV1574: $i,SV175: $i,SV1303: $i,SV805: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SV1303 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1574 @ SV1303 @ SV175 ) @ SV175 )
= $true )
| ( ( ~ ( c_lessequals @ SV805 @ SV1574 @ SV175 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5064]) ).
thf(5383,plain,
! [SV1575: $i,SV176: $i,SV1304: $i,SV806: $i] :
( ( ( c_lessequals @ SV806 @ SV1304 @ SV176 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1575 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SV1304 @ SV1575 @ SV176 ) @ SV176 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5065]) ).
thf(5384,plain,
! [SV1576: $i,SV177: $i,SV1305: $i,SV807: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1305 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1576 @ SV177 ) @ SV177 )
= $true )
| ( ( ~ ( c_lessequals @ SV1305 @ SV1576 @ SV177 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(5385,plain,
! [SV1577: $i,SV178: $i,SV1306: $i,SV808: $i] :
( ( ( c_lessequals @ SV808 @ SV1306 @ SV178 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV1306 @ SV178 ) @ SV178 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(5386,plain,
! [SV1578: $i,SV179: $i,SV1307: $i,SV809: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SV1307 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SV1578 @ SV1307 @ SV179 ) @ SV179 )
= $true )
| ( ( ~ ( c_lessequals @ SV809 @ SV1578 @ SV179 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5068]) ).
thf(5387,plain,
! [SV1579: $i,SV180: $i,SV1308: $i,SV810: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1308 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1579 @ SV180 ) @ SV180 )
= $true )
| ( ( ~ ( c_lessequals @ SV1308 @ SV1579 @ SV180 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(5388,plain,
! [SV181: $i,SV1309: $i,SV811: $i] :
( ( ( c_lessequals @ SV811 @ SV1309 @ SV181 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1309 @ SV811 @ SV181 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5070]) ).
thf(5389,plain,
! [SV183: $i,SV813: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV813 @ SV813 @ SV183 )
= $false )
| ( ( c_lessequals @ SV813 @ SV813 @ SV183 )
= $false )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5072]) ).
thf(5390,plain,
! [SV185: $i,SV1311: $i,SV815: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV815 @ SV1311 @ SV185 )
= $false )
| ( ( ~ ( c_lessequals @ SV1311 @ SV815 @ SV185 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5073]) ).
thf(5391,plain,
! [SV188: $i,SV1314: $i,SV818: $i] :
( ( ( c_lessequals @ SV818 @ SV1314 @ SV188 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1314 @ SV818 @ SV188 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5076]) ).
thf(5392,plain,
! [SV189: $i,SV819: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
= $true )
| ( ( ~ ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5393,plain,
! [SV820: $i,SV190: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
= $true )
| ( ( ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(5394,plain,
! [SV1580: $i,SV191: $i,SV1315: $i,SV821: $i] :
( ( ( c_lessequals @ SV821 @ SV1315 @ SV191 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(5395,plain,
! [SV1581: $i,SV193: $i,SV1316: $i,SV823: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(5396,plain,
! [SV1663: $i,SV1582: $i,SV1317: $i,SV824: $i,SV194: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
| ~ ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5397,plain,
! [SV825: $i,SV195: $i,SV1318: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5082]) ).
thf(5398,plain,
! [SV826: $i,SV1319: $i,SV196: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5083]) ).
thf(5399,plain,
! [SV1664: $i,SV1583: $i,SV1320: $i,SV827: $i,SV197: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
| ~ ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5400,plain,
! [SV828: $i,SV1321: $i,SV198: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(5401,plain,
! [SV829: $i,SV199: $i,SV1322: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5402,plain,
! [SV1665: $i,SV1584: $i,SV1323: $i,SV830: $i,SV200: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5087]) ).
thf(5403,plain,
! [SV1585: $i,SV1324: $i,SV831: $i,SV201: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV201 ) )
= $true )
| ( ( ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5404,plain,
! [SV1586: $i,SV1325: $i,SV832: $i,SV202: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV202 ) )
= $true )
| ( ( ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5089]) ).
thf(5405,plain,
! [SV1587: $i,SV1326: $i,SV833: $i,SV203: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV203 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5090]) ).
thf(5406,plain,
! [SV1588: $i,SV1327: $i,SV834: $i,SV204: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV204 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5091]) ).
thf(5407,plain,
! [SV1589: $i,SV208: $i,SV1328: $i,SV836: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5092]) ).
thf(5408,plain,
! [SV209: $i,SV1590: $i,SV1329: $i,SV837: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5093]) ).
thf(5409,plain,
! [SV1591: $i,SV210: $i,SV1330: $i,SV838: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
| ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5094]) ).
thf(5410,plain,
! [SV211: $i,SV1592: $i,SV1331: $i,SV839: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5095]) ).
thf(5411,plain,
! [SV1332: $i,SV840: $i,SV212: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ SV840 @ SV212 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV212 ) @ ( c_Power_Opower__class_Opower @ SV840 @ ( c_Suc @ SV1332 ) @ SV212 ) @ SV212 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5096]) ).
thf(5412,plain,
! [SV1333: $i,SV841: $i,SV213: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5097]) ).
thf(5413,plain,
! [SV853: $i,SV228: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
= $true )
| ( ( ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5102]) ).
thf(5414,plain,
! [SV1595: $i,SV1337: $i,SV855: $i,SV231: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV231 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5103]) ).
thf(5415,plain,
! [SV1596: $i,SV1338: $i,SV856: $i,SV232: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV232 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5104]) ).
thf(5416,plain,
! [SV1597: $i,SV1339: $i,SV857: $i,SV233: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV233 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5105]) ).
thf(5417,plain,
! [SV1598: $i,SV1340: $i,SV858: $i,SV234: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV234 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5106]) ).
thf(5418,plain,
! [SV863: $i,SV240: $i,SV1341: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(5419,plain,
! [SV864: $i,SV1342: $i,SV241: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5108]) ).
thf(5420,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5421,plain,
! [SV1344: $i,SV866: $i,SV243: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5422,plain,
! [SV244: $i,SV867: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5111]) ).
thf(5423,plain,
! [SV245: $i,SV1599: $i,SV1345: $i,SV868: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5112]) ).
thf(5424,plain,
! [SV1666: $i,SV1600: $i,SV1346: $i,SV869: $i,SV246: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV246 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1346 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1600 @ SV1666 @ SV246 ) @ SV246 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ SV869 @ SV1600 @ SV246 ) @ ( c_HOL_Oplus__class_Oplus @ SV1346 @ SV1666 @ SV246 ) @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5425,plain,
! [SV1601: $i,SV247: $i,SV1347: $i,SV870: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
| ~ ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5114]) ).
thf(5426,plain,
! [SV1602: $i,SV248: $i,SV1348: $i,SV871: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
| ~ ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5115]) ).
thf(5427,plain,
! [SV872: $i,SV1349: $i,SV249: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5116]) ).
thf(5428,plain,
! [SV873: $i,SV1350: $i,SV250: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5429,plain,
! [SV251: $i,SV874: $i,SV1351: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1351 @ SV874 @ SV251 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ SV874 @ SV1351 @ SV251 )
= ( c_HOL_Ozero__class_Ozero @ SV251 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5118]) ).
thf(5430,plain,
! [SV879: $i,SV257: $i,SV1352: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat ) )
= $true )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5120]) ).
thf(5431,plain,
! [SV881: $i,SV259: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV881 @ SV259 ) @ SV259 )
= $false )
| ( ( SV881
= ( c_HOL_Ozero__class_Ozero @ SV259 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV259 ) @ SV881 @ SV259 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5121]) ).
thf(5432,plain,
! [SV1353: $i,SV262: $i,SV882: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5433,plain,
! [SV883: $i,SV1354: $i,SV263: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5434,plain,
! [SV884: $i,SV1355: $i,SV264: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5435,plain,
! [SV1356: $i,SV265: $i,SV885: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5436,plain,
! [SV1357: $i,SV266: $i,SV886: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5437,plain,
! [SV887: $i,SV1358: $i,SV267: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5438,plain,
! [SV891: $i,SV273: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5439,plain,
! [SV892: $i,SV274: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5440,plain,
! [SV1603: $i,SV1360: $i,SV896: $i,SV280: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV280 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5132]) ).
thf(5441,plain,
! [SV1604: $i,SV284: $i,SV1361: $i,SV899: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5133]) ).
thf(5442,plain,
! [SV906: $i,SV1365: $i,SV291: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) )
= $true )
| ( ( c_lessequals @ SV906 @ SV1365 @ SV291 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5134]) ).
thf(5443,plain,
! [SV907: $i,SV1366: $i,SV292: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1366 @ SV907 @ SV292 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5444,plain,
! [SV1367: $i,SV293: $i,SV908: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) )
= $true )
| ( ( c_lessequals @ SV908 @ SV1367 @ SV293 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV293 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5445,plain,
! [SV1368: $i,SV294: $i,SV909: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1368 @ SV909 @ SV294 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5446,plain,
! [SV910: $i,SV296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5138]) ).
thf(5447,plain,
! [SV911: $i,SV297: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5139]) ).
thf(5448,plain,
! [SV912: $i,SV298: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5140]) ).
thf(5449,plain,
! [SV299: $i,SV913: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(5450,plain,
! [SV300: $i,SV1369: $i,SV914: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1369 @ SV300 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV914 @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV914 @ SV1369 @ SV300 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV300 ) @ ( c_HOL_Oone__class_Oone @ SV300 ) @ SV300 ) @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5142]) ).
thf(5451,plain,
! [SV301: $i,SV1370: $i,SV915: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV915 @ SV1370 @ SV301 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ SV915 @ SV1370 @ SV301 ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ SV301 ) @ ( c_HOL_Oone__class_Oone @ SV301 ) @ SV301 ) @ SV301 ) @ SV1370 @ SV301 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV301 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5143]) ).
thf(5452,plain,
! [SV306: $i,SV1608: $i,SV1374: $i,SV920: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5147]) ).
thf(5453,plain,
! [SV1667: $i,SV1609: $i,SV1376: $i,SV927: $i,SV313: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV313 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ SV927 @ SV1376 @ SV313 ) @ ( c_HOL_Oplus__class_Oplus @ SV1609 @ SV1667 @ SV313 ) @ SV313 )
= ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ SV927 @ SV1609 @ SV313 ) @ ( c_HOL_Ominus__class_Ominus @ SV1376 @ SV1667 @ SV313 ) @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5149]) ).
thf(5454,plain,
! [SV1378: $i,SV929: $i,SV315: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV315 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ SV929 @ SV1378 @ SV315 ) @ SV315 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV929 @ SV315 ) @ SV1378 @ SV315 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5455,plain,
! [SV1610: $i,SV316: $i,SV1379: $i,SV930: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SV1379 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SV1610 @ SV1379 @ SV316 ) @ SV316 )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SV1610 @ SV316 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5151]) ).
thf(5456,plain,
! [SV1380: $i,SV932: $i,SV319: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV319 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Odivide @ SV932 @ SV1380 @ SV319 ) @ SV319 )
= ( c_HOL_Oinverse__class_Odivide @ SV1380 @ SV932 @ SV319 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5153]) ).
thf(5457,plain,
! [SV1383: $i,SV337: $i,SV1613: $i,SV949: $i] :
( ( ( c_lessequals @ SV949 @ SV1613 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV337 @ SV1383 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1383 @ SV1613 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5158]) ).
thf(5458,plain,
! [SV361: $i,SV970: $i,SV1396: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1396 @ SV970 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1396 @ SV361 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV970 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV361 @ SV1396 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5159]) ).
thf(5459,plain,
! [SV1400: $i,SV974: $i,SV365: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV974 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ SV1400 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV365 @ ( c_HOL_Ominus__class_Ominus @ SV974 @ SV1400 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5160]) ).
thf(5460,plain,
! [SV373: $i,SV978: $i] :
( ( ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(5461,plain,
! [SV375: $i,SV979: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5162]) ).
thf(5462,plain,
! [SV376: $i,SV1402: $i,SV980: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV980 @ SV1402 @ SV376 ) @ ( c_HOL_Ozero__class_Ozero @ SV376 ) @ SV376 )
= $false )
| ( ( c_lessequals @ SV980 @ SV1402 @ SV376 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5163]) ).
thf(5463,plain,
! [SV377: $i,SV1403: $i,SV981: $i] :
( ( ( c_lessequals @ SV981 @ SV1403 @ SV377 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV981 @ SV1403 @ SV377 ) @ ( c_HOL_Ozero__class_Ozero @ SV377 ) @ SV377 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5164]) ).
thf(5464,plain,
! [SV1404: $i,SV982: $i,SV378: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ SV982 @ SV378 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV378 ) @ ( c_Power_Opower__class_Opower @ SV982 @ SV1404 @ SV378 ) @ SV378 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5465,plain,
! [SV1405: $i,SV983: $i,SV379: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ SV983 @ SV379 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV379 ) @ ( c_Power_Opower__class_Opower @ SV983 @ SV1405 @ SV379 ) @ SV379 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV379 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5166]) ).
thf(5466,plain,
! [SV1614: $i,SV380: $i,SV1406: $i,SV984: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
| ~ ( c_lessequals @ SV984 @ SV1614 @ SV380 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5167]) ).
thf(5467,plain,
! [SV1407: $i,SV381: $i,SV985: $i] :
( ( ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SV1407 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 ) )
= $true )
| ( ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5168]) ).
thf(5468,plain,
! [SV1408: $i,SV986: $i,SV382: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5169]) ).
thf(5469,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5470,plain,
! [SV1410: $i,SV988: $i,SV384: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ SV988 @ SV384 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV384 ) @ ( c_Power_Opower__class_Opower @ SV988 @ SV1410 @ SV384 ) @ SV384 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV384 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5471,plain,
! [SV1005: $i,SV1415: $i,SV406: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5472,plain,
! [SV407: $i,SV1006: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5174]) ).
thf(5473,plain,
! [SV408: $i,SV1007: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5175]) ).
thf(5474,plain,
! [SV410: $i,SV1009: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1009 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1009 @ SV410 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV410 @ SV1009 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5177]) ).
thf(5475,plain,
! [SV1416: $i,SV411: $i,SV1615: $i,SV1010: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1010 @ SV1615 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV411 @ SV1416 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1615 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5178]) ).
thf(5476,plain,
! [SV1668: $i,SV1616: $i,SV1417: $i,SV1011: $i,SV412: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5477,plain,
! [SV1012: $i,SV413: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5180]) ).
thf(5478,plain,
! [SV414: $i,SV1418: $i,SV1013: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1013 @ SV1418 @ SV414 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1013 @ SV1418 @ SV414 ) @ ( c_HOL_Ozero__class_Ozero @ SV414 ) @ SV414 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5181]) ).
thf(5479,plain,
! [SV415: $i,SV1419: $i,SV1014: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV1014 @ SV1419 @ SV415 ) @ ( c_HOL_Ozero__class_Ozero @ SV415 ) @ SV415 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1014 @ SV1419 @ SV415 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV415 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5182]) ).
thf(5480,plain,
! [SV1420: $i,SV416: $i,SV1015: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1015 @ SV416 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1420 @ SV416 ) @ SV416 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1015 @ SV1420 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5481,plain,
! [SV417: $i,SV1421: $i,SV1016: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1016 @ SV1421 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1016 @ SV417 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1421 @ SV417 ) @ SV417 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV417 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5482,plain,
! [SV1617: $i,SV422: $i,SV1422: $i,SV1019: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1422 @ SV422 ) @ SV1617 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1617 @ SV422 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1617 @ SV1422 @ SV422 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV422 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(5483,plain,
! [SV1029: $i,SV1425: $i,SV432: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5484,plain,
! [SV1030: $i,SV433: $i,SV1426: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV433 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5485,plain,
! [SV1427: $i,SV1031: $i,SV434: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5486,plain,
! [SV1428: $i,SV1032: $i,SV435: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5193]) ).
thf(5487,plain,
! [SV436: $i,SV1033: $i,SV1429: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1429 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1033 @ ( c_Power_Opower__class_Opower @ SV1033 @ SV1429 @ SV436 ) @ SV436 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5488,plain,
! [SV1618: $i,SV440: $i,SV1433: $i,SV1037: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1037 @ SV1433 @ SV440 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1433 @ SV440 ) @ SV440 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5489,plain,
! [SV1619: $i,SV441: $i,SV1434: $i,SV1038: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1434 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1619 @ SV441 ) @ SV441 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1434 @ SV1619 @ SV441 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5196]) ).
thf(5490,plain,
! [SV1620: $i,SV442: $i,SV1435: $i,SV1039: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1435 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1620 @ SV442 ) @ SV442 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1435 @ SV1620 @ SV442 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5197]) ).
thf(5491,plain,
! [SV1621: $i,SV443: $i,SV1436: $i,SV1040: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1040 @ SV1436 @ SV443 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SV1621 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SV1436 @ SV1621 @ SV443 ) @ SV443 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5492,plain,
! [SV1622: $i,SV444: $i,SV1437: $i,SV1041: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SV1437 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SV1622 @ SV1437 @ SV444 ) @ SV444 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1041 @ SV1622 @ SV444 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5199]) ).
thf(5493,plain,
! [SV1623: $i,SV445: $i,SV1438: $i,SV1042: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SV1438 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SV1623 @ SV1438 @ SV445 ) @ SV445 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1042 @ SV1623 @ SV445 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(5494,plain,
! [SV1043: $i,SV446: $i,SV1439: $i] :
( ( ( ~ ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5201]) ).
thf(5495,plain,
! [SV447: $i,SV1044: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5202]) ).
thf(5496,plain,
! [SV459: $i,SV1442: $i,SV1056: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1056 @ SV1442 @ SV459 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1442 @ SV1056 @ SV459 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5208]) ).
thf(5497,plain,
! [SV1057: $i,SV460: $i,SV1443: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV460 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1443 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV1057 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(5498,plain,
! [SV461: $i,SV1058: $i,SV1444: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1444 @ SV1058 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1444 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SV1444 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5210]) ).
thf(5499,plain,
! [SV462: $i,SV1445: $i,SV1059: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1059 @ SV1445 @ SV462 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1445 @ SV1059 @ SV462 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5211]) ).
thf(5500,plain,
! [SV463: $i,SV1446: $i,SV1060: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1060 @ SV1446 @ SV463 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1446 @ SV1060 @ SV463 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5212]) ).
thf(5501,plain,
! [SV464: $i,SV1447: $i,SV1061: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1061 @ SV1447 @ SV464 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1447 @ SV1061 @ SV464 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5213]) ).
thf(5502,plain,
! [SV1448: $i,SV1062: $i,SV465: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
| ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5214]) ).
thf(5503,plain,
! [SV1449: $i,SV1063: $i,SV466: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
= $false )
| ( ( ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5215]) ).
thf(5504,plain,
! [SV1450: $i,SV1064: $i,SV467: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5216]) ).
thf(5505,plain,
! [SV1451: $i,SV1065: $i,SV468: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
= $false )
| ( ( ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5506,plain,
! [SV1624: $i,SV1452: $i,SV1066: $i,SV469: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV469 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(5507,plain,
! [SV1625: $i,SV1453: $i,SV1067: $i,SV470: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV470 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(5508,plain,
! [SV1454: $i,SV1068: $i,SV471: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5220]) ).
thf(5509,plain,
! [SV1455: $i,SV1069: $i,SV472: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5221]) ).
thf(5510,plain,
! [SV1456: $i,SV1070: $i,SV473: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
= $false )
| ( ( ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5511,plain,
! [SV1457: $i,SV1071: $i,SV474: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
= $false )
| ( ( ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5512,plain,
! [SV1458: $i,SV1072: $i,SV475: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
= $false )
| ( ( ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5224]) ).
thf(5513,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
= $false )
| ( ( ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5225]) ).
thf(5514,plain,
! [SV484: $i,SV1081: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1081 @ SV1081 @ SV484 )
= ( c_HOL_Oone__class_Oone @ SV484 ) )
= $true )
| ( ( SV1081
= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV484 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5227]) ).
thf(5515,plain,
! [SV485: $i,SV1460: $i,SV1082: $i] :
( ( ( c_lessequals @ SV1082 @ SV1460 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1082 @ SV485 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1460 @ SV485 ) @ SV485 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5228]) ).
thf(5516,plain,
! [SV1461: $i,SV486: $i,SV1083: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1083 @ SV486 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1461 @ SV486 ) @ SV486 )
= $false )
| ( ( c_lessequals @ SV1083 @ SV1461 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV486 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5229]) ).
thf(5517,plain,
! [SV1462: $i,SV1084: $i,SV487: $i] :
( ( ( class_RealVector_Oreal__normed__field @ SV487 )
= $false )
| ( ( ( c_Transcendental_Oexp @ ( c_HOL_Ominus__class_Ominus @ SV1084 @ SV1462 @ SV487 ) @ SV487 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Oexp @ SV1084 @ SV487 ) @ ( c_Transcendental_Oexp @ SV1462 @ SV487 ) @ SV487 ) )
= $true )
| ( ( class_SEQ_Obanach @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5230]) ).
thf(5518,plain,
! [SV1626: $i,SV488: $i,SV1463: $i,SV1085: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1085 @ SV1463 @ SV488 ) @ SV1626 @ SV488 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1085 @ SV1626 @ SV488 ) @ ( c_Power_Opower__class_Opower @ SV1463 @ SV1626 @ SV488 ) @ SV488 ) )
= $true )
| ( ( SV1463
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5519,plain,
! [SV1669: $i,SV1627: $i,SV1464: $i,SV1086: $i,SV489: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
| ~ ( c_lessequals @ SV1464 @ SV1669 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5232]) ).
thf(5520,plain,
! [SV1670: $i,SV1628: $i,SV1465: $i,SV1087: $i,SV490: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
| ~ ( c_lessequals @ SV1465 @ SV1670 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5233]) ).
thf(5521,plain,
! [SV1629: $i,SV491: $i,SV1466: $i,SV1088: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1466 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1629 @ SV491 ) @ SV491 )
= $true )
| ( ( ~ ( c_lessequals @ SV1466 @ SV1629 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5234]) ).
thf(5522,plain,
! [SV1630: $i,SV1467: $i,SV492: $i,SV1089: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SV1630 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1630 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1630 @ SV1467 @ tc_nat )
| ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5235]) ).
thf(5523,plain,
! [SV493: $i,SV1090: $i,SV1468: $i] :
( ( ( ~ ( c_lessequals @ SV1468 @ SV1090 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1468 @ SV493 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5236]) ).
thf(5524,plain,
! [SV494: $i,SV1469: $i,SV1091: $i] :
( ( ( ~ ( c_lessequals @ SV1091 @ SV1469 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(5525,plain,
! [SV1101: $i,SV1475: $i,SV504: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1475 @ SV1101 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5238]) ).
thf(5526,plain,
! [SV1102: $i,SV1476: $i,SV505: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1102 @ SV1476 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5239]) ).
thf(5527,plain,
! [SV513: $i,SV1479: $i,SV1110: $i] :
( ( ( c_lessequals @ SV1110 @ SV1479 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV513 @ ( c_HOL_Ominus__class_Ominus @ SV1479 @ SV1110 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV513 @ SV1110 @ tc_nat ) @ SV1479 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5240]) ).
thf(5528,plain,
! [SV514: $i,SV1111: $i,SV1480: $i] :
( ( ( c_lessequals @ SV1480 @ SV1111 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV514 @ SV1480 @ tc_nat ) @ SV1111 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV514 @ ( c_HOL_Ominus__class_Ominus @ SV1111 @ SV1480 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5241]) ).
thf(5529,plain,
! [SV1112: $i,SV1481: $i,SV515: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV515 @ SV1481 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1112 @ SV515 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV515 @ SV1112 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ SV1112 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5242]) ).
thf(5530,plain,
! [SV1114: $i,SV517: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
= $true )
| ( ( ~ ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV517 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5243]) ).
thf(5531,plain,
! [SV518: $i,SV1115: $i] :
( ( ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5244]) ).
thf(5532,plain,
! [SV1116: $i,SV519: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5245]) ).
thf(5533,plain,
! [SV1117: $i,SV520: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV520 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5246]) ).
thf(5534,plain,
! [SV521: $i,SV1118: $i,SV1483: $i] :
( ( ( c_lessequals @ SV1483 @ SV1118 @ tc_nat )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1483 @ tc_nat ) @ SV521 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1118 @ SV521 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1483 @ SV521 ) @ SV521 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV521 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5247]) ).
thf(5535,plain,
! [SV1631: $i,SV522: $i,SV1484: $i,SV1119: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
= $true )
| ( ( ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5248]) ).
thf(5536,plain,
! [SV1632: $i,SV523: $i,SV1485: $i,SV1120: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
= $true )
| ( ( ~ ( c_lessequals @ SV1485 @ SV1632 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(5537,plain,
! [SV524: $i,SV1633: $i,SV1486: $i,SV1121: $i] :
( ( ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5538,plain,
! [SV525: $i,SV1634: $i,SV1487: $i,SV1122: $i] :
( ( ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5251]) ).
thf(5539,plain,
! [SV526: $i,SV1635: $i,SV1488: $i,SV1123: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SV1635 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1635 @ SV526 ) @ SV526 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1635 @ SV1488 @ tc_nat )
| ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5252]) ).
thf(5540,plain,
! [SV1636: $i,SV529: $i,SV1490: $i,SV1126: $i] :
( ( ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
= $true )
| ( ( ~ ( c_lessequals @ SV1126 @ SV1636 @ SV529 )
| ~ ( c_lessequals @ SV1636 @ SV1490 @ SV529 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(5541,plain,
! [SV1637: $i,SV530: $i,SV1491: $i,SV1127: $i] :
( ( ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
= $true )
| ( ( ~ ( c_lessequals @ SV1637 @ SV1491 @ SV530 )
| ~ ( c_lessequals @ SV1127 @ SV1637 @ SV530 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5542,plain,
! [SV1128: $i,SV1492: $i,SV532: $i] :
( ( ( c_lessequals @ SV532 @ SV1492 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1492 @ SV1128 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV532 @ SV1128 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5543,plain,
! [SV1493: $i,SV1131: $i,SV536: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ SV1131 @ SV536 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV536 ) @ ( c_Power_Opower__class_Opower @ SV1131 @ SV1493 @ SV536 ) @ SV536 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV536 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5544,plain,
! [SV1638: $i,SV538: $i,SV1494: $i,SV1133: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
| ~ ( c_lessequals @ SV1494 @ SV1638 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5258]) ).
thf(5545,plain,
! [SV541: $i,SV1495: $i,SV1136: $i] :
( ( ( ~ ( c_lessequals @ SV1136 @ SV1495 @ SV541 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1495 @ SV1136 @ SV541 ) )
= $true )
| ( ( SV1136 = SV1495 )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5259]) ).
thf(5546,plain,
! [SV543: $i,SV1138: $i,SV1496: $i] :
( ( ( ~ ( c_lessequals @ SV1496 @ SV1138 @ SV543 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1138 @ SV1496 @ SV543 ) )
= $true )
| ( ( SV1138 = SV1496 )
= $true )
| ( ( class_Orderings_Oorder @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5261]) ).
thf(5547,plain,
! [SV544: $i,SV1139: $i,SV1497: $i] :
( ( ( ~ ( c_lessequals @ SV1497 @ SV1139 @ SV544 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1139 @ SV1497 @ SV544 ) )
= $true )
| ( ( SV1139 = SV1497 )
= $true )
| ( ( class_Orderings_Oorder @ SV544 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5262]) ).
thf(5548,plain,
! [SV1639: $i,SV1498: $i,SV1140: $i,SV545: $i] :
( ( ( ~ ( class_Ring__and__Field_Odivision__by__zero @ SV545 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SV1498 @ SV545 ) @ SV1639 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SV1639 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SV1498 @ SV1639 @ SV545 ) @ SV545 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(5549,plain,
! [SV1501: $i,SV1143: $i,SV548: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV548 )
= $false )
| ( ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ ( c_Power_Opower__class_Opower @ SV1143 @ SV1501 @ SV548 ) @ SV548 )
= ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV548 ) @ SV1143 @ SV548 ) @ SV1501 @ SV548 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV548 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5266]) ).
thf(5550,plain,
! [SV549: $i,SV1144: $i,SV1502: $i] :
( ( ( ~ ( c_lessequals @ SV1502 @ SV1144 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1502 @ SV549 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(5551,plain,
! [SV550: $i,SV1503: $i,SV1145: $i] :
( ( ( ~ ( c_lessequals @ SV1145 @ SV1503 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV550 @ SV1503 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5268]) ).
thf(5552,plain,
! [SV1507: $i,SV555: $i,SV1150: $i] :
( ( ( c_lessequals @ SV1150 @ SV555 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1150 @ SV1507 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1150 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1507 @ SV1150 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV555 @ SV1507 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5269]) ).
thf(5553,plain,
! [SV1642: $i,SV577: $i,SV1508: $i,SV1152: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1508 @ SV577 )
!= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1642 @ SV577 ) )
= $true )
| ( ( SV1508 = SV1642 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5270]) ).
thf(5554,plain,
! [SV578: $i,SV1509: $i,SV1153: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1153 @ SV1509 @ SV578 )
= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= $false )
| ( ( SV1153
= ( c_HOL_Ozero__class_Ozero @ SV578 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5555,plain,
! [SV579: $i,SV1510: $i,SV1154: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1154 @ SV1510 @ SV579 )
= ( c_HOL_Ozero__class_Ozero @ SV579 ) )
= $false )
| ( ( SV1154 = SV1510 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV579 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5272]) ).
thf(5556,plain,
! [SV587: $i,SV1160: $i] :
( ( ( ( c_Transcendental_Oexp @ SV1160 @ SV587 )
= ( c_HOL_Ozero__class_Ozero @ SV587 ) )
= $false )
| ( ( class_RealVector_Oreal__normed__field @ SV587 )
= $false )
| ( ( class_SEQ_Obanach @ SV587 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5273]) ).
thf(5557,plain,
! [SV1678: $i,SV1671: $i,SV1643: $i,SV1511: $i,SV1161: $i,SV588: $i] :
( ( ( ~ ( class_Divides_Osemiring__div @ SV588 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5274]) ).
thf(5558,plain,
! [SV1672: $i,SV1644: $i,SV1512: $i,SV1162: $i,SV590: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
| ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5559,plain,
! [SV1513: $i,SV593: $i,SV1165: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
= $false )
| ( ( ( SV1165 = SV1513 )
| ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV593 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5560,plain,
! [SV1645: $i,SV595: $i,SV1514: $i,SV1167: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SV1514 @ SV595 )
!= ( c_HOL_Oplus__class_Oplus @ SV1645 @ SV1514 @ SV595 ) )
= $true )
| ( ( SV1167 = SV1645 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5277]) ).
thf(5561,plain,
! [SV1679: $i,SV1673: $i,SV1646: $i,SV1515: $i,SV1168: $i,SV596: $i] :
( ( ( ~ ( class_Divides_Oring__div @ SV596 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5278]) ).
thf(5562,plain,
! [SV1647: $i,SV598: $i,SV1516: $i,SV1170: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
!= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $true )
| ( ( ( SV1170 = SV1647 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5279]) ).
thf(5563,plain,
! [SV1674: $i,SV1648: $i,SV1517: $i,SV1171: $i,SV599: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
| ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SV1674 @ SV1648 @ SV599 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5564,plain,
! [SV1649: $i,SV601: $i,SV1173: $i,SV1518: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1518 @ SV1173 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV601 @ SV1649 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1518 @ SV1649 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5281]) ).
thf(5565,plain,
! [SV602: $i,SV1174: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
!= ( c_HOL_Oone__class_Oone @ SV602 ) )
= $true )
| ( ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV602 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5282]) ).
thf(5566,plain,
! [SV1650: $i,SV1519: $i,SV603: $i,SV1175: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
!= ( c_HOL_Ominus__class_Ominus @ SV1519 @ SV1650 @ SV603 ) )
= $true )
| ( ( SV1519 = SV1650 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV603 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5283]) ).
thf(5567,plain,
! [SV1675: $i,SV1651: $i,SV1520: $i,SV1176: $i,SV604: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV604 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1651 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1675 @ SV604 ) )
| ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SV1651 @ SV604 )
= SV1675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5284]) ).
thf(5568,plain,
! [SV606: $i,SV1521: $i,SV1178: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1178 @ SV1521 @ SV606 )
= ( c_HOL_Ozero__class_Ozero @ SV606 ) )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1521 @ SV1178 @ SV606 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV606 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5285]) ).
thf(5569,plain,
! [SV1652: $i,SV608: $i,SV1523: $i,SV1180: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1523 @ SV608 )
!= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1652 @ SV608 ) )
= $true )
| ( ( SV1523 = SV1652 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5286]) ).
thf(5570,plain,
! [SV1676: $i,SV1653: $i,SV1524: $i,SV1181: $i,SV610: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
| ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5287]) ).
thf(5571,plain,
! [SV1525: $i,SV1182: $i,SV611: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
= $false )
| ( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
| ( SV1182 = SV1525 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__ring @ SV611 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5572,plain,
! [SV1654: $i,SV614: $i,SV1526: $i,SV1185: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
!= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SV1526 = SV1654 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5291]) ).
thf(5573,plain,
! [SV1527: $i,SV1187: $i,SV617: $i] :
( ( ( class_Int_Onumber__ring @ SV617 )
= $false )
| ( ( ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
| ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV617 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5574,plain,
! [SV1528: $i,SV1190: $i,SV620: $i] :
( ( ( class_Int_Onumber__ring @ SV620 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
| ( SV1190 = SV1528 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5293]) ).
thf(5575,plain,
! [SV624: $i,SV1193: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
= $true )
| ( ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5295]) ).
thf(5576,plain,
! [SV1677: $i,SV1655: $i,SV1530: $i,SV1196: $i,SV628: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
| ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5296]) ).
thf(5577,plain,
! [SV630: $i,SV1531: $i,SV1198: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1198 @ SV1531 @ SV630 )
= ( c_HOL_Ozero__class_Ozero @ SV630 ) )
= $false )
| ( ( SV1198 = SV1531 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV630 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5297]) ).
thf(5578,plain,
! [SV632: $i,SV1532: $i,SV1200: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5579,plain,
! [SV1201: $i,SV633: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV633 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(5580,plain,
! [SV1656: $i,SV1533: $i,SV1202: $i,SV634: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV634 ) )
= $true )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
| ( SV1533 = SV1656 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(5581,plain,
! [SV635: $i,SV1534: $i,SV1203: $i] :
( ( ( c_lessequals @ SV1203 @ SV1534 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
| ( SV635 = SV1534 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5301]) ).
thf(5582,plain,
! [SV1657: $i,SV637: $i,SV1536: $i,SV1205: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SV1536 @ SV637 )
!= ( c_HOL_Ominus__class_Ominus @ SV1657 @ SV1657 @ SV637 ) )
= $true )
| ( ( SV1205 = SV1536 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5302]) ).
thf(5583,plain,
! [SV638: $i,SV1537: $i,SV1206: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(5584,plain,
! [SV1658: $i,SV639: $i,SV1538: $i,SV1207: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
!= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
= $true )
| ( ( ( SV1207 = SV1658 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5304]) ).
thf(5585,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV641 )
| ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5586,plain,
! [SV644: $i,SV1540: $i,SV1211: $i] :
( ( ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SV1540 @ SV644 )
= ( c_HOL_Oone__class_Oone @ SV644 ) )
= $false )
| ( ( ( SV1540
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
| ( SV1211 = SV1540 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV644 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5587,plain,
! [SV1541: $i,SV645: $i,SV1212: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV645 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV645 ) )
= $false )
| ( ( SV1212 = SV1541 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV645 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5588,plain,
! [SV1552: $i,SV1225: $i,SV659: $i,SV15: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5308]) ).
thf(5589,plain,
! [SV662: $i,SV21: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV21 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV662 @ SV21 ) @ SV21 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV662 @ SV21 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV21 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5310]) ).
thf(5590,plain,
! [SV663: $i,SV22: $i,SV1227: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5311]) ).
thf(5591,plain,
! [SV666: $i,SV25: $i,SV1228: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5592,plain,
! [SV1553: $i,SV667: $i,SV26: $i,SV1229: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5313]) ).
thf(5593,plain,
! [SV27: $i,SV668: $i] :
( ( ( c_lessequals @ SV668 @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV668 @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV27 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5594,plain,
! [SV28: $i,SV669: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV669 @ SV28 ) @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
= $false )
| ( ( c_lessequals @ SV669 @ ( c_HOL_Ozero__class_Ozero @ SV28 ) @ SV28 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV28 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5595,plain,
! [SV30: $i,SV671: $i] :
( ( ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5316]) ).
thf(5596,plain,
! [SV673: $i,SV32: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ SV673 @ SV32 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV32 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV673 @ SV32 ) @ SV32 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV32 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5597,plain,
! [SV674: $i,SV33: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV674 @ SV33 ) @ SV33 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV33 ) @ SV674 @ SV33 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV33 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5598,plain,
! [SV677: $i,SV36: $i,SV1231: $i,SV1555: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
= $true )
| ( ( class_Orderings_Opreorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5319]) ).
thf(5599,plain,
! [SV1232: $i,SV37: $i,SV1556: $i,SV678: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5320]) ).
thf(5600,plain,
! [SV1558: $i,SV1234: $i,SV688: $i,SV50: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
| ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5323]) ).
thf(5601,plain,
! [SV1559: $i,SV1235: $i,SV689: $i,SV51: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
= $false )
| ( ( ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
| ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5324]) ).
thf(5602,plain,
! [SV1241: $i,SV61: $i,SV1560: $i,SV699: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5325]) ).
thf(5603,plain,
! [SV62: $i,SV1561: $i,SV1242: $i,SV700: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5326]) ).
thf(5604,plain,
! [SV1562: $i,SV63: $i,SV1243: $i,SV701: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5327]) ).
thf(5605,plain,
! [SV1244: $i,SV64: $i,SV1563: $i,SV702: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5328]) ).
thf(5606,plain,
! [SV709: $i,SV72: $i,SV1245: $i] :
( ( ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5329]) ).
thf(5607,plain,
! [SV710: $i,SV73: $i,SV1246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $false )
| ( ( ~ ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5330]) ).
thf(5608,plain,
! [SV74: $i,SV711: $i] :
( ( ( c_lessequals @ SV711 @ ( c_HOL_Ozero__class_Ozero @ SV74 ) @ SV74 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV711 @ SV74 ) @ ( c_HOL_Oone__class_Oone @ SV74 ) @ SV74 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV74 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5609,plain,
! [SV736: $i,SV99: $i,SV1261: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5338]) ).
thf(5610,plain,
! [SV739: $i,SV103: $i,SV1262: $i,SV1564: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5339]) ).
thf(5611,plain,
! [SV742: $i,SV108: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV108 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV742 @ SV108 ) @ SV108 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ SV742 @ SV108 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV108 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5341]) ).
thf(5612,plain,
! [SV743: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV109 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV109 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5342]) ).
thf(5613,plain,
! [SV1266: $i,SV113: $i,SV1565: $i,SV747: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5344]) ).
thf(5614,plain,
! [SV1267: $i,SV116: $i,SV750: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5346]) ).
thf(5615,plain,
! [SV1268: $i,SV117: $i,SV751: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5347]) ).
thf(5616,plain,
! [SV1269: $i,SV118: $i,SV752: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5348]) ).
thf(5617,plain,
! [SV1270: $i,SV753: $i,SV119: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5349]) ).
thf(5618,plain,
! [SV1271: $i,SV120: $i,SV754: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5350]) ).
thf(5619,plain,
! [SV1272: $i,SV755: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(5620,plain,
! [SV1273: $i,SV122: $i,SV756: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5352]) ).
thf(5621,plain,
! [SV1659: $i,SV1566: $i,SV151: $i,SV1282: $i,SV781: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
= $true )
| ( ( ~ ( c_lessequals @ SV1282 @ SV1659 @ SV151 )
| ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5361]) ).
thf(5622,plain,
! [SV1660: $i,SV1567: $i,SV152: $i,SV1283: $i,SV782: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 )
| ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5362]) ).
thf(5623,plain,
! [SV786: $i,SV156: $i,SV1284: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5363]) ).
thf(5624,plain,
! [SV157: $i,SV787: $i,SV1285: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5364]) ).
thf(5625,plain,
! [SV1286: $i,SV158: $i,SV1568: $i,SV788: $i] :
( ( ( ~ ( c_lessequals @ SV788 @ SV1568 @ SV158 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
= $true )
| ( ( class_Orderings_Oorder @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5365]) ).
thf(5626,plain,
! [SV1287: $i,SV159: $i,SV1569: $i,SV789: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1569 @ SV1287 @ SV159 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
= $true )
| ( ( class_Orderings_Oorder @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5366]) ).
thf(5627,plain,
! [SV1661: $i,SV160: $i,SV1570: $i,SV1288: $i,SV790: $i] :
( ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
= $true )
| ( ( ~ ( c_lessequals @ SV1661 @ SV1570 @ SV160 )
| ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5367]) ).
thf(5628,plain,
! [SV791: $i,SV161: $i,SV1289: $i,SV1571: $i] :
( ( ( ~ ( c_lessequals @ SV1571 @ SV1289 @ SV161 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
= $true )
| ( ( class_Orderings_Opreorder @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5368]) ).
thf(5629,plain,
! [SV792: $i,SV162: $i,SV1290: $i,SV1572: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV792 @ SV1572 @ SV162 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
= $true )
| ( ( class_Orderings_Opreorder @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5369]) ).
thf(5630,plain,
! [SV165: $i,SV1293: $i,SV795: $i] :
( ( ( c_lessequals @ SV795 @ SV1293 @ SV165 )
= $false )
| ( ( c_lessequals @ SV1293 @ SV795 @ SV165 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1293 @ SV165 )
= $true )
| ( ( class_Orderings_Opreorder @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5631,plain,
! [SV1662: $i,SV1573: $i,SV166: $i,SV1294: $i,SV796: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
= $true )
| ( ( ~ ( c_lessequals @ SV1294 @ SV1662 @ SV166 )
| ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5373]) ).
thf(5632,plain,
! [SV167: $i,SV1295: $i,SV797: $i] :
( ( ( c_lessequals @ SV797 @ SV1295 @ SV167 )
= $false )
| ( ( SV1295 = SV797 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1295 @ SV167 )
= $true )
| ( ( class_Orderings_Oorder @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5633,plain,
! [SV168: $i,SV1296: $i,SV798: $i] :
( ( ( c_lessequals @ SV798 @ SV1296 @ SV168 )
= $false )
| ( ( SV1296 = SV798 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV798 @ SV1296 @ SV168 )
= $true )
| ( ( class_Orderings_Oorder @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5375]) ).
thf(5634,plain,
! [SV169: $i,SV1297: $i,SV799: $i] :
( ( ( c_lessequals @ SV799 @ SV1297 @ SV169 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1297 @ SV169 )
= $true )
| ( ( SV799 = SV1297 )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5376]) ).
thf(5635,plain,
! [SV170: $i,SV1298: $i,SV800: $i] :
( ( ( c_lessequals @ SV800 @ SV1298 @ SV170 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV800 @ SV1298 @ SV170 )
= $true )
| ( ( SV800 = SV1298 )
= $true )
| ( ( class_Orderings_Olinorder @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5636,plain,
! [SV171: $i,SV1299: $i,SV801: $i] :
( ( ( c_lessequals @ SV801 @ SV1299 @ SV171 )
= $false )
| ( ( SV801 = SV1299 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV801 @ SV1299 @ SV171 )
= $true )
| ( ( class_Orderings_Oorder @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5378]) ).
thf(5637,plain,
! [SV172: $i,SV1300: $i,SV802: $i] :
( ( ( c_lessequals @ SV802 @ SV1300 @ SV172 )
= $false )
| ( ( SV802 = SV1300 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV802 @ SV1300 @ SV172 )
= $true )
| ( ( class_Orderings_Oorder @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5379]) ).
thf(5638,plain,
! [SV173: $i,SV1301: $i,SV803: $i] :
( ( ( c_lessequals @ SV803 @ SV1301 @ SV173 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV803 @ SV1301 @ SV173 )
= $true )
| ( ( SV803 = SV1301 )
= $true )
| ( ( class_Orderings_Oorder @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5380]) ).
thf(5639,plain,
! [SV174: $i,SV1302: $i,SV804: $i] :
( ( ( c_lessequals @ SV804 @ SV1302 @ SV174 )
= $false )
| ( ( SV804 = SV1302 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1302 @ SV174 )
= $true )
| ( ( class_Orderings_Oorder @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5381]) ).
thf(5640,plain,
! [SV1303: $i,SV175: $i,SV1574: $i,SV805: $i] :
( ( ( c_lessequals @ SV805 @ SV1574 @ SV175 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV805 @ SV1303 @ SV175 ) @ ( c_HOL_Oplus__class_Oplus @ SV1574 @ SV1303 @ SV175 ) @ SV175 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV175 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5382]) ).
thf(5641,plain,
! [SV1304: $i,SV176: $i,SV1575: $i,SV806: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV806 @ SV1575 @ SV176 ) @ ( c_HOL_Oplus__class_Oplus @ SV1304 @ SV1575 @ SV176 ) @ SV176 )
= $false )
| ( ( c_lessequals @ SV806 @ SV1304 @ SV176 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5642,plain,
! [SV807: $i,SV177: $i,SV1576: $i,SV1305: $i] :
( ( ( c_lessequals @ SV1305 @ SV1576 @ SV177 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1305 @ SV177 ) @ ( c_HOL_Oplus__class_Oplus @ SV807 @ SV1576 @ SV177 ) @ SV177 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV177 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5384]) ).
thf(5643,plain,
! [SV1306: $i,SV178: $i,SV808: $i,SV1577: $i] :
( ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV808 @ SV178 ) @ ( c_HOL_Oplus__class_Oplus @ SV1577 @ SV1306 @ SV178 ) @ SV178 )
= $false )
| ( ( c_lessequals @ SV808 @ SV1306 @ SV178 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5385]) ).
thf(5644,plain,
! [SV1307: $i,SV179: $i,SV1578: $i,SV809: $i] :
( ( ( c_lessequals @ SV809 @ SV1578 @ SV179 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV809 @ SV1307 @ SV179 ) @ ( c_HOL_Oplus__class_Oplus @ SV1578 @ SV1307 @ SV179 ) @ SV179 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5386]) ).
thf(5645,plain,
! [SV810: $i,SV180: $i,SV1579: $i,SV1308: $i] :
( ( ( c_lessequals @ SV1308 @ SV1579 @ SV180 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1308 @ SV180 ) @ ( c_HOL_Oplus__class_Oplus @ SV810 @ SV1579 @ SV180 ) @ SV180 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5387]) ).
thf(5646,plain,
! [SV181: $i,SV811: $i,SV1309: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1309 @ SV811 @ SV181 )
= $false )
| ( ( c_lessequals @ SV811 @ SV1309 @ SV181 )
= $false )
| ( ( class_Orderings_Opreorder @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5647,plain,
! [SV185: $i,SV815: $i,SV1311: $i] :
( ( ( c_lessequals @ SV1311 @ SV815 @ SV185 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV815 @ SV1311 @ SV185 )
= $false )
| ( ( class_Orderings_Olinorder @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5390]) ).
thf(5648,plain,
! [SV188: $i,SV818: $i,SV1314: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1314 @ SV818 @ SV188 )
= $false )
| ( ( c_lessequals @ SV818 @ SV1314 @ SV188 )
= $false )
| ( ( class_Orderings_Olinorder @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5649,plain,
! [SV189: $i,SV819: $i] :
( ( ( c_lessequals @ SV819 @ ( c_HOL_Ozero__class_Ozero @ SV189 ) @ SV189 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV819 @ SV189 ) @ ( c_HOL_Oone__class_Oone @ SV189 ) @ SV189 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV189 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5392]) ).
thf(5650,plain,
! [SV190: $i,SV820: $i] :
( ( ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5393]) ).
thf(5651,plain,
! [SV1580: $i,SV821: $i,SV1315: $i,SV191: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 ) )
= $true )
| ( ( c_lessequals @ SV821 @ SV1315 @ SV191 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5394]) ).
thf(5652,plain,
! [SV1581: $i,SV823: $i,SV1316: $i,SV193: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5395]) ).
thf(5653,plain,
! [SV1663: $i,SV1582: $i,SV194: $i,SV1317: $i,SV824: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( ~ ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5396]) ).
thf(5654,plain,
! [SV825: $i,SV195: $i,SV1318: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
= $false )
| ( ( ~ ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5655,plain,
! [SV826: $i,SV1319: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5398]) ).
thf(5656,plain,
! [SV1664: $i,SV1583: $i,SV197: $i,SV1320: $i,SV827: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( ~ ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5399]) ).
thf(5657,plain,
! [SV828: $i,SV1321: $i,SV198: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 )
= $false )
| ( ( ~ ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5400]) ).
thf(5658,plain,
! [SV829: $i,SV199: $i,SV1322: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5401]) ).
thf(5659,plain,
! [SV1665: $i,SV1584: $i,SV200: $i,SV1323: $i,SV830: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5402]) ).
thf(5660,plain,
! [SV1585: $i,SV1324: $i,SV831: $i,SV201: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
= $false )
| ( ( ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
| ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5403]) ).
thf(5661,plain,
! [SV1586: $i,SV1325: $i,SV832: $i,SV202: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5404]) ).
thf(5662,plain,
! [SV1587: $i,SV1326: $i,SV833: $i,SV203: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5405]) ).
thf(5663,plain,
! [SV1588: $i,SV1327: $i,SV834: $i,SV204: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
| ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5664,plain,
! [SV836: $i,SV208: $i,SV1589: $i,SV1328: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5407]) ).
thf(5665,plain,
! [SV1329: $i,SV209: $i,SV837: $i,SV1590: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5408]) ).
thf(5666,plain,
! [SV1591: $i,SV1330: $i,SV838: $i,SV210: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5409]) ).
thf(5667,plain,
! [SV1331: $i,SV211: $i,SV839: $i,SV1592: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5410]) ).
thf(5668,plain,
! [SV1333: $i,SV213: $i,SV841: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5412]) ).
thf(5669,plain,
! [SV228: $i,SV853: $i] :
( ( ( ~ ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5413]) ).
thf(5670,plain,
! [SV1595: $i,SV1337: $i,SV855: $i,SV231: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(5671,plain,
! [SV1596: $i,SV1338: $i,SV856: $i,SV232: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5672,plain,
! [SV1597: $i,SV1339: $i,SV857: $i,SV233: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5416]) ).
thf(5673,plain,
! [SV1598: $i,SV1340: $i,SV858: $i,SV234: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
| ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5674,plain,
! [SV863: $i,SV240: $i,SV1341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5418]) ).
thf(5675,plain,
! [SV864: $i,SV1342: $i,SV241: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5676,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5420]) ).
thf(5677,plain,
! [SV1344: $i,SV866: $i,SV243: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5421]) ).
thf(5678,plain,
! [SV867: $i,SV244: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV244 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV867 @ SV244 ) @ SV244 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV867 @ ( c_HOL_Oone__class_Oone @ SV244 ) @ SV244 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV244 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5422]) ).
thf(5679,plain,
! [SV1345: $i,SV245: $i,SV1599: $i,SV868: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5423]) ).
thf(5680,plain,
! [SV1601: $i,SV870: $i,SV1347: $i,SV247: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5425]) ).
thf(5681,plain,
! [SV871: $i,SV1602: $i,SV248: $i,SV1348: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5426]) ).
thf(5682,plain,
! [SV872: $i,SV1349: $i,SV249: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5427]) ).
thf(5683,plain,
! [SV873: $i,SV1350: $i,SV250: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5428]) ).
thf(5684,plain,
! [SV879: $i,SV257: $i,SV1352: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
= $false )
| ( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5430]) ).
thf(5685,plain,
! [SV1353: $i,SV262: $i,SV882: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5432]) ).
thf(5686,plain,
! [SV883: $i,SV1354: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5433]) ).
thf(5687,plain,
! [SV884: $i,SV1355: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5434]) ).
thf(5688,plain,
! [SV1356: $i,SV265: $i,SV885: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5435]) ).
thf(5689,plain,
! [SV1357: $i,SV266: $i,SV886: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5690,plain,
! [SV887: $i,SV1358: $i,SV267: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5691,plain,
! [SV891: $i,SV273: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV891 @ SV273 ) @ SV273 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV273 ) @ SV891 @ SV273 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV273 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5692,plain,
! [SV892: $i,SV274: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ SV892 @ SV274 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV274 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV892 @ SV274 ) @ SV274 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV274 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5439]) ).
thf(5693,plain,
! [SV1603: $i,SV1360: $i,SV896: $i,SV280: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
| ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5440]) ).
thf(5694,plain,
! [SV1361: $i,SV1604: $i,SV284: $i,SV899: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5441]) ).
thf(5695,plain,
! [SV906: $i,SV1365: $i,SV291: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 ) )
= $true )
| ( ( c_lessequals @ SV906 @ SV1365 @ SV291 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5696,plain,
! [SV907: $i,SV1366: $i,SV292: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 )
= $false )
| ( ( ~ ( c_lessequals @ SV1366 @ SV907 @ SV292 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5697,plain,
! [SV1367: $i,SV293: $i,SV908: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 ) )
= $true )
| ( ( c_lessequals @ SV908 @ SV1367 @ SV293 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5444]) ).
thf(5698,plain,
! [SV1368: $i,SV294: $i,SV909: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
= $false )
| ( ( ~ ( c_lessequals @ SV1368 @ SV909 @ SV294 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5699,plain,
! [SV910: $i,SV296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV910 @ SV296 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV296 ) @ SV910 @ SV296 ) @ SV296 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV296 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5700,plain,
! [SV911: $i,SV297: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV297 ) @ SV911 @ SV297 ) @ SV297 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV297 ) @ SV911 @ SV297 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV297 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5701,plain,
! [SV298: $i,SV912: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV912 @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV298 ) @ SV912 @ SV298 ) @ ( c_HOL_Ozero__class_Ozero @ SV298 ) @ SV298 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV298 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5702,plain,
! [SV913: $i,SV299: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV299 ) @ SV913 @ SV299 ) @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV913 @ ( c_HOL_Ozero__class_Ozero @ SV299 ) @ SV299 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV299 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5449]) ).
thf(5703,plain,
! [SV1374: $i,SV306: $i,SV1608: $i,SV920: $i] :
( ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5452]) ).
thf(5704,plain,
! [SV1379: $i,SV316: $i,SV1610: $i,SV930: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV930 @ SV1610 @ SV316 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV930 @ SV1379 @ SV316 ) @ ( c_Power_Opower__class_Opower @ SV1610 @ SV1379 @ SV316 ) @ SV316 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5705,plain,
! [SV1613: $i,SV949: $i,SV1383: $i,SV337: $i] :
( ( ( c_lessequals @ SV337 @ SV1383 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV949 @ SV1613 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV337 @ SV949 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1383 @ SV1613 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5457]) ).
thf(5706,plain,
! [SV978: $i,SV373: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV373 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV978 @ SV373 ) @ SV373 )
= $false )
| ( ( c_lessequals @ SV978 @ ( c_HOL_Oone__class_Oone @ SV373 ) @ SV373 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV373 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5707,plain,
! [SV979: $i,SV375: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV979 @ SV375 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV979 @ SV375 ) @ ( c_HOL_Oone__class_Oone @ SV375 ) @ SV375 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV375 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5708,plain,
! [SV1406: $i,SV1614: $i,SV984: $i,SV380: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV984 @ SV1614 @ SV380 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5709,plain,
! [SV381: $i,SV1407: $i,SV985: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV985 @ SV1407 @ SV381 ) @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
= $false )
| ( ( c_lessequals @ SV985 @ ( c_HOL_Ozero__class_Ozero @ SV381 ) @ SV381 )
= $true )
| ( ( SV985
= ( c_HOL_Ozero__class_Ozero @ SV381 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5467]) ).
thf(5710,plain,
! [SV1408: $i,SV986: $i,SV382: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
= $true )
| ( ( ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
| ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5468]) ).
thf(5711,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5469]) ).
thf(5712,plain,
! [SV1005: $i,SV1415: $i,SV406: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5471]) ).
thf(5713,plain,
! [SV407: $i,SV1006: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1006 @ SV407 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1006 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV407 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5472]) ).
thf(5714,plain,
! [SV408: $i,SV1007: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1007 @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1007 @ SV408 ) @ ( c_HOL_Ozero__class_Ozero @ SV408 ) @ SV408 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV408 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5473]) ).
thf(5715,plain,
! [SV1615: $i,SV1010: $i,SV1416: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV411 @ SV1416 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1010 @ SV1615 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV411 @ SV1010 @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ SV1416 @ SV1615 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5716,plain,
! [SV1668: $i,SV1616: $i,SV412: $i,SV1417: $i,SV1011: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 )
| ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5476]) ).
thf(5717,plain,
! [SV413: $i,SV1012: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5477]) ).
thf(5718,plain,
! [SV1019: $i,SV422: $i,SV1422: $i,SV1617: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1617 @ SV1422 @ SV422 )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1422 @ SV422 ) @ SV1617 @ SV422 )
= ( c_Divides_Odiv__class_Omod @ SV1019 @ SV1617 @ SV422 ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV422 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5482]) ).
thf(5719,plain,
! [SV1029: $i,SV1425: $i,SV432: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5720,plain,
! [SV1030: $i,SV433: $i,SV1426: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5484]) ).
thf(5721,plain,
! [SV434: $i,SV1427: $i,SV1031: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5485]) ).
thf(5722,plain,
! [SV435: $i,SV1428: $i,SV1032: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
| ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5486]) ).
thf(5723,plain,
! [SV1433: $i,SV440: $i,SV1037: $i,SV1618: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1037 @ SV440 ) @ ( c_HOL_Oplus__class_Oplus @ SV1618 @ SV1433 @ SV440 ) @ SV440 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1037 @ SV1433 @ SV440 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5488]) ).
thf(5724,plain,
! [SV1038: $i,SV441: $i,SV1619: $i,SV1434: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1434 @ SV1619 @ SV441 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1434 @ SV441 ) @ ( c_HOL_Oplus__class_Oplus @ SV1038 @ SV1619 @ SV441 ) @ SV441 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5489]) ).
thf(5725,plain,
! [SV1039: $i,SV442: $i,SV1620: $i,SV1435: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1435 @ SV1620 @ SV442 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1435 @ SV442 ) @ ( c_HOL_Oplus__class_Oplus @ SV1039 @ SV1620 @ SV442 ) @ SV442 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV442 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5490]) ).
thf(5726,plain,
! [SV1436: $i,SV443: $i,SV1621: $i,SV1040: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1040 @ SV1621 @ SV443 ) @ ( c_HOL_Oplus__class_Oplus @ SV1436 @ SV1621 @ SV443 ) @ SV443 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1040 @ SV1436 @ SV443 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV443 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5727,plain,
! [SV1437: $i,SV444: $i,SV1622: $i,SV1041: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1041 @ SV1622 @ SV444 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1041 @ SV1437 @ SV444 ) @ ( c_HOL_Oplus__class_Oplus @ SV1622 @ SV1437 @ SV444 ) @ SV444 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5492]) ).
thf(5728,plain,
! [SV1438: $i,SV445: $i,SV1623: $i,SV1042: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1042 @ SV1623 @ SV445 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1042 @ SV1438 @ SV445 ) @ ( c_HOL_Oplus__class_Oplus @ SV1623 @ SV1438 @ SV445 ) @ SV445 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5493]) ).
thf(5729,plain,
! [SV1043: $i,SV446: $i,SV1439: $i] :
( ( ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $false )
| ( ( ~ ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5730,plain,
! [SV1044: $i,SV447: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV1044 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1044 @ SV447 ) @ ( c_HOL_Oone__class_Oone @ SV447 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV447 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5731,plain,
! [SV459: $i,SV1056: $i,SV1442: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1442 @ SV1056 @ SV459 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1056 @ SV1442 @ SV459 )
= $false )
| ( ( class_Orderings_Opreorder @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5496]) ).
thf(5732,plain,
! [SV1057: $i,SV1443: $i,SV460: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1443 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV460 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1443 @ SV1057 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV460 @ SV1057 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5497]) ).
thf(5733,plain,
! [SV1058: $i,SV1444: $i,SV461: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1444 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1444 @ SV1058 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1058 @ SV1444 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV461 @ SV1058 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5498]) ).
thf(5734,plain,
! [SV462: $i,SV1059: $i,SV1445: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1445 @ SV1059 @ SV462 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1059 @ SV1445 @ SV462 )
= $false )
| ( ( class_Orderings_Opreorder @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5735,plain,
! [SV463: $i,SV1060: $i,SV1446: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1446 @ SV1060 @ SV463 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1060 @ SV1446 @ SV463 )
= $false )
| ( ( class_Orderings_Olinorder @ SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5500]) ).
thf(5736,plain,
! [SV464: $i,SV1061: $i,SV1447: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1447 @ SV1061 @ SV464 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1061 @ SV1447 @ SV464 )
= $false )
| ( ( class_Orderings_Oorder @ SV464 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5501]) ).
thf(5737,plain,
! [SV1448: $i,SV1062: $i,SV465: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
= $true )
| ( ( ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5502]) ).
thf(5738,plain,
! [SV1449: $i,SV466: $i,SV1063: $i] :
( ( ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
= $true )
| ( ( ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5503]) ).
thf(5739,plain,
! [SV1450: $i,SV1064: $i,SV467: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5504]) ).
thf(5740,plain,
! [SV1451: $i,SV468: $i,SV1065: $i] :
( ( ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5505]) ).
thf(5741,plain,
! [SV1624: $i,SV1452: $i,SV1066: $i,SV469: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5506]) ).
thf(5742,plain,
! [SV1625: $i,SV1453: $i,SV1067: $i,SV470: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5743,plain,
! [SV471: $i,SV1454: $i,SV1068: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
| ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5508]) ).
thf(5744,plain,
! [SV472: $i,SV1455: $i,SV1069: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
= $true )
| ( ( ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5509]) ).
thf(5745,plain,
! [SV1456: $i,SV473: $i,SV1070: $i] :
( ( ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5510]) ).
thf(5746,plain,
! [SV1457: $i,SV474: $i,SV1071: $i] :
( ( ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5511]) ).
thf(5747,plain,
! [SV1458: $i,SV475: $i,SV1072: $i] :
( ( ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5512]) ).
thf(5748,plain,
! [SV1459: $i,SV476: $i,SV1073: $i] :
( ( ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5513]) ).
thf(5749,plain,
! [SV1669: $i,SV1627: $i,SV489: $i,SV1464: $i,SV1086: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
= $true )
| ( ( ~ ( c_lessequals @ SV1464 @ SV1669 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5519]) ).
thf(5750,plain,
! [SV1670: $i,SV1628: $i,SV490: $i,SV1465: $i,SV1087: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
= $true )
| ( ( ~ ( c_lessequals @ SV1465 @ SV1670 @ tc_nat )
| ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5520]) ).
thf(5751,plain,
! [SV491: $i,SV1088: $i,SV1629: $i,SV1466: $i] :
( ( ( c_lessequals @ SV1466 @ SV1629 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1466 @ SV491 ) @ ( c_Power_Opower__class_Opower @ SV1088 @ SV1629 @ SV491 ) @ SV491 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV491 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5521]) ).
thf(5752,plain,
! [SV492: $i,SV1089: $i,SV1467: $i,SV1630: $i] :
( ( ( ~ ( c_lessequals @ SV1630 @ SV1467 @ tc_nat ) )
= $true )
| ( ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SV1630 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1630 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5522]) ).
thf(5753,plain,
! [SV493: $i,SV1090: $i,SV1468: $i] :
( ( ( c_lessequals @ SV1468 @ SV1090 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1468 @ SV493 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5523]) ).
thf(5754,plain,
! [SV494: $i,SV1469: $i,SV1091: $i] :
( ( ( c_lessequals @ SV1091 @ SV1469 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1091 @ SV494 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5755,plain,
! [SV1101: $i,SV1475: $i,SV504: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1475 @ SV1101 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5756,plain,
! [SV1102: $i,SV1476: $i,SV505: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1102 @ SV1476 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(5757,plain,
! [SV517: $i,SV1114: $i] :
( ( ( c_lessequals @ SV1114 @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV517 ) @ SV1114 @ SV517 ) @ ( c_HOL_Ozero__class_Ozero @ SV517 ) @ SV517 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV517 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV517 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5530]) ).
thf(5758,plain,
! [SV1115: $i,SV518: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV518 ) @ SV1115 @ SV518 ) @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
= $false )
| ( ( c_lessequals @ SV1115 @ ( c_HOL_Ozero__class_Ozero @ SV518 ) @ SV518 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV518 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(5759,plain,
! [SV1116: $i,SV519: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ SV1116 @ SV519 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV519 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV519 ) @ SV1116 @ SV519 ) @ SV519 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV519 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5532]) ).
thf(5760,plain,
! [SV1117: $i,SV520: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ SV520 ) @ SV1117 @ SV520 ) @ SV520 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV520 ) @ SV1117 @ SV520 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV520 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV520 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5761,plain,
! [SV1484: $i,SV1631: $i,SV522: $i,SV1119: $i] :
( ( ( ~ ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5535]) ).
thf(5762,plain,
! [SV1120: $i,SV523: $i,SV1632: $i,SV1485: $i] :
( ( ( ~ ( c_lessequals @ SV1485 @ SV1632 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5536]) ).
thf(5763,plain,
! [SV1486: $i,SV524: $i,SV1121: $i,SV1633: $i] :
( ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 ) )
= $true )
| ( ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5537]) ).
thf(5764,plain,
! [SV1487: $i,SV525: $i,SV1122: $i,SV1634: $i] :
( ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 ) )
= $true )
| ( ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5538]) ).
thf(5765,plain,
! [SV526: $i,SV1123: $i,SV1488: $i,SV1635: $i] :
( ( ( ~ ( c_lessequals @ SV1635 @ SV1488 @ tc_nat ) )
= $true )
| ( ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SV1635 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1635 @ SV526 ) @ SV526 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV526 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5539]) ).
thf(5766,plain,
! [SV1490: $i,SV529: $i,SV1636: $i,SV1126: $i] :
( ( ( ~ ( c_lessequals @ SV1126 @ SV1636 @ SV529 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1636 @ SV1490 @ SV529 ) )
= $true )
| ( ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
= $true )
| ( ( class_Orderings_Oorder @ SV529 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5540]) ).
thf(5767,plain,
! [SV1127: $i,SV530: $i,SV1491: $i,SV1637: $i] :
( ( ( ~ ( c_lessequals @ SV1637 @ SV1491 @ SV530 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1127 @ SV1637 @ SV530 ) )
= $true )
| ( ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
= $true )
| ( ( class_Orderings_Opreorder @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5541]) ).
thf(5768,plain,
! [SV1638: $i,SV1494: $i,SV1133: $i,SV538: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1494 @ SV1638 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV538 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5544]) ).
thf(5769,plain,
! [SV541: $i,SV1495: $i,SV1136: $i] :
( ( ( c_lessequals @ SV1136 @ SV1495 @ SV541 )
= $false )
| ( ( ~ ( c_lessequals @ SV1495 @ SV1136 @ SV541 ) )
= $true )
| ( ( SV1136 = SV1495 )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5545]) ).
thf(5770,plain,
! [SV543: $i,SV1138: $i,SV1496: $i] :
( ( ( c_lessequals @ SV1496 @ SV1138 @ SV543 )
= $false )
| ( ( ~ ( c_lessequals @ SV1138 @ SV1496 @ SV543 ) )
= $true )
| ( ( SV1138 = SV1496 )
= $true )
| ( ( class_Orderings_Oorder @ SV543 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5546]) ).
thf(5771,plain,
! [SV544: $i,SV1139: $i,SV1497: $i] :
( ( ( c_lessequals @ SV1497 @ SV1139 @ SV544 )
= $false )
| ( ( ~ ( c_lessequals @ SV1139 @ SV1497 @ SV544 ) )
= $true )
| ( ( SV1139 = SV1497 )
= $true )
| ( ( class_Orderings_Oorder @ SV544 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5547]) ).
thf(5772,plain,
! [SV1639: $i,SV1498: $i,SV1140: $i,SV545: $i] :
( ( ( class_Ring__and__Field_Odivision__by__zero @ SV545 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ SV1140 @ SV1498 @ SV545 ) @ SV1639 @ SV545 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1140 @ SV1639 @ SV545 ) @ ( c_Power_Opower__class_Opower @ SV1498 @ SV1639 @ SV545 ) @ SV545 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5548]) ).
thf(5773,plain,
! [SV549: $i,SV1144: $i,SV1502: $i] :
( ( ( c_lessequals @ SV1502 @ SV1144 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1502 @ SV549 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5550]) ).
thf(5774,plain,
! [SV550: $i,SV1503: $i,SV1145: $i] :
( ( ( c_lessequals @ SV1145 @ SV1503 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1145 @ SV550 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV550 @ SV1503 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5551]) ).
thf(5775,plain,
! [SV1642: $i,SV577: $i,SV1508: $i,SV1152: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1508 @ SV577 )
= ( c_HOL_Oplus__class_Oplus @ SV1152 @ SV1642 @ SV577 ) )
= $false )
| ( ( SV1508 = SV1642 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5553]) ).
thf(5776,plain,
! [SV1678: $i,SV1671: $i,SV1643: $i,SV1511: $i,SV1161: $i,SV588: $i] :
( ( ( class_Divides_Osemiring__div @ SV588 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(5777,plain,
! [SV1672: $i,SV1644: $i,SV590: $i,SV1512: $i,SV1162: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
!= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
= $true )
| ( ( ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5558]) ).
thf(5778,plain,
! [SV593: $i,SV1513: $i,SV1165: $i] :
( ( ( SV1165 = SV1513 )
= $true )
| ( ( ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
| ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) ) )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5559]) ).
thf(5779,plain,
! [SV1645: $i,SV595: $i,SV1514: $i,SV1167: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1167 @ SV1514 @ SV595 )
= ( c_HOL_Oplus__class_Oplus @ SV1645 @ SV1514 @ SV595 ) )
= $false )
| ( ( SV1167 = SV1645 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV595 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5560]) ).
thf(5780,plain,
! [SV1679: $i,SV1673: $i,SV1646: $i,SV1515: $i,SV1168: $i,SV596: $i] :
( ( ( class_Divides_Oring__div @ SV596 )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(5781,plain,
! [SV1647: $i,SV598: $i,SV1516: $i,SV1170: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( ( SV1170 = SV1647 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5562]) ).
thf(5782,plain,
! [SV1674: $i,SV1648: $i,SV599: $i,SV1517: $i,SV1171: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
!= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
= $true )
| ( ( ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SV1674 @ SV1648 @ SV599 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5563]) ).
thf(5783,plain,
! [SV1649: $i,SV601: $i,SV1173: $i,SV1518: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1518 @ SV1173 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV601 @ SV1649 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV601 @ SV1173 @ tc_nat )
= ( c_HOL_Oplus__class_Oplus @ SV1518 @ SV1649 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5564]) ).
thf(5784,plain,
! [SV602: $i,SV1174: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1174 @ SV602 )
= ( c_HOL_Oone__class_Oone @ SV602 ) )
= $false )
| ( ( SV1174
= ( c_HOL_Oone__class_Oone @ SV602 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV602 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV602 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5565]) ).
thf(5785,plain,
! [SV1650: $i,SV1519: $i,SV603: $i,SV1175: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1175 @ SV1175 @ SV603 )
= ( c_HOL_Ominus__class_Ominus @ SV1519 @ SV1650 @ SV603 ) )
= $false )
| ( ( SV1519 = SV1650 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV603 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5566]) ).
thf(5786,plain,
! [SV1675: $i,SV604: $i,SV1651: $i,SV1520: $i,SV1176: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1651 @ SV604 ) @ SV604 )
!= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1675 @ SV604 ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SV1651 @ SV604 )
= SV1675 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(5787,plain,
! [SV1652: $i,SV608: $i,SV1523: $i,SV1180: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1523 @ SV608 )
= ( c_HOL_Oplus__class_Oplus @ SV1180 @ SV1652 @ SV608 ) )
= $false )
| ( ( SV1523 = SV1652 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV608 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5569]) ).
thf(5788,plain,
! [SV1676: $i,SV1653: $i,SV610: $i,SV1524: $i,SV1181: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
!= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5570]) ).
thf(5789,plain,
! [SV1525: $i,SV611: $i,SV1182: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
!= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
= $true )
| ( ( SV1182 = SV1525 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV611 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5571]) ).
thf(5790,plain,
! [SV1654: $i,SV614: $i,SV1526: $i,SV1185: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
| ( SV1526 = SV1654 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5572]) ).
thf(5791,plain,
! [SV617: $i,SV1527: $i,SV1187: $i] :
( ( ( SV1187
!= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
= $true )
| ( ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV617 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV617 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5573]) ).
thf(5792,plain,
! [SV620: $i,SV1528: $i,SV1190: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
!= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
= $true )
| ( ( SV1190 = SV1528 )
= $true )
| ( ( class_Int_Onumber__ring @ SV620 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV620 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5574]) ).
thf(5793,plain,
! [SV624: $i,SV1193: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1193 @ SV624 )
= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
= $false )
| ( ( SV1193
= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV624 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(5794,plain,
! [SV1677: $i,SV1655: $i,SV628: $i,SV1530: $i,SV1196: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
!= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5576]) ).
thf(5795,plain,
! [SV1200: $i,SV1532: $i,SV632: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(5796,plain,
! [SV1201: $i,SV633: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV633 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV633 )
| ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(5797,plain,
! [SV1656: $i,SV1533: $i,SV1202: $i,SV634: $i] :
( ( ( class_Int_Onumber__ring @ SV634 )
= $false )
| ( ( ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
| ( SV1533 = SV1656 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5580]) ).
thf(5798,plain,
! [SV1534: $i,SV635: $i,SV1203: $i] :
( ( ( ~ ( c_lessequals @ SV1203 @ SV635 @ tc_nat ) )
= $true )
| ( ( SV635 = SV1534 )
= $true )
| ( ( c_lessequals @ SV1203 @ SV1534 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5581]) ).
thf(5799,plain,
! [SV1657: $i,SV637: $i,SV1536: $i,SV1205: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1205 @ SV1536 @ SV637 )
= ( c_HOL_Ominus__class_Ominus @ SV1657 @ SV1657 @ SV637 ) )
= $false )
| ( ( SV1205 = SV1536 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(5800,plain,
! [SV1206: $i,SV1537: $i,SV638: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5583]) ).
thf(5801,plain,
! [SV1658: $i,SV639: $i,SV1538: $i,SV1207: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
= $false )
| ( ( ( SV1207 = SV1658 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5584]) ).
thf(5802,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV641 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5585]) ).
thf(5803,plain,
! [SV1211: $i,SV644: $i,SV1540: $i] :
( ( ( SV1540
= ( c_HOL_Ozero__class_Ozero @ SV644 ) )
= $true )
| ( ( SV1211 = SV1540 )
= $true )
| ( ( ( c_HOL_Oinverse__class_Odivide @ SV1211 @ SV1540 @ SV644 )
= ( c_HOL_Oone__class_Oone @ SV644 ) )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV644 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5586]) ).
thf(5804,plain,
! [SV15: $i,SV1552: $i,SV1225: $i,SV659: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5588]) ).
thf(5805,plain,
! [SV1227: $i,SV663: $i,SV22: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ SV663 @ SV22 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1227 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV22 ) @ ( c_Power_Opower__class_Opower @ SV663 @ SV1227 @ SV22 ) @ SV22 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5590]) ).
thf(5806,plain,
! [SV1228: $i,SV25: $i,SV666: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV666 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1228 @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV666 @ SV1228 @ SV25 ) @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5591]) ).
thf(5807,plain,
! [SV1553: $i,SV667: $i,SV26: $i,SV1229: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5592]) ).
thf(5808,plain,
! [SV30: $i,SV671: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV671 @ SV30 ) @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV30 )
= $false )
| ( ( c_lessequals @ SV671 @ ( c_HOL_Ozero__class_Ozero @ SV30 ) @ SV30 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV671 @ SV30 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV30 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5809,plain,
! [SV677: $i,SV36: $i,SV1231: $i,SV1555: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
= $true )
| ( ( class_Orderings_Opreorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5810,plain,
! [SV1232: $i,SV37: $i,SV1556: $i,SV678: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5599]) ).
thf(5811,plain,
! [SV50: $i,SV1558: $i,SV1234: $i,SV688: $i] :
( ( ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
= $true )
| ( ( ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5600]) ).
thf(5812,plain,
! [SV51: $i,SV1559: $i,SV1235: $i,SV689: $i] :
( ( ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
= $true )
| ( ( ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5601]) ).
thf(5813,plain,
! [SV1241: $i,SV61: $i,SV1560: $i,SV699: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5602]) ).
thf(5814,plain,
! [SV62: $i,SV1561: $i,SV1242: $i,SV700: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5603]) ).
thf(5815,plain,
! [SV1562: $i,SV63: $i,SV1243: $i,SV701: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5604]) ).
thf(5816,plain,
! [SV1244: $i,SV64: $i,SV1563: $i,SV702: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5605]) ).
thf(5817,plain,
! [SV1245: $i,SV72: $i,SV709: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV709 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $false )
| ( ( c_lessequals @ SV1245 @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV709 @ SV1245 @ SV72 ) @ ( c_HOL_Ozero__class_Ozero @ SV72 ) @ SV72 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5606]) ).
thf(5818,plain,
! [SV1246: $i,SV73: $i,SV710: $i] :
( ( ( c_lessequals @ SV710 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1246 @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV710 @ SV1246 @ SV73 ) @ ( c_HOL_Ozero__class_Ozero @ SV73 ) @ SV73 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5607]) ).
thf(5819,plain,
! [SV736: $i,SV1261: $i,SV99: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV1261 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV99 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1261 @ SV736 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV736 @ SV1261 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV99 @ SV736 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5609]) ).
thf(5820,plain,
! [SV739: $i,SV103: $i,SV1262: $i,SV1564: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5610]) ).
thf(5821,plain,
! [SV743: $i,SV109: $i] :
( ( ( ~ ( class_Power_Opower @ SV109 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5612]) ).
thf(5822,plain,
! [SV1266: $i,SV113: $i,SV1565: $i,SV747: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5613]) ).
thf(5823,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5614]) ).
thf(5824,plain,
! [SV751: $i,SV1268: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5615]) ).
thf(5825,plain,
! [SV752: $i,SV1269: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5616]) ).
thf(5826,plain,
! [SV1270: $i,SV119: $i,SV753: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5617]) ).
thf(5827,plain,
! [SV754: $i,SV120: $i,SV1271: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5618]) ).
thf(5828,plain,
! [SV755: $i,SV1272: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5619]) ).
thf(5829,plain,
! [SV1273: $i,SV756: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5620]) ).
thf(5830,plain,
! [SV1566: $i,SV781: $i,SV151: $i,SV1659: $i,SV1282: $i] :
( ( ( ~ ( c_lessequals @ SV1282 @ SV1659 @ SV151 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(5831,plain,
! [SV1567: $i,SV782: $i,SV152: $i,SV1660: $i,SV1283: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5622]) ).
thf(5832,plain,
! [SV156: $i,SV1284: $i,SV786: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV786 @ SV1284 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1284 @ SV156 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV1284 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV156 @ SV786 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5623]) ).
thf(5833,plain,
! [SV157: $i,SV1285: $i,SV787: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV787 @ SV1285 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV787 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1285 @ SV157 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV157 @ SV787 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(5834,plain,
! [SV1286: $i,SV158: $i,SV1568: $i,SV788: $i] :
( ( ( c_lessequals @ SV788 @ SV1568 @ SV158 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
= $true )
| ( ( class_Orderings_Oorder @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5625]) ).
thf(5835,plain,
! [SV1287: $i,SV159: $i,SV1569: $i,SV789: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 )
= $false )
| ( ( ~ ( c_lessequals @ SV1569 @ SV1287 @ SV159 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
= $true )
| ( ( class_Orderings_Oorder @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(5836,plain,
! [SV1288: $i,SV790: $i,SV160: $i,SV1570: $i,SV1661: $i] :
( ( ( ~ ( c_lessequals @ SV1661 @ SV1570 @ SV160 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 ) )
= $true )
| ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5627]) ).
thf(5837,plain,
! [SV791: $i,SV161: $i,SV1289: $i,SV1571: $i] :
( ( ( c_lessequals @ SV1571 @ SV1289 @ SV161 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
= $true )
| ( ( class_Orderings_Opreorder @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5628]) ).
thf(5838,plain,
! [SV792: $i,SV162: $i,SV1290: $i,SV1572: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 )
= $false )
| ( ( ~ ( c_lessequals @ SV792 @ SV1572 @ SV162 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
= $true )
| ( ( class_Orderings_Opreorder @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5629]) ).
thf(5839,plain,
! [SV1573: $i,SV796: $i,SV166: $i,SV1662: $i,SV1294: $i] :
( ( ( ~ ( c_lessequals @ SV1294 @ SV1662 @ SV166 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5631]) ).
thf(5840,plain,
! [SV190: $i,SV820: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV820 @ SV190 ) @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV190 )
= $false )
| ( ( c_lessequals @ SV820 @ ( c_HOL_Ozero__class_Ozero @ SV190 ) @ SV190 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV190 ) @ SV820 @ SV190 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV190 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5650]) ).
thf(5841,plain,
! [SV1580: $i,SV821: $i,SV1315: $i,SV191: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 ) )
= $true )
| ( ( c_lessequals @ SV821 @ SV1315 @ SV191 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5651]) ).
thf(5842,plain,
! [SV1581: $i,SV823: $i,SV1316: $i,SV193: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5652]) ).
thf(5843,plain,
! [SV1582: $i,SV824: $i,SV194: $i,SV1317: $i,SV1663: $i] :
( ( ( ~ ( c_lessequals @ SV1663 @ SV1317 @ SV194 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5653]) ).
thf(5844,plain,
! [SV1318: $i,SV195: $i,SV825: $i] :
( ( ( c_lessequals @ SV825 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1318 @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ SV195 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV195 ) @ ( c_HOL_Oinverse__class_Odivide @ SV825 @ SV1318 @ SV195 ) @ SV195 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5654]) ).
thf(5845,plain,
! [SV1319: $i,SV826: $i,SV196: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV826 @ SV196 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ SV1319 @ SV196 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV196 ) @ ( c_HOL_Oinverse__class_Odivide @ SV826 @ SV1319 @ SV196 ) @ SV196 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5655]) ).
thf(5846,plain,
! [SV1583: $i,SV827: $i,SV197: $i,SV1320: $i,SV1664: $i] :
( ( ( ~ ( c_lessequals @ SV1664 @ SV1320 @ SV197 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5656]) ).
thf(5847,plain,
! [SV1321: $i,SV198: $i,SV828: $i] :
( ( ( c_lessequals @ SV828 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV1321 @ SV198 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV828 @ SV1321 @ SV198 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5657]) ).
thf(5848,plain,
! [SV1322: $i,SV829: $i,SV199: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV829 @ SV199 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV829 @ SV1322 @ SV199 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5658]) ).
thf(5849,plain,
! [SV1584: $i,SV830: $i,SV200: $i,SV1323: $i,SV1665: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5659]) ).
thf(5850,plain,
! [SV201: $i,SV1585: $i,SV1324: $i,SV831: $i] :
( ( ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
= $true )
| ( ( ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5660]) ).
thf(5851,plain,
! [SV1586: $i,SV1325: $i,SV202: $i,SV832: $i] :
( ( ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5661]) ).
thf(5852,plain,
! [SV1587: $i,SV203: $i,SV1326: $i,SV833: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
| ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5662]) ).
thf(5853,plain,
! [SV1588: $i,SV1327: $i,SV834: $i,SV204: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5663]) ).
thf(5854,plain,
! [SV836: $i,SV208: $i,SV1589: $i,SV1328: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(5855,plain,
! [SV1329: $i,SV209: $i,SV837: $i,SV1590: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5665]) ).
thf(5856,plain,
! [SV1591: $i,SV1330: $i,SV838: $i,SV210: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5666]) ).
thf(5857,plain,
! [SV1331: $i,SV211: $i,SV839: $i,SV1592: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5667]) ).
thf(5858,plain,
! [SV1333: $i,SV841: $i,SV213: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5668]) ).
thf(5859,plain,
! [SV228: $i,SV853: $i] :
( ( ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5669]) ).
thf(5860,plain,
! [SV1595: $i,SV1337: $i,SV855: $i,SV231: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5670]) ).
thf(5861,plain,
! [SV1596: $i,SV232: $i,SV1338: $i,SV856: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
| ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5671]) ).
thf(5862,plain,
! [SV1597: $i,SV1339: $i,SV233: $i,SV857: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5672]) ).
thf(5863,plain,
! [SV234: $i,SV1598: $i,SV1340: $i,SV858: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5673]) ).
thf(5864,plain,
! [SV1341: $i,SV240: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1341 @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ SV240 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV240 ) @ ( c_HOL_Oinverse__class_Odivide @ SV863 @ SV1341 @ SV240 ) @ SV240 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5674]) ).
thf(5865,plain,
! [SV1342: $i,SV864: $i,SV241: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV864 @ SV241 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ SV1342 @ SV241 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV241 ) @ ( c_HOL_Oinverse__class_Odivide @ SV864 @ SV1342 @ SV241 ) @ SV241 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(5866,plain,
! [SV865: $i,SV1343: $i,SV242: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5676]) ).
thf(5867,plain,
! [SV866: $i,SV243: $i,SV1344: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5677]) ).
thf(5868,plain,
! [SV1345: $i,SV245: $i,SV1599: $i,SV868: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(5869,plain,
! [SV1601: $i,SV870: $i,SV1347: $i,SV247: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5680]) ).
thf(5870,plain,
! [SV871: $i,SV1602: $i,SV248: $i,SV1348: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5681]) ).
thf(5871,plain,
! [SV1349: $i,SV872: $i,SV249: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV872 @ SV249 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ SV1349 @ SV249 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV249 ) @ ( c_HOL_Oplus__class_Oplus @ SV872 @ SV1349 @ SV249 ) @ SV249 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5682]) ).
thf(5872,plain,
! [SV1350: $i,SV873: $i,SV250: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV873 @ SV250 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ SV1350 @ SV250 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV250 ) @ ( c_HOL_Oplus__class_Oplus @ SV873 @ SV1350 @ SV250 ) @ SV250 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5683]) ).
thf(5873,plain,
! [SV257: $i,SV879: $i,SV1352: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5684]) ).
thf(5874,plain,
! [SV1353: $i,SV882: $i,SV262: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV262 ) @ SV882 @ SV262 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV882 @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV882 @ ( c_Suc @ SV1353 ) @ SV262 ) @ ( c_HOL_Oone__class_Oone @ SV262 ) @ SV262 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5685]) ).
thf(5875,plain,
! [SV883: $i,SV263: $i,SV1354: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1354 @ SV263 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV883 @ SV263 ) @ SV263 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV1354 @ SV263 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV883 @ SV1354 @ SV263 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5686]) ).
thf(5876,plain,
! [SV264: $i,SV884: $i,SV1355: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1355 @ SV884 @ SV264 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV1355 @ SV264 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV884 @ SV264 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1355 @ SV264 ) @ SV264 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5687]) ).
thf(5877,plain,
! [SV885: $i,SV265: $i,SV1356: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV1356 @ SV265 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV885 @ SV265 ) @ SV265 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV885 @ ( c_HOL_Ozero__class_Ozero @ SV265 ) @ SV265 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV885 @ SV1356 @ SV265 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5688]) ).
thf(5878,plain,
! [SV266: $i,SV886: $i,SV1357: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1357 @ SV886 @ SV266 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV886 @ ( c_HOL_Ozero__class_Ozero @ SV266 ) @ SV266 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ SV886 @ SV266 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1357 @ SV266 ) @ SV266 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5689]) ).
thf(5879,plain,
! [SV1358: $i,SV887: $i,SV267: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV887 @ SV267 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ SV1358 @ SV267 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV267 ) @ ( c_HOL_Oplus__class_Oplus @ SV887 @ SV1358 @ SV267 ) @ SV267 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV267 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5690]) ).
thf(5880,plain,
! [SV280: $i,SV1603: $i,SV1360: $i,SV896: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
= $true )
| ( ( ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5693]) ).
thf(5881,plain,
! [SV1361: $i,SV1604: $i,SV284: $i,SV899: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(5882,plain,
! [SV906: $i,SV291: $i,SV1365: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1365 @ SV291 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV906 @ SV291 ) @ SV291 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV291 ) @ SV1365 @ SV291 )
= $false )
| ( ( c_lessequals @ SV906 @ SV1365 @ SV291 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(5883,plain,
! [SV292: $i,SV907: $i,SV1366: $i] :
( ( ( c_lessequals @ SV1366 @ SV907 @ SV292 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV292 ) @ SV1366 @ SV292 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV907 @ SV292 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1366 @ SV292 ) @ SV292 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(5884,plain,
! [SV908: $i,SV293: $i,SV1367: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV1367 @ SV293 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV908 @ SV293 ) @ SV293 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV908 @ ( c_HOL_Ozero__class_Ozero @ SV293 ) @ SV293 )
= $false )
| ( ( c_lessequals @ SV908 @ SV1367 @ SV293 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(5885,plain,
! [SV294: $i,SV909: $i,SV1368: $i] :
( ( ( c_lessequals @ SV1368 @ SV909 @ SV294 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV909 @ ( c_HOL_Ozero__class_Ozero @ SV294 ) @ SV294 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ SV909 @ SV294 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1368 @ SV294 ) @ SV294 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(5886,plain,
! [SV1374: $i,SV306: $i,SV1608: $i,SV920: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5703]) ).
thf(5887,plain,
! [SV1406: $i,SV1614: $i,SV984: $i,SV380: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
= $false )
| ( ( ~ ( c_lessequals @ SV984 @ SV1614 @ SV380 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(5888,plain,
! [SV986: $i,SV382: $i,SV1408: $i] :
( ( ( ~ ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5710]) ).
thf(5889,plain,
! [SV987: $i,SV1409: $i,SV383: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5711]) ).
thf(5890,plain,
! [SV1415: $i,SV1005: $i,SV406: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1005 @ SV406 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV1415 @ SV406 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ ( c_HOL_Oplus__class_Oplus @ SV1005 @ SV1415 @ SV406 ) @ SV406 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5712]) ).
thf(5891,plain,
! [SV1616: $i,SV1011: $i,SV412: $i,SV1668: $i,SV1417: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5716]) ).
thf(5892,plain,
! [SV413: $i,SV1012: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(5893,plain,
! [SV1425: $i,SV432: $i,SV1029: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1029 @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV1425 @ SV432 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1029 @ SV1425 @ SV432 ) @ ( c_HOL_Ozero__class_Ozero @ SV432 ) @ SV432 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(5894,plain,
! [SV1426: $i,SV1030: $i,SV433: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV1030 @ SV433 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1426 @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1030 @ SV1426 @ SV433 ) @ ( c_HOL_Ozero__class_Ozero @ SV433 ) @ SV433 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV433 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(5895,plain,
! [SV1031: $i,SV434: $i,SV1427: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5721]) ).
thf(5896,plain,
! [SV1032: $i,SV1428: $i,SV435: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5722]) ).
thf(5897,plain,
! [SV1439: $i,SV446: $i,SV1043: $i] :
( ( ( c_lessequals @ SV1043 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $false )
| ( ( c_lessequals @ SV1439 @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV1043 @ SV1439 @ SV446 ) @ ( c_HOL_Ozero__class_Ozero @ SV446 ) @ SV446 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(5898,plain,
! [SV1448: $i,SV465: $i,SV1062: $i] :
( ( ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5737]) ).
thf(5899,plain,
! [SV1063: $i,SV466: $i,SV1449: $i] :
( ( ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 ) )
= $true )
| ( ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV466 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5738]) ).
thf(5900,plain,
! [SV1064: $i,SV1450: $i,SV467: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5739]) ).
thf(5901,plain,
! [SV1451: $i,SV1065: $i,SV468: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 ) )
= $true )
| ( ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV468 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5740]) ).
thf(5902,plain,
! [SV1624: $i,SV469: $i,SV1452: $i,SV1066: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
= $true )
| ( ( ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
| ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5903,plain,
! [SV1625: $i,SV470: $i,SV1453: $i,SV1067: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
| ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(5904,plain,
! [SV1068: $i,SV1454: $i,SV471: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5743]) ).
thf(5905,plain,
! [SV1069: $i,SV472: $i,SV1455: $i] :
( ( ( ~ ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5744]) ).
thf(5906,plain,
! [SV1456: $i,SV1070: $i,SV473: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 ) )
= $true )
| ( ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5745]) ).
thf(5907,plain,
! [SV1071: $i,SV1457: $i,SV474: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 ) )
= $true )
| ( ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5746]) ).
thf(5908,plain,
! [SV1072: $i,SV1458: $i,SV475: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 ) )
= $true )
| ( ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5747]) ).
thf(5909,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 ) )
= $true )
| ( ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5748]) ).
thf(5910,plain,
! [SV1627: $i,SV489: $i,SV1086: $i,SV1669: $i,SV1464: $i] :
( ( ( ~ ( c_lessequals @ SV1464 @ SV1669 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5749]) ).
thf(5911,plain,
! [SV490: $i,SV1628: $i,SV1087: $i,SV1670: $i,SV1465: $i] :
( ( ( ~ ( c_lessequals @ SV1465 @ SV1670 @ tc_nat ) )
= $true )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5750]) ).
thf(5912,plain,
! [SV492: $i,SV1089: $i,SV1467: $i,SV1630: $i] :
( ( ( c_lessequals @ SV1630 @ SV1467 @ tc_nat )
= $false )
| ( ( SV1089
= ( c_HOL_Ozero__class_Ozero @ SV492 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ SV1089 @ SV492 ) @ ( c_HOL_Ominus__class_Ominus @ SV1467 @ SV1630 @ tc_nat ) @ SV492 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1630 @ SV492 ) @ ( c_Power_Opower__class_Opower @ SV1089 @ SV1467 @ SV492 ) @ SV492 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV492 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5752]) ).
thf(5913,plain,
! [SV1090: $i,SV493: $i,SV1468: $i] :
( ( ( c_lessequals @ SV1468 @ SV493 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1468 @ SV1090 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV493 @ SV1468 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1090 @ SV1468 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV493 @ SV1090 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5753]) ).
thf(5914,plain,
! [SV1469: $i,SV494: $i,SV1091: $i] :
( ( ( c_lessequals @ SV1091 @ SV494 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1091 @ SV1469 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV494 @ SV1469 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV494 @ SV1091 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1469 @ SV1091 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5754]) ).
thf(5915,plain,
! [SV1475: $i,SV1101: $i,SV504: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ ( c_HOL_Ominus__class_Ominus @ SV1101 @ SV1475 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1475 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1475 @ SV1101 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV504 @ SV1101 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(5916,plain,
! [SV1102: $i,SV1476: $i,SV505: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ ( c_HOL_Ominus__class_Ominus @ SV1476 @ SV1102 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1476 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1102 @ SV1476 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV505 @ SV1102 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(5917,plain,
! [SV1484: $i,SV1631: $i,SV522: $i,SV1119: $i] :
( ( ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
| ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5761]) ).
thf(5918,plain,
! [SV1120: $i,SV523: $i,SV1632: $i,SV1485: $i] :
( ( ( c_lessequals @ SV1485 @ SV1632 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5762]) ).
thf(5919,plain,
! [SV1486: $i,SV524: $i,SV1121: $i,SV1633: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 ) )
= $true )
| ( ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5763]) ).
thf(5920,plain,
! [SV1487: $i,SV525: $i,SV1122: $i,SV1634: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 ) )
= $true )
| ( ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5764]) ).
thf(5921,plain,
! [SV526: $i,SV1123: $i,SV1488: $i,SV1635: $i] :
( ( ( c_lessequals @ SV1635 @ SV1488 @ tc_nat )
= $false )
| ( ( SV1123
= ( c_HOL_Ozero__class_Ozero @ SV526 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1123 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ SV1635 @ tc_nat ) @ SV526 )
= ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1488 @ SV526 ) @ ( c_Power_Opower__class_Opower @ SV1123 @ SV1635 @ SV526 ) @ SV526 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV526 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5765]) ).
thf(5922,plain,
! [SV1490: $i,SV529: $i,SV1636: $i,SV1126: $i] :
( ( ( c_lessequals @ SV1126 @ SV1636 @ SV529 )
= $false )
| ( ( ~ ( c_lessequals @ SV1636 @ SV1490 @ SV529 ) )
= $true )
| ( ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
= $true )
| ( ( class_Orderings_Oorder @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5766]) ).
thf(5923,plain,
! [SV1127: $i,SV530: $i,SV1491: $i,SV1637: $i] :
( ( ( c_lessequals @ SV1637 @ SV1491 @ SV530 )
= $false )
| ( ( ~ ( c_lessequals @ SV1127 @ SV1637 @ SV530 ) )
= $true )
| ( ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
= $true )
| ( ( class_Orderings_Opreorder @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5767]) ).
thf(5924,plain,
! [SV1638: $i,SV1494: $i,SV1133: $i,SV538: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
= $false )
| ( ( ~ ( c_lessequals @ SV1494 @ SV1638 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5768]) ).
thf(5925,plain,
! [SV541: $i,SV1136: $i,SV1495: $i] :
( ( ( c_lessequals @ SV1495 @ SV1136 @ SV541 )
= $false )
| ( ( c_lessequals @ SV1136 @ SV1495 @ SV541 )
= $false )
| ( ( SV1136 = SV1495 )
= $true )
| ( ( class_Orderings_Oorder @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(5926,plain,
! [SV543: $i,SV1496: $i,SV1138: $i] :
( ( ( c_lessequals @ SV1138 @ SV1496 @ SV543 )
= $false )
| ( ( c_lessequals @ SV1496 @ SV1138 @ SV543 )
= $false )
| ( ( SV1138 = SV1496 )
= $true )
| ( ( class_Orderings_Oorder @ SV543 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(5927,plain,
! [SV544: $i,SV1497: $i,SV1139: $i] :
( ( ( c_lessequals @ SV1139 @ SV1497 @ SV544 )
= $false )
| ( ( c_lessequals @ SV1497 @ SV1139 @ SV544 )
= $false )
| ( ( SV1139 = SV1497 )
= $true )
| ( ( class_Orderings_Oorder @ SV544 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5771]) ).
thf(5928,plain,
! [SV1144: $i,SV549: $i,SV1502: $i] :
( ( ( c_lessequals @ SV1502 @ SV549 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1502 @ SV1144 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV549 @ SV1502 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1144 @ SV1502 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV549 @ SV1144 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(5929,plain,
! [SV1503: $i,SV550: $i,SV1145: $i] :
( ( ( c_lessequals @ SV1145 @ SV550 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1145 @ SV1503 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV550 @ SV1503 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV550 @ SV1145 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1503 @ SV1145 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5774]) ).
thf(5930,plain,
! [SV1678: $i,SV1671: $i,SV1643: $i,SV588: $i,SV1511: $i,SV1161: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5776]) ).
thf(5931,plain,
! [SV1672: $i,SV1644: $i,SV590: $i,SV1512: $i,SV1162: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
= $false )
| ( ( ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
| ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5777]) ).
thf(5932,plain,
! [SV1165: $i,SV593: $i,SV1513: $i] :
( ( ( SV1513
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
= $true )
| ( ( SV1165
= ( c_HOL_Ozero__class_Ozero @ SV593 ) )
= $true )
| ( ( SV1165 = SV1513 )
= $true )
| ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1165 @ SV593 )
= ( c_HOL_Oinverse__class_Oinverse @ SV1513 @ SV593 ) )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV593 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5778]) ).
thf(5933,plain,
! [SV1679: $i,SV1673: $i,SV1646: $i,SV596: $i,SV1515: $i,SV1168: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
= $true )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) )
= $true )
| ( ( class_Divides_Oring__div @ SV596 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5780]) ).
thf(5934,plain,
! [SV598: $i,SV1516: $i,SV1647: $i,SV1170: $i] :
( ( ( SV1170 = SV1647 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(5935,plain,
! [SV1674: $i,SV1648: $i,SV599: $i,SV1517: $i,SV1171: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
= $false )
| ( ( ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
| ~ ( c_lessequals @ SV1674 @ SV1648 @ SV599 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(5936,plain,
! [SV1675: $i,SV604: $i,SV1651: $i,SV1520: $i,SV1176: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1651 @ SV604 ) @ SV604 )
= ( c_HOL_Oplus__class_Oplus @ SV1520 @ SV1675 @ SV604 ) )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1176 @ SV1651 @ SV604 )
= SV1675 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5786]) ).
thf(5937,plain,
! [SV1676: $i,SV1653: $i,SV610: $i,SV1524: $i,SV1181: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
| ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5938,plain,
! [SV1525: $i,SV611: $i,SV1182: $i] :
( ( ( ( c_HOL_Oinverse__class_Oinverse @ SV1182 @ SV611 )
= ( c_HOL_Oinverse__class_Oinverse @ SV1525 @ SV611 ) )
= $false )
| ( ( SV1182 = SV1525 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV611 )
= $false )
| ( ( class_Ring__and__Field_Odivision__ring @ SV611 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5939,plain,
! [SV1654: $i,SV1526: $i,SV1185: $i,SV614: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 ) )
= $true )
| ( ( SV1526 = SV1654 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5790]) ).
thf(5940,plain,
! [SV617: $i,SV1527: $i,SV1187: $i] :
( ( ( SV1187
= ( c_HOL_Oplus__class_Oplus @ SV1187 @ SV1527 @ SV617 ) )
= $false )
| ( ( SV1527
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV617 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV617 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5791]) ).
thf(5941,plain,
! [SV620: $i,SV1528: $i,SV1190: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1190 @ SV1528 @ SV620 )
= ( c_HOL_Ozero__class_Ozero @ SV620 ) )
= $false )
| ( ( SV1190 = SV1528 )
= $true )
| ( ( class_Int_Onumber__ring @ SV620 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV620 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5792]) ).
thf(5942,plain,
! [SV1677: $i,SV1655: $i,SV628: $i,SV1530: $i,SV1196: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
| ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5794]) ).
thf(5943,plain,
! [SV1200: $i,SV1532: $i,SV632: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
| ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5795]) ).
thf(5944,plain,
! [SV1201: $i,SV633: $i] :
( ( ( ~ ( class_Power_Opower @ SV633 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(5945,plain,
! [SV1656: $i,SV634: $i,SV1533: $i,SV1202: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
!= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
= $true )
| ( ( SV1533 = SV1656 )
= $true )
| ( ( class_Int_Onumber__ring @ SV634 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5797]) ).
thf(5946,plain,
! [SV1534: $i,SV635: $i,SV1203: $i] :
( ( ( c_lessequals @ SV1203 @ SV635 @ tc_nat )
= $false )
| ( ( SV635 = SV1534 )
= $true )
| ( ( c_lessequals @ SV1203 @ SV1534 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV635 @ SV1203 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1534 @ SV1203 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5798]) ).
thf(5947,plain,
! [SV1206: $i,SV1537: $i,SV638: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) ) )
= $true )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5800]) ).
thf(5948,plain,
! [SV1538: $i,SV639: $i,SV1658: $i,SV1207: $i] :
( ( ( SV1207 = SV1658 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5801]) ).
thf(5949,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV641 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV641 )
| ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5802]) ).
thf(5950,plain,
! [SV1225: $i,SV15: $i,SV1552: $i,SV659: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5804]) ).
thf(5951,plain,
! [SV1229: $i,SV1553: $i,SV667: $i,SV26: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5807]) ).
thf(5952,plain,
! [SV1231: $i,SV36: $i,SV1555: $i,SV677: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1555 @ SV36 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1555 @ SV1231 @ SV36 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV677 @ SV1231 @ SV36 )
= $true )
| ( ( class_Orderings_Opreorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5809]) ).
thf(5953,plain,
! [SV678: $i,SV37: $i,SV1232: $i,SV1556: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1556 @ SV1232 @ SV37 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1556 @ SV37 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV678 @ SV1232 @ SV37 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5810]) ).
thf(5954,plain,
! [SV1234: $i,SV50: $i,SV1558: $i,SV688: $i] :
( ( ( ~ ( c_lessequals @ SV688 @ SV1558 @ SV50 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true )
| ( ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5811]) ).
thf(5955,plain,
! [SV1559: $i,SV51: $i,SV1235: $i,SV689: $i] :
( ( ( ~ ( c_lessequals @ SV689 @ SV1235 @ SV51 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true )
| ( ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5812]) ).
thf(5956,plain,
! [SV1560: $i,SV61: $i,SV1241: $i,SV699: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1241 @ SV61 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ SV1560 @ SV61 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV699 @ ( c_Divides_Odiv__class_Omod @ SV1241 @ SV1560 @ SV61 ) @ SV61 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5813]) ).
thf(5957,plain,
! [SV1242: $i,SV62: $i,SV1561: $i,SV700: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1561 @ SV62 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ ( c_Divides_Odiv__class_Omod @ SV1242 @ SV1561 @ SV62 ) @ SV62 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV700 @ SV1242 @ SV62 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5814]) ).
thf(5958,plain,
! [SV1243: $i,SV63: $i,SV1562: $i,SV701: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1562 @ SV63 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ SV1243 @ SV63 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV701 @ ( c_Divides_Odiv__class_Omod @ SV1243 @ SV1562 @ SV63 ) @ SV63 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(5959,plain,
! [SV64: $i,SV1563: $i,SV1244: $i,SV702: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ ( c_Divides_Odiv__class_Omod @ SV1244 @ SV1563 @ SV64 ) @ SV64 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1563 @ SV64 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV702 @ SV1244 @ SV64 )
= $true )
| ( ( class_Divides_Osemiring__div @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5816]) ).
thf(5960,plain,
! [SV1262: $i,SV103: $i,SV1564: $i,SV739: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1564 @ SV103 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1564 @ SV1262 @ SV103 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV739 @ SV1262 @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(5961,plain,
! [SV743: $i,SV109: $i] :
( ( ( class_Power_Opower @ SV109 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
| ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(5962,plain,
! [SV1565: $i,SV747: $i,SV1266: $i,SV113: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1266 @ SV113 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ SV1565 @ SV113 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ ( c_HOL_Oplus__class_Oplus @ SV1266 @ SV1565 @ SV113 ) @ SV113 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5822]) ).
thf(5963,plain,
! [SV1267: $i,SV750: $i,SV116: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ ( c_HOL_Oinverse__class_Odivide @ SV750 @ SV1267 @ SV116 ) @ SV116 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV750 @ SV116 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV750 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV116 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5823]) ).
thf(5964,plain,
! [SV751: $i,SV1268: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1268 @ SV751 @ SV117 ) @ SV117 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV1268 @ SV117 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV751 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV117 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5824]) ).
thf(5965,plain,
! [SV1269: $i,SV752: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ ( c_HOL_Oinverse__class_Odivide @ SV752 @ SV1269 @ SV118 ) @ SV118 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV1269 @ SV118 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV752 @ ( c_HOL_Ozero__class_Ozero @ SV118 ) @ SV118 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV118 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5825]) ).
thf(5966,plain,
! [SV119: $i,SV753: $i,SV1270: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1270 @ SV753 @ SV119 ) @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV753 @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV119 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV119 ) @ SV753 @ SV119 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV119 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(5967,plain,
! [SV120: $i,SV1271: $i,SV754: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV754 @ SV1271 @ SV120 ) @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1271 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV754 @ ( c_HOL_Ozero__class_Ozero @ SV120 ) @ SV120 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV120 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(5968,plain,
! [SV121: $i,SV755: $i,SV1272: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1272 @ SV755 @ SV121 ) @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV121 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV1272 @ SV121 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV121 ) @ SV755 @ SV121 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV121 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5828]) ).
thf(5969,plain,
! [SV122: $i,SV1273: $i,SV756: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV756 @ SV1273 @ SV122 ) @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV756 @ SV122 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV756 @ ( c_HOL_Ozero__class_Ozero @ SV122 ) @ SV122 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV122 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(5970,plain,
! [SV1566: $i,SV781: $i,SV151: $i,SV1659: $i,SV1282: $i] :
( ( ( c_lessequals @ SV1282 @ SV1659 @ SV151 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5830]) ).
thf(5971,plain,
! [SV1567: $i,SV782: $i,SV152: $i,SV1660: $i,SV1283: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 )
= $false )
| ( ( ~ ( c_lessequals @ SV782 @ SV1567 @ SV152 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(5972,plain,
! [SV788: $i,SV158: $i,SV1286: $i,SV1568: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1568 @ SV1286 @ SV158 )
= $false )
| ( ( c_lessequals @ SV788 @ SV1568 @ SV158 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV788 @ SV1286 @ SV158 )
= $true )
| ( ( class_Orderings_Oorder @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5834]) ).
thf(5973,plain,
! [SV789: $i,SV159: $i,SV1287: $i,SV1569: $i] :
( ( ( c_lessequals @ SV1569 @ SV1287 @ SV159 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1569 @ SV159 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV789 @ SV1287 @ SV159 )
= $true )
| ( ( class_Orderings_Oorder @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5835]) ).
thf(5974,plain,
! [SV1288: $i,SV790: $i,SV160: $i,SV1570: $i,SV1661: $i] :
( ( ( c_lessequals @ SV1661 @ SV1570 @ SV160 )
= $false )
| ( ( ~ ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 ) )
= $true )
| ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5836]) ).
thf(5975,plain,
! [SV1289: $i,SV161: $i,SV1571: $i,SV791: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1571 @ SV161 )
= $false )
| ( ( c_lessequals @ SV1571 @ SV1289 @ SV161 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV791 @ SV1289 @ SV161 )
= $true )
| ( ( class_Orderings_Opreorder @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5837]) ).
thf(5976,plain,
! [SV1290: $i,SV162: $i,SV1572: $i,SV792: $i] :
( ( ( c_lessequals @ SV792 @ SV1572 @ SV162 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1572 @ SV1290 @ SV162 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1290 @ SV162 )
= $true )
| ( ( class_Orderings_Opreorder @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5838]) ).
thf(5977,plain,
! [SV1573: $i,SV796: $i,SV166: $i,SV1662: $i,SV1294: $i] :
( ( ( c_lessequals @ SV1294 @ SV1662 @ SV166 )
= $false )
| ( ( ~ ( c_lessequals @ SV796 @ SV1573 @ SV166 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5839]) ).
thf(5978,plain,
! [SV1315: $i,SV191: $i,SV1580: $i,SV821: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV821 @ ( c_Suc @ SV1580 ) @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1315 @ ( c_Suc @ SV1580 ) @ SV191 ) @ SV191 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV191 ) @ SV1315 @ SV191 )
= $false )
| ( ( c_lessequals @ SV821 @ SV1315 @ SV191 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5841]) ).
thf(5979,plain,
! [SV1316: $i,SV193: $i,SV1581: $i,SV823: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV823 @ SV1581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV1316 @ SV1581 @ SV193 ) @ SV193 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV193 ) @ SV1316 @ SV193 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1316 @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5842]) ).
thf(5980,plain,
! [SV1582: $i,SV824: $i,SV194: $i,SV1317: $i,SV1663: $i] :
( ( ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
| ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(5981,plain,
! [SV1583: $i,SV827: $i,SV197: $i,SV1320: $i,SV1664: $i] :
( ( ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
| ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5982,plain,
! [SV1584: $i,SV830: $i,SV200: $i,SV1323: $i,SV1665: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
| ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(5983,plain,
! [SV1324: $i,SV1585: $i,SV201: $i,SV831: $i] :
( ( ( ~ ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true )
| ( ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5850]) ).
thf(5984,plain,
! [SV1586: $i,SV832: $i,SV202: $i,SV1325: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
| ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true )
| ( ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5851]) ).
thf(5985,plain,
! [SV833: $i,SV1326: $i,SV1587: $i,SV203: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5852]) ).
thf(5986,plain,
! [SV834: $i,SV1588: $i,SV204: $i,SV1327: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
| ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5853]) ).
thf(5987,plain,
! [SV1589: $i,SV1328: $i,SV836: $i,SV208: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV208 ) @ SV836 @ SV208 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1328 @ SV1589 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV836 @ SV1328 @ SV208 ) @ ( c_Power_Opower__class_Opower @ SV836 @ SV1589 @ SV208 ) @ SV208 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(5988,plain,
! [SV1329: $i,SV837: $i,SV1590: $i,SV209: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV209 ) @ SV1590 @ SV209 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1590 @ SV837 @ SV209 ) @ ( c_Power_Opower__class_Opower @ SV1590 @ SV1329 @ SV209 ) @ SV209 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1329 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5855]) ).
thf(5989,plain,
! [SV838: $i,SV210: $i,SV1591: $i,SV1330: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1330 @ SV1591 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV210 ) @ SV838 @ SV210 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV838 @ SV1330 @ SV210 ) @ ( c_Power_Opower__class_Opower @ SV838 @ SV1591 @ SV210 ) @ SV210 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5856]) ).
thf(5990,plain,
! [SV1331: $i,SV839: $i,SV1592: $i,SV211: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV211 ) @ SV1592 @ SV211 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1592 @ SV839 @ SV211 ) @ ( c_Power_Opower__class_Opower @ SV1592 @ SV1331 @ SV211 ) @ SV211 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1331 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(5991,plain,
! [SV841: $i,SV1333: $i,SV213: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1333 @ SV841 @ SV213 ) @ SV213 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV841 @ SV213 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV841 @ ( c_HOL_Ozero__class_Ozero @ SV213 ) @ SV213 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV213 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(5992,plain,
! [SV853: $i,SV228: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ SV853 @ SV228 )
= $false )
| ( ( c_lessequals @ SV853 @ ( c_HOL_Oone__class_Oone @ SV228 ) @ SV228 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV228 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV853 @ SV228 ) @ SV228 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV228 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(5993,plain,
! [SV855: $i,SV1595: $i,SV231: $i,SV1337: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5860]) ).
thf(5994,plain,
! [SV856: $i,SV1338: $i,SV1596: $i,SV232: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5861]) ).
thf(5995,plain,
! [SV1597: $i,SV857: $i,SV233: $i,SV1339: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
| ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5862]) ).
thf(5996,plain,
! [SV1340: $i,SV1598: $i,SV234: $i,SV858: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5863]) ).
thf(5997,plain,
! [SV865: $i,SV1343: $i,SV242: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5866]) ).
thf(5998,plain,
! [SV866: $i,SV243: $i,SV1344: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5867]) ).
thf(5999,plain,
! [SV1599: $i,SV245: $i,SV1345: $i,SV868: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1345 @ SV245 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ SV1599 @ SV245 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV868 @ ( c_HOL_Oplus__class_Oplus @ SV1345 @ SV1599 @ SV245 ) @ SV245 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV245 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(6000,plain,
! [SV1347: $i,SV247: $i,SV1601: $i,SV870: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV870 @ SV1601 @ SV247 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV247 ) @ SV1347 @ SV247 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV870 @ SV1347 @ SV247 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1601 @ SV1347 @ SV247 ) @ SV247 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(6001,plain,
! [SV1348: $i,SV248: $i,SV871: $i,SV1602: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1602 @ SV871 @ SV248 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1348 @ ( c_HOL_Ozero__class_Ozero @ SV248 ) @ SV248 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV871 @ SV1348 @ SV248 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1602 @ SV1348 @ SV248 ) @ SV248 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5870]) ).
thf(6002,plain,
! [SV257: $i,SV1352: $i,SV879: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV879 @ SV1352 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV879 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1352 @ SV257 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV1352 @ tc_nat )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV257 @ SV879 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5873]) ).
thf(6003,plain,
! [SV1360: $i,SV280: $i,SV1603: $i,SV896: $i] :
( ( ( ~ ( c_lessequals @ SV896 @ SV1603 @ SV280 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5880]) ).
thf(6004,plain,
! [SV1361: $i,SV1604: $i,SV899: $i,SV284: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5881]) ).
thf(6005,plain,
! [SV1608: $i,SV306: $i,SV1374: $i,SV920: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1374 @ SV306 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ SV1608 @ SV306 )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV920 @ ( c_HOL_Ominus__class_Ominus @ SV1374 @ SV1608 @ SV306 ) @ SV306 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__ring__1 @ SV306 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5886]) ).
thf(6006,plain,
! [SV1406: $i,SV380: $i,SV1614: $i,SV984: $i] :
( ( ( c_lessequals @ SV984 @ SV1614 @ SV380 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV380 ) @ SV984 @ SV380 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV984 @ SV1406 @ SV380 ) @ ( c_Power_Opower__class_Opower @ SV1614 @ SV1406 @ SV380 ) @ SV380 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5887]) ).
thf(6007,plain,
! [SV986: $i,SV382: $i,SV1408: $i] :
( ( ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
= $false )
| ( ( ~ ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5888]) ).
thf(6008,plain,
! [SV987: $i,SV1409: $i,SV383: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5889]) ).
thf(6009,plain,
! [SV1616: $i,SV1011: $i,SV412: $i,SV1668: $i,SV1417: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5891]) ).
thf(6010,plain,
! [SV1012: $i,SV413: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV413 ) @ SV1012 @ SV413 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1012 @ ( c_HOL_Oone__class_Oone @ SV413 ) @ SV413 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV413 ) @ ( c_HOL_Oinverse__class_Oinverse @ SV1012 @ SV413 ) @ SV413 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV413 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV413 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(6011,plain,
! [SV1031: $i,SV434: $i,SV1427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5895]) ).
thf(6012,plain,
! [SV1032: $i,SV1428: $i,SV435: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5896]) ).
thf(6013,plain,
! [SV465: $i,SV1062: $i,SV1448: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1448 @ SV1062 @ SV465 ) @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
= $false )
| ( ( c_lessequals @ SV1062 @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV465 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV465 ) @ SV1062 @ SV465 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV465 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5898]) ).
thf(6014,plain,
! [SV466: $i,SV1449: $i,SV1063: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1063 @ SV1449 @ SV466 ) @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
= $false )
| ( ( c_lessequals @ SV1449 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
= $true )
| ( ( c_lessequals @ SV1063 @ ( c_HOL_Ozero__class_Ozero @ SV466 ) @ SV466 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV466 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV466 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5899]) ).
thf(6015,plain,
! [SV467: $i,SV1064: $i,SV1450: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1450 @ SV1064 @ SV467 ) @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV467 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1450 @ SV467 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV467 ) @ SV1064 @ SV467 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV467 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5900]) ).
thf(6016,plain,
! [SV468: $i,SV1451: $i,SV1065: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1065 @ SV1451 @ SV468 ) @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV1065 @ SV468 )
= $true )
| ( ( c_lessequals @ SV1065 @ ( c_HOL_Ozero__class_Ozero @ SV468 ) @ SV468 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV468 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV468 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5901]) ).
thf(6017,plain,
! [SV1066: $i,SV1624: $i,SV469: $i,SV1452: $i] :
( ( ( ~ ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5902]) ).
thf(6018,plain,
! [SV1625: $i,SV1067: $i,SV1453: $i,SV470: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5903]) ).
thf(6019,plain,
! [SV1068: $i,SV1454: $i,SV471: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
= $false )
| ( ( ~ ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5904]) ).
thf(6020,plain,
! [SV1069: $i,SV472: $i,SV1455: $i] :
( ( ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5905]) ).
thf(6021,plain,
! [SV1070: $i,SV1456: $i,SV473: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1456 @ SV1070 @ SV473 ) @ SV473 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV1070 @ SV473 )
= $true )
| ( ( c_lessequals @ SV1070 @ ( c_HOL_Ozero__class_Ozero @ SV473 ) @ SV473 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV473 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5906]) ).
thf(6022,plain,
! [SV1457: $i,SV1071: $i,SV474: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1071 @ SV1457 @ SV474 ) @ SV474 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV1457 @ SV474 )
= $true )
| ( ( c_lessequals @ SV1071 @ ( c_HOL_Ozero__class_Ozero @ SV474 ) @ SV474 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV474 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5907]) ).
thf(6023,plain,
! [SV1072: $i,SV1458: $i,SV475: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1458 @ SV1072 @ SV475 ) @ SV475 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV1458 @ SV475 )
= $true )
| ( ( c_lessequals @ SV1072 @ ( c_HOL_Ozero__class_Ozero @ SV475 ) @ SV475 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV475 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(6024,plain,
! [SV1459: $i,SV1073: $i,SV476: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1073 @ SV1459 @ SV476 ) @ SV476 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV1073 @ SV476 )
= $true )
| ( ( c_lessequals @ SV1073 @ ( c_HOL_Ozero__class_Ozero @ SV476 ) @ SV476 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV476 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5909]) ).
thf(6025,plain,
! [SV1627: $i,SV489: $i,SV1086: $i,SV1669: $i,SV1464: $i] :
( ( ( c_lessequals @ SV1464 @ SV1669 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(6026,plain,
! [SV490: $i,SV1628: $i,SV1087: $i,SV1670: $i,SV1465: $i] :
( ( ( c_lessequals @ SV1465 @ SV1670 @ tc_nat )
= $false )
| ( ( ~ ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 ) )
= $true )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5911]) ).
thf(6027,plain,
! [SV1484: $i,SV1631: $i,SV1119: $i,SV522: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5917]) ).
thf(6028,plain,
! [SV1632: $i,SV1485: $i,SV1120: $i,SV523: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV523 ) @ SV1120 @ SV523 )
= $false )
| ( ( c_lessequals @ SV1485 @ SV1632 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1485 @ SV523 ) @ ( c_Power_Opower__class_Opower @ SV1120 @ SV1632 @ SV523 ) @ SV523 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5918]) ).
thf(6029,plain,
! [SV1486: $i,SV1121: $i,SV1633: $i,SV524: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV524 ) @ SV1633 @ SV524 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1121 @ SV524 ) @ ( c_Power_Opower__class_Opower @ SV1633 @ SV1486 @ SV524 ) @ SV524 )
= $false )
| ( ( c_lessequals @ SV1121 @ SV1486 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5919]) ).
thf(6030,plain,
! [SV1487: $i,SV1122: $i,SV1634: $i,SV525: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV525 ) @ SV1634 @ SV525 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1122 @ SV525 ) @ ( c_Power_Opower__class_Opower @ SV1634 @ SV1487 @ SV525 ) @ SV525 )
= $false )
| ( ( c_lessequals @ SV1122 @ SV1487 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5920]) ).
thf(6031,plain,
! [SV1126: $i,SV529: $i,SV1490: $i,SV1636: $i] :
( ( ( c_lessequals @ SV1636 @ SV1490 @ SV529 )
= $false )
| ( ( c_lessequals @ SV1126 @ SV1636 @ SV529 )
= $false )
| ( ( c_lessequals @ SV1126 @ SV1490 @ SV529 )
= $true )
| ( ( class_Orderings_Oorder @ SV529 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5922]) ).
thf(6032,plain,
! [SV1491: $i,SV530: $i,SV1637: $i,SV1127: $i] :
( ( ( c_lessequals @ SV1127 @ SV1637 @ SV530 )
= $false )
| ( ( c_lessequals @ SV1637 @ SV1491 @ SV530 )
= $false )
| ( ( c_lessequals @ SV1127 @ SV1491 @ SV530 )
= $true )
| ( ( class_Orderings_Opreorder @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5923]) ).
thf(6033,plain,
! [SV1133: $i,SV538: $i,SV1638: $i,SV1494: $i] :
( ( ( c_lessequals @ SV1494 @ SV1638 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV538 ) @ SV1133 @ SV538 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1494 @ SV538 ) @ ( c_Power_Opower__class_Opower @ SV1133 @ SV1638 @ SV538 ) @ SV538 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV538 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5924]) ).
thf(6034,plain,
! [SV1678: $i,SV1671: $i,SV1643: $i,SV588: $i,SV1511: $i,SV1161: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) ) )
= $true )
| ( ( class_Divides_Osemiring__div @ SV588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5930]) ).
thf(6035,plain,
! [SV1162: $i,SV1512: $i,SV590: $i,SV1644: $i,SV1672: $i] :
( ( ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
= $true )
| ( ( ~ ( c_lessequals @ SV1512 @ SV1162 @ SV590 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5931]) ).
thf(6036,plain,
! [SV1679: $i,SV1673: $i,SV1646: $i,SV596: $i,SV1515: $i,SV1168: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
= $false )
| ( ( ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
| ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) ) )
= $true )
| ( ( class_Divides_Oring__div @ SV596 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5933]) ).
thf(6037,plain,
! [SV1170: $i,SV1647: $i,SV598: $i,SV1516: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( SV1170 = SV1647 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5934]) ).
thf(6038,plain,
! [SV1648: $i,SV1674: $i,SV599: $i,SV1171: $i,SV1517: $i] :
( ( ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
= $true )
| ( ( ~ ( c_lessequals @ SV1674 @ SV1648 @ SV599 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5935]) ).
thf(6039,plain,
! [SV1524: $i,SV1181: $i,SV610: $i,SV1676: $i,SV1653: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5937]) ).
thf(6040,plain,
! [SV1654: $i,SV1526: $i,SV1185: $i,SV614: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV614 ) @ SV1185 @ SV614 )
= $false )
| ( ( SV1526 = SV1654 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1185 @ SV1526 @ SV614 )
= ( c_Power_Opower__class_Opower @ SV1185 @ SV1654 @ SV614 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5939]) ).
thf(6041,plain,
! [SV1677: $i,SV1655: $i,SV628: $i,SV1530: $i,SV1196: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5942]) ).
thf(6042,plain,
! [SV1532: $i,SV1200: $i,SV632: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 ) )
= $true )
| ( ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5943]) ).
thf(6043,plain,
! [SV1201: $i,SV633: $i] :
( ( ( class_Power_Opower @ SV633 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
!= ( c_HOL_Ozero__class_Ozero @ SV633 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5944]) ).
thf(6044,plain,
! [SV1656: $i,SV634: $i,SV1533: $i,SV1202: $i] :
( ( ( ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1533 @ SV634 )
= ( c_HOL_Oplus__class_Oplus @ SV1202 @ SV1656 @ SV634 ) )
= $false )
| ( ( SV1533 = SV1656 )
= $true )
| ( ( class_Int_Onumber__ring @ SV634 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5945]) ).
thf(6045,plain,
! [SV1537: $i,SV1206: $i,SV638: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 ) )
= $true )
| ( ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5947]) ).
thf(6046,plain,
! [SV1538: $i,SV1207: $i,SV1658: $i,SV639: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true )
| ( ( SV1207 = SV1658 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5948]) ).
thf(6047,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( ~ ( class_Power_Opower @ SV641 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5949]) ).
thf(6048,plain,
! [SV1225: $i,SV15: $i,SV1552: $i,SV659: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5950]) ).
thf(6049,plain,
! [SV1229: $i,SV1553: $i,SV667: $i,SV26: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5951]) ).
thf(6050,plain,
! [SV1234: $i,SV50: $i,SV1558: $i,SV688: $i] :
( ( ( c_lessequals @ SV688 @ SV1558 @ SV50 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 ) )
= $true )
| ( ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5954]) ).
thf(6051,plain,
! [SV1559: $i,SV51: $i,SV1235: $i,SV689: $i] :
( ( ( c_lessequals @ SV689 @ SV1235 @ SV51 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 ) )
= $true )
| ( ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5955]) ).
thf(6052,plain,
! [SV743: $i,SV109: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV743 @ SV109 )
= ( c_HOL_Ozero__class_Ozero @ SV109 ) )
= $true )
| ( ( SV743
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV109 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5961]) ).
thf(6053,plain,
! [SV1659: $i,SV1282: $i,SV151: $i,SV1566: $i,SV781: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV781 @ SV1566 @ SV151 )
= $false )
| ( ( c_lessequals @ SV1282 @ SV1659 @ SV151 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV781 @ SV1282 @ SV151 ) @ ( c_HOL_Oplus__class_Oplus @ SV1566 @ SV1659 @ SV151 ) @ SV151 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5970]) ).
thf(6054,plain,
! [SV1660: $i,SV1283: $i,SV152: $i,SV1567: $i,SV782: $i] :
( ( ( c_lessequals @ SV782 @ SV1567 @ SV152 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1283 @ SV1660 @ SV152 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV782 @ SV1283 @ SV152 ) @ ( c_HOL_Oplus__class_Oplus @ SV1567 @ SV1660 @ SV152 ) @ SV152 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5971]) ).
thf(6055,plain,
! [SV1570: $i,SV160: $i,SV1661: $i,SV1288: $i,SV790: $i] :
( ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1661 @ SV160 ) @ SV160 )
= $false )
| ( ( c_lessequals @ SV1661 @ SV1570 @ SV160 )
= $false )
| ( ( c_lessequals @ SV790 @ ( c_HOL_Oplus__class_Oplus @ SV1288 @ SV1570 @ SV160 ) @ SV160 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5974]) ).
thf(6056,plain,
! [SV1662: $i,SV1294: $i,SV166: $i,SV1573: $i,SV796: $i] :
( ( ( c_lessequals @ SV796 @ SV1573 @ SV166 )
= $false )
| ( ( c_lessequals @ SV1294 @ SV1662 @ SV166 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ SV796 @ SV1294 @ SV166 ) @ ( c_HOL_Oplus__class_Oplus @ SV1573 @ SV1662 @ SV166 ) @ SV166 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5977]) ).
thf(6057,plain,
! [SV1317: $i,SV1582: $i,SV824: $i,SV1663: $i,SV194: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5980]) ).
thf(6058,plain,
! [SV1320: $i,SV1583: $i,SV827: $i,SV1664: $i,SV197: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5981]) ).
thf(6059,plain,
! [SV1323: $i,SV1584: $i,SV830: $i,SV1665: $i,SV200: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5982]) ).
thf(6060,plain,
! [SV1324: $i,SV1585: $i,SV201: $i,SV831: $i] :
( ( ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 ) )
= $true )
| ( ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5983]) ).
thf(6061,plain,
! [SV1586: $i,SV832: $i,SV1325: $i,SV202: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
= $true )
| ( ( ~ ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5984]) ).
thf(6062,plain,
! [SV833: $i,SV1326: $i,SV1587: $i,SV203: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(6063,plain,
! [SV834: $i,SV1588: $i,SV1327: $i,SV204: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5986]) ).
thf(6064,plain,
! [SV855: $i,SV1595: $i,SV1337: $i,SV231: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5993]) ).
thf(6065,plain,
! [SV856: $i,SV1338: $i,SV1596: $i,SV232: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5994]) ).
thf(6066,plain,
! [SV1597: $i,SV857: $i,SV1339: $i,SV233: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5995]) ).
thf(6067,plain,
! [SV1340: $i,SV1598: $i,SV234: $i,SV858: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5996]) ).
thf(6068,plain,
! [SV1343: $i,SV865: $i,SV242: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV865 @ SV242 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ SV1343 @ SV242 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV242 ) @ ( c_HOL_Oinverse__class_Odivide @ SV865 @ SV1343 @ SV242 ) @ SV242 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV242 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5997]) ).
thf(6069,plain,
! [SV1344: $i,SV243: $i,SV866: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV866 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1344 @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ SV243 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV243 ) @ ( c_HOL_Oinverse__class_Odivide @ SV866 @ SV1344 @ SV243 ) @ SV243 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV243 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5998]) ).
thf(6070,plain,
! [SV1360: $i,SV280: $i,SV1603: $i,SV896: $i] :
( ( ( c_lessequals @ SV896 @ SV1603 @ SV280 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6003]) ).
thf(6071,plain,
! [SV1361: $i,SV1604: $i,SV899: $i,SV284: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6004]) ).
thf(6072,plain,
! [SV1408: $i,SV382: $i,SV986: $i] :
( ( ( c_lessequals @ SV986 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
= $false )
| ( ( c_lessequals @ SV1408 @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ SV382 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV382 ) @ ( c_HOL_Oinverse__class_Odivide @ SV986 @ SV1408 @ SV382 ) @ SV382 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV382 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6007]) ).
thf(6073,plain,
! [SV1409: $i,SV987: $i,SV383: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV987 @ SV383 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ SV1409 @ SV383 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV383 ) @ ( c_HOL_Oinverse__class_Odivide @ SV987 @ SV1409 @ SV383 ) @ SV383 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV383 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6008]) ).
thf(6074,plain,
! [SV1668: $i,SV1417: $i,SV412: $i,SV1616: $i,SV1011: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1011 @ SV1616 @ SV412 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1417 @ SV1668 @ SV412 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ SV1011 @ SV1417 @ SV412 ) @ ( c_HOL_Oplus__class_Oplus @ SV1616 @ SV1668 @ SV412 ) @ SV412 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6009]) ).
thf(6075,plain,
! [SV1427: $i,SV1031: $i,SV434: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV1031 @ SV434 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1427 @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1031 @ SV1427 @ SV434 ) @ ( c_HOL_Ozero__class_Ozero @ SV434 ) @ SV434 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV434 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV434 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6076,plain,
! [SV1428: $i,SV435: $i,SV1032: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1032 @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV1428 @ SV435 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1032 @ SV1428 @ SV435 ) @ ( c_HOL_Ozero__class_Ozero @ SV435 ) @ SV435 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV435 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6012]) ).
thf(6077,plain,
! [SV1066: $i,SV1624: $i,SV469: $i,SV1452: $i] :
( ( ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
= $false )
| ( ( ~ ( c_lessequals @ SV1624 @ SV1066 @ SV469 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(6078,plain,
! [SV1625: $i,SV1067: $i,SV1453: $i,SV470: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
= $false )
| ( ( ~ ( c_lessequals @ SV1067 @ SV1625 @ SV470 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6079,plain,
! [SV1454: $i,SV471: $i,SV1068: $i] :
( ( ( c_lessequals @ SV1068 @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV1454 @ SV471 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1068 @ SV1454 @ SV471 ) @ ( c_HOL_Ozero__class_Ozero @ SV471 ) @ SV471 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6019]) ).
thf(6080,plain,
! [SV1455: $i,SV1069: $i,SV472: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV1069 @ SV472 )
= $false )
| ( ( c_lessequals @ SV1455 @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1069 @ SV1455 @ SV472 ) @ ( c_HOL_Ozero__class_Ozero @ SV472 ) @ SV472 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV472 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV472 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6020]) ).
thf(6081,plain,
! [SV1464: $i,SV1627: $i,SV489: $i,SV1669: $i,SV1086: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1669 @ SV489 ) @ SV1627 @ SV489 )
= $false )
| ( ( c_lessequals @ SV1464 @ SV1669 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1086 @ SV1464 @ SV489 ) @ SV1627 @ SV489 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6025]) ).
thf(6082,plain,
! [SV1670: $i,SV1465: $i,SV490: $i,SV1628: $i,SV1087: $i] :
( ( ( c_Ring__and__Field_Odvd__class_Odvd @ SV1087 @ SV1628 @ SV490 )
= $false )
| ( ( c_lessequals @ SV1465 @ SV1670 @ tc_nat )
= $false )
| ( ( c_Ring__and__Field_Odvd__class_Odvd @ ( c_Power_Opower__class_Opower @ SV1087 @ SV1465 @ SV490 ) @ ( c_Power_Opower__class_Opower @ SV1628 @ SV1670 @ SV490 ) @ SV490 )
= $true )
| ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV490 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6026]) ).
thf(6083,plain,
! [SV1484: $i,SV1631: $i,SV1119: $i,SV522: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
= $false )
| ( ( ~ ( c_lessequals @ SV1631 @ SV1484 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6027]) ).
thf(6084,plain,
! [SV1643: $i,SV1161: $i,SV1678: $i,SV588: $i,SV1511: $i,SV1671: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
!= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV588 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6034]) ).
thf(6085,plain,
! [SV1644: $i,SV1672: $i,SV590: $i,SV1162: $i,SV1512: $i] :
( ( ( c_lessequals @ SV1512 @ SV1162 @ SV590 )
= $false )
| ( ( c_lessequals @ SV1672 @ SV1644 @ SV590 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1162 @ SV1512 @ SV590 )
= ( c_HOL_Ominus__class_Ominus @ SV1644 @ SV1672 @ SV590 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV590 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6035]) ).
thf(6086,plain,
! [SV1646: $i,SV1168: $i,SV1679: $i,SV596: $i,SV1515: $i,SV1673: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
!= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
= $false )
| ( ( class_Divides_Oring__div @ SV596 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6036]) ).
thf(6087,plain,
! [SV1170: $i,SV1647: $i,SV598: $i,SV1516: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( SV1170 = SV1647 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(6088,plain,
! [SV1171: $i,SV1517: $i,SV599: $i,SV1648: $i,SV1674: $i] :
( ( ( c_lessequals @ SV1674 @ SV1648 @ SV599 )
= $false )
| ( ( c_lessequals @ SV1517 @ SV1171 @ SV599 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1171 @ SV1517 @ SV599 )
= ( c_HOL_Ominus__class_Ominus @ SV1648 @ SV1674 @ SV599 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV599 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6038]) ).
thf(6089,plain,
! [SV1676: $i,SV1653: $i,SV610: $i,SV1524: $i,SV1181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1181 @ SV1524 @ SV610 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1653 @ SV1676 @ SV610 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1524 @ SV610 )
= ( c_HOL_Ominus__class_Ominus @ SV1653 @ SV1676 @ SV610 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV610 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6039]) ).
thf(6090,plain,
! [SV1530: $i,SV1196: $i,SV628: $i,SV1677: $i,SV1655: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1655 @ SV1677 @ SV628 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1196 @ SV1530 @ SV628 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1196 @ SV1530 @ SV628 )
= ( c_HOL_Ominus__class_Ominus @ SV1655 @ SV1677 @ SV628 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV628 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6041]) ).
thf(6091,plain,
! [SV1532: $i,SV1200: $i,SV632: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1200 @ SV632 )
= $false )
| ( ( SV1532
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV632 ) @ SV1532 @ SV632 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1200 @ SV1532 @ SV632 )
= ( c_HOL_Ozero__class_Ozero @ SV632 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV632 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6042]) ).
thf(6092,plain,
! [SV633: $i,SV1201: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1201 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV633 )
= ( c_HOL_Ozero__class_Ozero @ SV633 ) )
= $false )
| ( ( class_Power_Opower @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV633 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV633 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6043]) ).
thf(6093,plain,
! [SV1537: $i,SV1206: $i,SV638: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1206 @ SV638 )
= $false )
| ( ( SV1206
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV638 ) @ SV1537 @ SV638 )
= $false )
| ( ( ( c_HOL_Oplus__class_Oplus @ SV1206 @ SV1537 @ SV638 )
= ( c_HOL_Ozero__class_Ozero @ SV638 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV638 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6094,plain,
! [SV1538: $i,SV1207: $i,SV1658: $i,SV639: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 ) )
= $true )
| ( ( SV1207 = SV1658 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6046]) ).
thf(6095,plain,
! [SV1539: $i,SV1209: $i,SV641: $i] :
( ( ( class_Power_Opower @ SV641 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
| ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6047]) ).
thf(6096,plain,
! [SV1552: $i,SV659: $i,SV1225: $i,SV15: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV15 ) @ SV1225 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1552 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ ( c_HOL_Oplus__class_Oplus @ SV1225 @ SV1552 @ SV15 ) @ SV15 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV15 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6048]) ).
thf(6097,plain,
! [SV1229: $i,SV26: $i,SV1553: $i,SV667: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV667 @ SV1553 @ SV26 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ SV667 @ SV26 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1229 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV667 @ SV1229 @ SV26 ) @ ( c_Power_Opower__class_Opower @ SV1553 @ SV1229 @ SV26 ) @ SV26 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6049]) ).
thf(6098,plain,
! [SV1558: $i,SV688: $i,SV1234: $i,SV50: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV50 ) @ SV1234 @ SV50 )
= $false )
| ( ( c_lessequals @ SV688 @ SV1558 @ SV50 )
= $false )
| ( ( c_lessequals @ SV688 @ ( c_HOL_Oplus__class_Oplus @ SV1234 @ SV1558 @ SV50 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV50 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6050]) ).
thf(6099,plain,
! [SV1235: $i,SV689: $i,SV1559: $i,SV51: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV51 ) @ SV1559 @ SV51 )
= $false )
| ( ( c_lessequals @ SV689 @ SV1235 @ SV51 )
= $false )
| ( ( c_lessequals @ SV689 @ ( c_HOL_Oplus__class_Oplus @ SV1235 @ SV1559 @ SV51 ) @ SV51 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV51 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6051]) ).
thf(6100,plain,
! [SV1317: $i,SV1582: $i,SV824: $i,SV1663: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
= $false )
| ( ( ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6057]) ).
thf(6101,plain,
! [SV1320: $i,SV1583: $i,SV827: $i,SV1664: $i,SV197: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6058]) ).
thf(6102,plain,
! [SV1323: $i,SV1584: $i,SV830: $i,SV1665: $i,SV200: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
= $false )
| ( ( ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6059]) ).
thf(6103,plain,
! [SV1324: $i,SV831: $i,SV201: $i,SV1585: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1585 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV1585 @ SV201 )
= $true )
| ( ( c_lessequals @ SV831 @ ( c_HOL_Ozero__class_Ozero @ SV201 ) @ SV201 )
= $false )
| ( ( c_lessequals @ SV831 @ ( c_HOL_Oinverse__class_Odivide @ SV1324 @ SV1585 @ SV201 ) @ SV201 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV201 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6060]) ).
thf(6104,plain,
! [SV202: $i,SV1325: $i,SV1586: $i,SV832: $i] :
( ( ( c_lessequals @ SV832 @ ( c_HOL_Oinverse__class_Odivide @ SV1586 @ SV1325 @ SV202 ) @ SV202 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV1325 @ SV202 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1325 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( c_lessequals @ SV832 @ ( c_HOL_Ozero__class_Ozero @ SV202 ) @ SV202 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV202 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6061]) ).
thf(6105,plain,
! [SV833: $i,SV1587: $i,SV203: $i,SV1326: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1326 @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV203 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1326 @ SV203 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV203 ) @ SV1587 @ SV203 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV833 @ SV1326 @ SV203 ) @ SV1587 @ SV203 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV203 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6062]) ).
thf(6106,plain,
! [SV834: $i,SV204: $i,SV1327: $i,SV1588: $i] :
( ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1588 @ SV1327 @ SV204 ) @ SV834 @ SV204 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV1327 @ SV204 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1327 @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV204 )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV204 ) @ SV834 @ SV204 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV204 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6063]) ).
thf(6107,plain,
! [SV855: $i,SV231: $i,SV1337: $i,SV1595: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV1595 @ SV1337 @ SV231 ) @ SV855 @ SV231 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV1337 @ SV231 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1337 @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV231 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV231 ) @ SV855 @ SV231 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV231 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6064]) ).
thf(6108,plain,
! [SV856: $i,SV1596: $i,SV232: $i,SV1338: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1338 @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV232 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1338 @ SV232 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV232 ) @ SV1596 @ SV232 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV856 @ SV1338 @ SV232 ) @ SV1596 @ SV232 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV232 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6065]) ).
thf(6109,plain,
! [SV233: $i,SV1339: $i,SV1597: $i,SV857: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Oinverse__class_Odivide @ SV1597 @ SV1339 @ SV233 ) @ SV233 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV1339 @ SV233 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1339 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV857 @ ( c_HOL_Ozero__class_Ozero @ SV233 ) @ SV233 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV233 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6066]) ).
thf(6110,plain,
! [SV1340: $i,SV858: $i,SV234: $i,SV1598: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1598 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV1598 @ SV234 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Ozero__class_Ozero @ SV234 ) @ SV234 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV858 @ ( c_HOL_Oinverse__class_Odivide @ SV1340 @ SV1598 @ SV234 ) @ SV234 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV234 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6067]) ).
thf(6111,plain,
! [SV1603: $i,SV896: $i,SV1360: $i,SV280: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV280 ) @ SV1360 @ SV280 )
= $false )
| ( ( c_lessequals @ SV896 @ SV1603 @ SV280 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV896 @ ( c_HOL_Oplus__class_Oplus @ SV1360 @ SV1603 @ SV280 ) @ SV280 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV280 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV280 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(6112,plain,
! [SV899: $i,SV284: $i,SV1361: $i,SV1604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1604 @ SV1361 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV284 ) @ SV899 @ SV284 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Oone__class_Oone @ SV284 ) @ SV284 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV899 @ SV1361 @ SV284 ) @ ( c_Power_Opower__class_Opower @ SV899 @ SV1604 @ SV284 ) @ SV284 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6071]) ).
thf(6113,plain,
! [SV1452: $i,SV469: $i,SV1066: $i,SV1624: $i] :
( ( ( c_lessequals @ SV1624 @ SV1066 @ SV469 )
= $false )
| ( ( c_lessequals @ SV1452 @ ( c_HOL_Ozero__class_Ozero @ SV469 ) @ SV469 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1066 @ SV1452 @ SV469 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1624 @ SV1452 @ SV469 ) @ SV469 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV469 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV469 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6077]) ).
thf(6114,plain,
! [SV1453: $i,SV470: $i,SV1625: $i,SV1067: $i] :
( ( ( c_lessequals @ SV1067 @ SV1625 @ SV470 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV470 ) @ SV1453 @ SV470 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV1067 @ SV1453 @ SV470 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1625 @ SV1453 @ SV470 ) @ SV470 )
= $true )
| ( ( class_Ring__and__Field_Odivision__by__zero @ SV470 )
= $false )
| ( ( class_Ring__and__Field_Oordered__field @ SV470 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6078]) ).
thf(6115,plain,
! [SV1119: $i,SV522: $i,SV1484: $i,SV1631: $i] :
( ( ( c_lessequals @ SV1631 @ SV1484 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV522 ) @ SV1119 @ SV522 )
= $false )
| ( ( c_lessequals @ SV1119 @ ( c_HOL_Oone__class_Oone @ SV522 ) @ SV522 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1484 @ SV522 ) @ ( c_Power_Opower__class_Opower @ SV1119 @ SV1631 @ SV522 ) @ SV522 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV522 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6083]) ).
thf(6116,plain,
! [SV1643: $i,SV1161: $i,SV1678: $i,SV588: $i,SV1511: $i,SV1671: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1671 @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ SV1678 @ SV1511 @ SV588 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1671 @ SV1161 @ SV588 ) @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Oplus__class_Oplus @ SV1678 @ SV1643 @ SV588 ) @ SV1511 @ SV588 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1161 @ SV1511 @ SV588 )
= ( c_Divides_Odiv__class_Omod @ SV1643 @ SV1511 @ SV588 ) )
= $false )
| ( ( class_Divides_Osemiring__div @ SV588 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6084]) ).
thf(6117,plain,
! [SV1646: $i,SV1168: $i,SV1679: $i,SV596: $i,SV1515: $i,SV1673: $i] :
( ( ( ( c_Divides_Odiv__class_Omod @ SV1673 @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ SV1679 @ SV1515 @ SV596 ) )
= $false )
| ( ( ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1673 @ SV1168 @ SV596 ) @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ ( c_HOL_Ominus__class_Ominus @ SV1679 @ SV1646 @ SV596 ) @ SV1515 @ SV596 ) )
= $true )
| ( ( ( c_Divides_Odiv__class_Omod @ SV1168 @ SV1515 @ SV596 )
= ( c_Divides_Odiv__class_Omod @ SV1646 @ SV1515 @ SV596 ) )
= $false )
| ( ( class_Divides_Oring__div @ SV596 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6086]) ).
thf(6118,plain,
! [SV1516: $i,SV1170: $i,SV1647: $i,SV598: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
= $false )
| ( ( SV1170 = SV1647 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6087]) ).
thf(6119,plain,
! [SV1538: $i,SV1658: $i,SV1207: $i,SV639: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1207 @ SV639 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV639 ) @ SV1658 @ SV639 )
= $false )
| ( ( SV1207 = SV1658 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1207 @ ( c_Suc @ SV1538 ) @ SV639 )
= ( c_Power_Opower__class_Opower @ SV1658 @ ( c_Suc @ SV1538 ) @ SV639 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6094]) ).
thf(6120,plain,
! [SV641: $i,SV1539: $i,SV1209: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
!= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $true )
| ( ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $true )
| ( ( class_Power_Opower @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6095]) ).
thf(6121,plain,
! [SV1317: $i,SV1663: $i,SV194: $i,SV1582: $i,SV824: $i] :
( ( ( ~ ( c_lessequals @ SV824 @ SV1582 @ SV194 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
= $false )
| ( ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6100]) ).
thf(6122,plain,
! [SV1320: $i,SV1664: $i,SV197: $i,SV1583: $i,SV827: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
= $false )
| ( ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6101]) ).
thf(6123,plain,
! [SV1323: $i,SV1665: $i,SV200: $i,SV1584: $i,SV830: $i] :
( ( ( ~ ( c_lessequals @ SV830 @ SV1584 @ SV200 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6102]) ).
thf(6124,plain,
! [SV1516: $i,SV1170: $i,SV1647: $i,SV598: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
= $false )
| ( ( SV1170 = SV1647 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6118]) ).
thf(6125,plain,
! [SV641: $i,SV1539: $i,SV1209: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1209 @ SV1539 @ SV641 )
= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $false )
| ( ( SV1209
= ( c_HOL_Ozero__class_Ozero @ SV641 ) )
= $true )
| ( ( class_Power_Opower @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV641 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV641 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(6126,plain,
! [SV1317: $i,SV1663: $i,SV194: $i,SV1582: $i,SV824: $i] :
( ( ( c_lessequals @ SV824 @ SV1582 @ SV194 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
= $false )
| ( ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6121]) ).
thf(6127,plain,
! [SV1320: $i,SV1664: $i,SV197: $i,SV1583: $i,SV827: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
= $false )
| ( ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6122]) ).
thf(6128,plain,
! [SV1323: $i,SV1665: $i,SV200: $i,SV1584: $i,SV830: $i] :
( ( ( c_lessequals @ SV830 @ SV1584 @ SV200 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6123]) ).
thf(6129,plain,
! [SV1516: $i,SV1647: $i,SV1170: $i,SV598: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1170 @ SV598 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV598 ) @ SV1647 @ SV598 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1516 @ tc_nat )
= $false )
| ( ( SV1170 = SV1647 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1170 @ SV1516 @ SV598 )
= ( c_Power_Opower__class_Opower @ SV1647 @ SV1516 @ SV598 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV598 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6124]) ).
thf(6130,plain,
! [SV1317: $i,SV1663: $i,SV1582: $i,SV824: $i,SV194: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV824 @ SV194 )
= $false )
| ( ( c_lessequals @ SV824 @ SV1582 @ SV194 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV194 ) @ SV1663 @ SV194 )
= $false )
| ( ( c_lessequals @ SV1663 @ SV1317 @ SV194 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ SV824 @ SV1317 @ SV194 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1582 @ SV1663 @ SV194 ) @ SV194 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6126]) ).
thf(6131,plain,
! [SV1320: $i,SV1664: $i,SV1583: $i,SV827: $i,SV197: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV827 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1583 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV197 ) @ SV1664 @ SV197 )
= $false )
| ( ( c_lessequals @ SV1664 @ SV1320 @ SV197 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV827 @ SV1320 @ SV197 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1583 @ SV1664 @ SV197 ) @ SV197 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6127]) ).
thf(6132,plain,
! [SV1323: $i,SV1665: $i,SV1584: $i,SV830: $i,SV200: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV830 @ SV200 )
= $false )
| ( ( c_lessequals @ SV830 @ SV1584 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV200 ) @ SV1665 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1665 @ SV1323 @ SV200 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ SV830 @ SV1323 @ SV200 ) @ ( c_HOL_Oinverse__class_Odivide @ SV1584 @ SV1665 @ SV200 ) @ SV200 )
= $true )
| ( ( class_Ring__and__Field_Oordered__field @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6128]) ).
thf(6133,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1379,6132,6131,6130,6129,6125,6119,6117,6116,6115,6114,6113,6112,6111,6110,6109,6108,6107,6106,6105,6104,6103,6099,6098,6097,6096,6093,6092,6091,6090,6089,6088,6085,6082,6081,6080,6079,6076,6075,6074,6073,6072,6069,6068,6056,6055,6054,6053,6052,6044,6040,6033,6032,6031,6030,6029,6028,6024,6023,6022,6021,6016,6015,6014,6013,6010,6006,6005,6002,6001,6000,5999,5992,5991,5990,5989,5988,5987,5979,5978,5976,5975,5973,5972,5969,5968,5967,5966,5965,5964,5963,5962,5960,5959,5958,5957,5956,5953,5952,5946,5941,5940,5938,5936,5932,5929,5928,5927,5926,5925,5921,5916,5915,5914,5913,5912,5897,5894,5893,5890,5885,5884,5883,5882,5879,5878,5877,5876,5875,5874,5872,5871,5865,5864,5848,5847,5845,5844,5840,5833,5832,5819,5818,5817,5808,5806,5805,5803,5799,5793,5787,5785,5784,5783,5779,5775,5772,5760,5759,5758,5757,5751,5736,5735,5734,5733,5732,5731,5730,5728,5727,5726,5725,5724,5723,5718,5715,5714,5713,5709,5707,5706,5705,5704,5702,5701,5700,5699,5692,5691,5678,5649,5648,5647,5646,5645,5644,5643,5642,5641,5640,5639,5638,5637,5636,5635,5634,5633,5632,5630,5611,5608,5597,5596,5594,5593,5589,5587,5577,5568,5556,5555,5554,5552,5549,5543,5542,5534,5529,5528,5527,5518,5517,5516,5515,5514,5487,5481,5480,5479,5478,5474,5470,5465,5464,5463,5462,5459,5458,5456,5454,5453,5451,5450,5431,5429,5424,5411,5389,5371,5370,5360,5359,5358,5357,5356,5355,5354,5353,5345,5343,5340,5337,5336,5335,5334,5333,5332,5322,5321,5309,5294,5290,5289,5265,5264,5260,5253,5226,5207,5206,5205,5204,5203,5189,5188,5186,5185,5176,5172,5157,5156,5155,5154,5152,5148,5146,5145,5144,5131,5130,5119,5101,5100,5099,5098,5075,5074,5071,5034,5019,5012,5011,5010,5009,5008,5007,5006,5001,5000,4999,4998,4991,4990,4988,4984,4981,4971,4970,4969,4968,4967,4966,4965,4964,4963,4962,4958,4954,4947,4945,4942,4941,4933,4931,4922,4917,4916,4911,4910,4883,4879,4878,4875,4874,4873,4872,4871,4859,4858,4825,4824,4823,4817,4816,4798,4797,4796,4795,4794,4793,4778,4777,4776,4775,4774,4773,4772,4771,4770,4769,4768,4767,4766,4765,4764,4763,4762,4755,4751,4749,4743,4736,4731,4730,4729,4726,4721,4712,4698,4688,4687,4680,4667,4659,4610,4609,4600,4599,4598,4597,4596,4595,4594,4593,4569,4568,4567,4566,4565,4554,4549,4538,4527,4516,4514,4512,4503,4502,4496,4487,4484,4479,4478,4474,4472,4470,4466,4452,4451,4449,4447,4446,4427,4426,4423,4422,4421,4415,4414,4413,4412,4395,4394,4393,4392,4370,4351,4350,4327,4326,4325,4324,4319,4307,4286,4285,4284,4283,4282,4281,4278,4275,4265,4264,4263,4262,4242,4241,4233,4232,4223,4221,4201,4197,4196,4191,4190,4189,4188,4181,4130,4129,4128,4117,4116,4115,4114,4112,4111,4110,4109,4108,4093,4090,4070,4066,4064,4056,4046,4045,4044,4043,4039,4019,3989,3986,3973,3964,3937,3936,3935,3934,3933,3932,3931,3930,3929,3928,3927,3926,3925,3924,3923,3922,3921,3920,3919,3918,3916,3892,3819,3817,3795,3794,3788,3765,3764,3763,3761,3760,3748,3745,3743,3742,3741,3735,3728,3666,3652,3637,3635,3634,3629,3619,3618,3604,3531,3523,3460,3459,3456,3427,3426,3419,3406,3400,3395,3361,3357,3353,3325,3229,3223,3222,3205,3195,3177,3176,3147,3146,3139,3135,3117,3116,3115,3114,3109,3069,3064,3063,3052,3045,3044,3039,3021,2931,2930,2929,2928,2927,2926,2857,2840,2839,2838,2815,2814,2809,2719,2676,2674,2564,2563,2538,2536,2510,2508,2507,2497,2493,2422,2419,2418,2275,2274,2273,2247,2246,2242,2212,2161,2160,2153,2065,2064,2063,2062,2061,2060,2059,2058,2057,2056,2055,2054,2053,2052,2051,2050,2049,2048,2047,2046,2045,2044,2043,2021,1995,1899,1881,1843,1823,1762,1679,1471,1433,1427]) ).
thf(6134,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV678-1 : 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
% 0.12/0.20 % Computer : n014.cluster.edu
% 0.12/0.20 % Model : x86_64 x86_64
% 0.12/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.20 % Memory : 8046.5625MB
% 0.12/0.20 % OS : Linux 6.8.0-71-generic
% 0.12/0.20 % CPULimit : 300
% 0.12/0.20 % WCLimit : 300
% 0.12/0.20 % DateTime : Tue Oct 6 16:41:11 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 153.86/26.04 .....
% 153.86/26.04
% 153.86/26.04 No.of.Axioms: 687
% 153.86/26.04
% 153.86/26.04 Length.of.Defs: 0
% 153.86/26.04
% 153.86/26.04 Contains.Choice.Funs: false
% 153.86/26.04 ...........................................................................................................................................................................
% 153.86/26.04
% 153.86/26.04 ********************************
% 153.86/26.04 * All subproblems solved! *
% 153.86/26.04 ********************************
% 153.86/26.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:687,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6133,loop_count:0,foatp_calls:1,translation:fof_full)
% 153.86/26.04
% 153.86/26.04 %**** Beginning of derivation protocol ****
% 153.86/26.04 % SZS output start CNFRefutation
% See solution above
% 25.95/26.07
% 25.95/26.07 %**** End of derivation protocol ****
% 25.95/26.07 %**** no. of clauses in derivation: 6134 ****
% 25.95/26.07 %**** clause counter: 6133 ****
% 25.95/26.07
% 25.95/26.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:687,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:296,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6133,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------